The document proposes a new analytical framework called the Empirical Law of Active Management to assess the skill and diversification of portfolio managers. It generalizes the Fundamental Law of Active Management. The author applies this framework to analyze the evolution of skill and diversification among 2,798 U.S. mutual funds since 1980. The analysis finds that skill has declined while diversification has increased among U.S. mutual funds. The author proposes two explanations for the decrease in skill: 1) growth in mutual fund assets has made it harder to outperform the market, and 2) funds have responded to demand by creating less informationally-content funds.
The document discusses probability-based approaches for calculating expected returns and variance under uncertainty. It provides an example using return data for a stock to calculate the expected return of 9.25% and variance of 0.02%. It also discusses how portfolio return and variance depends on asset weights, the individual asset expected returns and variances, and the correlation between the assets. Assuming the two example assets are perfectly negatively correlated, it calculates the asset weights needed for a zero risk portfolio and the expected return of that portfolio as 25.36%. Finally, it discusses limits to diversification in practice, such as the inability to hold all securities and that only unsystematic risk can be reduced through diversification.
This document discusses the relationship between risk and return in investments. It defines total risk as the sum of systematic and unsystematic risk. Systematic risk stems from external market factors that affect all investments, while unsystematic risk is specific to a particular company. The expected return and risk of individual stocks varies, with higher risk investments generally offering higher returns. A portfolio combines multiple assets to reduce overall risk through diversification. The portfolio risk depends on the covariance and correlation between the individual assets' returns. Diversifying across assets with low correlation is an effective way to reduce risk.
This document discusses portfolio risk and return, including expected return, measures of risk like variance and standard deviation, and how diversification can reduce risk. It provides examples of calculating expected return, variance, and standard deviation for individual stocks and portfolios. It then introduces the Capital Asset Pricing Model (CAPM), which specifies the relationship between risk and required return of individual stocks based on the stock's beta. It provides examples of using the CAPM equation to calculate required return given beta and market factors, and calculating beta given expected return and market factors.
This study explores performance persistence in mutual funds. The authors find:
1) Funds that perform relatively poorly compared to peers and benchmarks are more likely to disappear, indicating survivorship bias can be relevant in mutual fund studies.
2) Mutual fund performance persists from year to year on a risk-adjusted basis, though much of the persistence is due to repeated underperformance relative to benchmarks.
3) Persistence patterns vary dramatically between time periods, suggesting performance is correlated across managers due to common strategies not captured by risk adjustments. Poorly performing funds also persist instead of being fully eliminated by the market.
The document discusses how portfolio risk is reduced through diversification by combining assets that have returns affected in opposite directions by changes in economic variables. It provides an example where investing in two stocks, PIA and POL, reduces risk compared to investing in just one. While the average return of a portfolio is a weighted average, the risk is lower because negative impacts on one asset from economic changes are offset by positive impacts on the other asset. The covariance and correlation coefficient between assets are used to calculate the risk of the combined portfolio. Lower covariance means returns move in opposite directions, reducing overall risk more than assets with high positive covariance that move in the same direction.
This chapter discusses portfolio risk and return. It introduces the concept that investors should care about systematic risk rather than total risk, as total risk can be reduced through diversification while systematic risk cannot. It outlines how modern portfolio theory uses beta to measure the sensitivity of an asset to market movements, representing systematic risk. The chapter also discusses how diversification reduces nonsystematic or idiosyncratic risk but not market risk, and how portfolio risk decreases as the number of assets in the portfolio increases, up to a certain point.
- Peter Lynch purchased 100 shares of Iomega Corp. 3 months ago at $50 per share. He received $0.25 dividends per share last month. The shares are now worth $56 each.
- The document discusses concepts related to risk and return such as random variables, probability, moments, variance, standard deviation, and covariance. It provides an example of computing these statistics for two companies.
- Portfolio theory holds that combining securities reduces risk through diversification. The correlation between securities also impacts the risk of a portfolio. The portfolio with the highest expected return for a given level of risk makes up the efficient frontier.
Retirement saving with contribution payments and labor income as a benchmark ...Nicha Tatsaneeyapan
This document summarizes a research paper about modeling retirement savings when contributions are made and labor income is used as a benchmark for investments. The key points are:
1) A retirement savings model is presented where a plan sponsor makes contributions to finance an employee's retirement. The goal is to ensure the employee can maintain their consumption after retiring based on their labor income.
2) Dynamic programming is used to derive optimal investment and contribution strategies as functions of the wealth-to-income ratio and wage growth rate.
3) The analysis finds that contribution payments significantly increase risk-taking at low wealth levels. It also finds that considering downside risk can paradoxically increase risky investing at low wealth levels due to increasing relative risk
The document discusses probability-based approaches for calculating expected returns and variance under uncertainty. It provides an example using return data for a stock to calculate the expected return of 9.25% and variance of 0.02%. It also discusses how portfolio return and variance depends on asset weights, the individual asset expected returns and variances, and the correlation between the assets. Assuming the two example assets are perfectly negatively correlated, it calculates the asset weights needed for a zero risk portfolio and the expected return of that portfolio as 25.36%. Finally, it discusses limits to diversification in practice, such as the inability to hold all securities and that only unsystematic risk can be reduced through diversification.
This document discusses the relationship between risk and return in investments. It defines total risk as the sum of systematic and unsystematic risk. Systematic risk stems from external market factors that affect all investments, while unsystematic risk is specific to a particular company. The expected return and risk of individual stocks varies, with higher risk investments generally offering higher returns. A portfolio combines multiple assets to reduce overall risk through diversification. The portfolio risk depends on the covariance and correlation between the individual assets' returns. Diversifying across assets with low correlation is an effective way to reduce risk.
This document discusses portfolio risk and return, including expected return, measures of risk like variance and standard deviation, and how diversification can reduce risk. It provides examples of calculating expected return, variance, and standard deviation for individual stocks and portfolios. It then introduces the Capital Asset Pricing Model (CAPM), which specifies the relationship between risk and required return of individual stocks based on the stock's beta. It provides examples of using the CAPM equation to calculate required return given beta and market factors, and calculating beta given expected return and market factors.
This study explores performance persistence in mutual funds. The authors find:
1) Funds that perform relatively poorly compared to peers and benchmarks are more likely to disappear, indicating survivorship bias can be relevant in mutual fund studies.
2) Mutual fund performance persists from year to year on a risk-adjusted basis, though much of the persistence is due to repeated underperformance relative to benchmarks.
3) Persistence patterns vary dramatically between time periods, suggesting performance is correlated across managers due to common strategies not captured by risk adjustments. Poorly performing funds also persist instead of being fully eliminated by the market.
The document discusses how portfolio risk is reduced through diversification by combining assets that have returns affected in opposite directions by changes in economic variables. It provides an example where investing in two stocks, PIA and POL, reduces risk compared to investing in just one. While the average return of a portfolio is a weighted average, the risk is lower because negative impacts on one asset from economic changes are offset by positive impacts on the other asset. The covariance and correlation coefficient between assets are used to calculate the risk of the combined portfolio. Lower covariance means returns move in opposite directions, reducing overall risk more than assets with high positive covariance that move in the same direction.
This chapter discusses portfolio risk and return. It introduces the concept that investors should care about systematic risk rather than total risk, as total risk can be reduced through diversification while systematic risk cannot. It outlines how modern portfolio theory uses beta to measure the sensitivity of an asset to market movements, representing systematic risk. The chapter also discusses how diversification reduces nonsystematic or idiosyncratic risk but not market risk, and how portfolio risk decreases as the number of assets in the portfolio increases, up to a certain point.
- Peter Lynch purchased 100 shares of Iomega Corp. 3 months ago at $50 per share. He received $0.25 dividends per share last month. The shares are now worth $56 each.
- The document discusses concepts related to risk and return such as random variables, probability, moments, variance, standard deviation, and covariance. It provides an example of computing these statistics for two companies.
- Portfolio theory holds that combining securities reduces risk through diversification. The correlation between securities also impacts the risk of a portfolio. The portfolio with the highest expected return for a given level of risk makes up the efficient frontier.
Retirement saving with contribution payments and labor income as a benchmark ...Nicha Tatsaneeyapan
This document summarizes a research paper about modeling retirement savings when contributions are made and labor income is used as a benchmark for investments. The key points are:
1) A retirement savings model is presented where a plan sponsor makes contributions to finance an employee's retirement. The goal is to ensure the employee can maintain their consumption after retiring based on their labor income.
2) Dynamic programming is used to derive optimal investment and contribution strategies as functions of the wealth-to-income ratio and wage growth rate.
3) The analysis finds that contribution payments significantly increase risk-taking at low wealth levels. It also finds that considering downside risk can paradoxically increase risky investing at low wealth levels due to increasing relative risk
This document discusses risk and return relationships in investment and portfolio management. It covers key concepts such as:
- The relationship between risk and expected return of individual assets. Higher risk is generally associated with higher expected returns.
- How portfolio risk and return are calculated based on the individual assets within the portfolio, their weights, and the covariance between the assets. A portfolio's risk can be lower than the risks of individual assets due to diversification.
- Important portfolio theory concepts like the efficient frontier and capital market line that show the tradeoff between risk and return for efficient portfolios.
Performance Of Fo F Do Experience And Size Matterchardingsmith
This summary provides the key information from the document in 3 sentences:
The document discusses the performance of funds of hedge funds (FHFs), analyzing whether experience and size impact performance. It uses quantile regression to study the effect of these factors on various return levels rather than just average return. The empirical results suggest that experience and size have a negative effect on performance at higher quantiles, but size has a positive effect at lower quantiles, with both factors showing no significant effect at the median.
This document summarizes a research paper that examines how financial distress affects the cross-section of equity returns. The paper develops a simple model that considers financial leverage in equity valuation and the potential for shareholder recovery during financial distress. The model shows that the possibility of shareholder recovery can reduce equity risk for highly distressed stocks. This helps explain various empirical patterns, such as lower returns for distressed stocks, stronger value effects for high default risk firms, and momentum profits concentrated in low credit quality stocks. The model predicts a hump-shaped relationship between value premiums and default probability, as well as stronger momentum profits for nearly distressed firms with higher potential recovery. Empirical tests on market data generally confirm these predictions.
Superior performance by combining Rsik Parity with Momentum?Wilhelm Fritsche
This document examines different strategies for global asset allocation between equities, bonds, commodities and real estate. It finds that applying trend following rules substantially improves risk-adjusted performance compared to traditional buy-and-hold portfolios. It also finds trend following to be superior to risk parity approaches. Combining momentum strategies with trend following further improves returns while reducing volatility and drawdowns. A flexible approach that allocates capital based on volatility-weighted momentum rankings of 95 markets produces attractive, consistent risk-adjusted returns.
Measurement of Risk and Calculation of Portfolio RiskDhrumil Shah
This document discusses measuring risk and calculating portfolio risk. It defines risk as the probability of loss and explains that higher investment means higher risk but also higher potential return. It then discusses measuring the risk of individual assets using variance and standard deviation calculated from the asset's probability distribution of returns. The document also explains how to calculate the expected return, variance and standard deviation of a portfolio by taking the weighted average of the individual assets. Diversifying a portfolio can reduce overall risk since the returns on different assets may not move in the same direction.
Lodging REIT Analysis - Keynote Presentation for Research Committee by Brad K...Brad Kuskin
Although numerous studies examine REIT performance over extended periods of time, many online and data-driven investment tools do not adequately provide existing and prospective investors with the tools necessary to extract business management risk out of lodging REIT returns. Given investors' current reliance on technology and graphic-oriented return analysis, it is critical that lodging REIT shareholders understand that not all equity REITs are equal. Typically, investors govern by a combination of return on capital and diversification. However, lodging REITs are inherently misleading due to their "equity REIT" classification.
As lodging REITs expand to encompass a vast portion of the hospitality industry, particularly marquis lodging assets in primary metropolitan markets, an accurate comprehension of inherent risks is critical for any investor considering deploying capital into a lodging REIT.
Managerial Finance. "Risk and Return". Types of risk. Required return. Correlation. Diversification. Beta coefficient. Risk of a portfolio. Capital Asset Pricing Model. Security Market Line.
The document discusses risk and return in investing. It explains that equity investments like stocks historically have higher average returns of over 10% compared to debt investments like bonds that return 3-4%, but stocks are also more volatile. It defines risk as the variability of returns, and introduces the concepts of systematic risk that affects all stocks equally and unsystematic risk that is specific to individual stocks. Diversification can reduce unsystematic risk but not systematic risk. It also discusses measuring market risk through a stock's beta value, which represents its volatility relative to the overall market.
This document discusses the myth of diversification and correlation asymmetries between asset classes. It finds that empirical correlations are often asymmetric, with higher correlations during downturns when diversification is needed most. Through an analysis of various equity, style, size, hedge fund, and fixed income indices, it shows exceedance correlations are generally higher on the downside and lower on the upside compared to theoretical normal distributions. This suggests diversification works best during good times but fails when markets decline.
This document summarizes a paper that explores how actuaries can apply techniques from financial economics in their work. It presents several case studies using concepts like risk discount rates, locking-in adjustments, and risk neutral methodologies. The case studies value a personal equity plan and examine asset-liability studies and capital adequacy from the perspective of financial economics. It includes computer code with examples to demonstrate stochastic modeling and valuation. The paper aims to bring these new techniques into the actuarial profession for discussion and potential wider application.
- Direct real estate outperformed other asset classes on a risk-adjusted basis based on summary statistics of returns from 1987-1999 in the UK. Bonds also outperformed equities during this period.
- Direct real estate had a negative correlation with other asset classes, providing diversification benefits, while indirect real estate was strongly positively correlated with equities.
- During an economic downturn from 1993-1995 in the UK, direct real estate increased while other asset classes declined, demonstrating its diversification properties.
- A mean variance analysis found that an optimal portfolio allocated 57% to direct real estate, 41% to bonds, 2% to equities, and 0% to indirect real estate, achieving the highest risk
Diversification and portfolio analysis@ bec domsBabasab Patil
- Diversification reduces risk by combining assets whose returns are not perfectly positively correlated, thereby lowering portfolio risk without reducing expected returns. Markowitz diversification is more analytical than simple diversification by considering assets' correlations.
- Portfolio analysis involves calculating a portfolio's expected return and risk. The expected return is a weighted average of assets' individual expected returns, while risk is measured by portfolio standard deviation rather than a simple weighted average of individual risks. Correlations between assets are important for determining portfolio risk.
- The efficient frontier shows the set of optimal portfolios that offer the maximum expected return for a given level of risk. Individual investors will select different portfolios on the efficient frontier depending on their unique risk tolerances and utility
These Lecture series are relating the use R language software, its interface and functions required to evaluate financial risk models. Furthermore, R software applications relating financial market data, measuring risk, modern portfolio theory, risk modeling relating returns generalized hyperbolic and lambda distributions, Value at Risk (VaR) modelling, extreme value methods and models, the class of ARCH models, GARCH risk models and portfolio optimization approaches.
This document introduces a new measure called Active Share to quantify active portfolio management. Active Share describes the percentage of portfolio holdings that differ from the portfolio's benchmark index. It argues that Active Share, combined with tracking error, provides a comprehensive picture of a fund's active management approach. The authors apply this two-dimensional framework to analyze mutual funds, finding that the most active stock pickers outperform, while closet indexers and funds focusing on factor bets underperform after fees.
The Markowitz Model assists investors in selecting efficient portfolios by analyzing possible combinations of securities. It helps reduce risk through diversification by choosing securities whose price movements are not perfectly correlated. The model determines the efficient set of portfolios and allows investors to select the optimal portfolio based on their preferred risk-return tradeoff. Markowitz introduced diversification and showed holding multiple lower-risk securities can reduce overall portfolio risk compared to a single higher-risk security. The model calculates expected returns, variances, and correlations between securities to determine the minimum risk portfolio for a given level of return.
This report analyzes liability-driven investment strategies to hedge risks for pension funds. It first discusses the pension crisis and identifies key risks like shifting demographics, market volatility, and interest rates. It then models pension liabilities using actuarial assumptions and cash flow projections. Several hedging strategies are proposed, including duration matching with futures. Back-testing finds that combining corporate bond and long-term Treasury futures best hedges risks. The results suggest heavier weighting of corporate bonds and stocks for underfunded plans.
This document summarizes a student paper on the low-volatility anomaly. The paper examines whether low-volatility stocks achieve higher risk-adjusted returns compared to predictions of CAPM and MPT. It reviews literature explaining the anomaly through various behavioral biases. The paper tests the anomaly using 30 S&P 500 stocks over 20 years. Regression analysis finds no significant relationship between past stock volatility and future returns, providing no support for either CAPM or the low-volatility anomaly based on the sample. Statistical tests confirm the results and inability to reject the null hypothesis of no relationship between risk and return.
Measuring luck in estimated alphas barras scailletbfmresearch
This paper develops a new technique to account for "false discoveries" or luck-driven significant performance estimates when evaluating the abilities of multiple mutual fund managers simultaneously. The technique estimates the proportion of funds with true zero alphas, without alphas, and with positive alphas. Applying this to a large dataset of US equity mutual funds, the analysis finds that 75.4% of funds have zero true alpha, 24.0% have negative alphas, and only 0.6% have positive alphas, suggesting very few truly skilled managers despite some funds appearing successful due to luck. This challenges previous work suggesting more widespread manager skill.
Performance persistence of fixed income funds dromsbfmresearch
This study examines the performance persistence of fixed income mutual funds between 1990 and 1999. It uses a methodology that ranks funds based on their annual returns, with the top 50% labeled as "winners" and bottom 50% labeled as "losers". It then analyzes whether winners and losers in one period remain winners or losers in the next period. The study finds some evidence of short-term persistence in fund performance driven by changes in interest rates, with statistical significance and consistency between the direction of persistence and bond returns. However, the nature of persistence is shown to be dependent on shifts in interest rates over time.
This document summarizes a study that examines whether mutual fund managers can pick stocks by analyzing the performance of stocks that funds buy and sell around subsequent quarterly earnings announcements. The study finds:
1) On average, stocks that mutual funds buy outperform stocks they sell by about 10 basis points in the 3 days around the next earnings announcement.
2) This performance persists after benchmarking against stocks with similar characteristics, and funds that perform best tend to have a growth style.
3) Mutual fund trades forecast future earnings surprises, indicating managers can predict fundamentals.
4) Abnormal returns around earnings announcements account for 18-51% of total abnormal returns to stocks funds trade.
This study examines persistence in mutual fund performance over 1962-1993 using a survivorship-bias-free database. The author finds:
1) Common factors in stock returns and differences in mutual fund expenses explain almost all persistence in mutual fund returns, with the exception of strong underperformance by the worst-performing funds.
2) The "hot hands effect" documented in prior literature is driven by the one-year momentum effect in stock returns, but individual funds do not earn higher returns from actively following momentum strategies after accounting for costs.
3) Expenses have a negative impact on performance of at least one-for-one, and higher turnover also negatively impacts performance, reducing returns by around 0.95
This document discusses risk and return relationships in investment and portfolio management. It covers key concepts such as:
- The relationship between risk and expected return of individual assets. Higher risk is generally associated with higher expected returns.
- How portfolio risk and return are calculated based on the individual assets within the portfolio, their weights, and the covariance between the assets. A portfolio's risk can be lower than the risks of individual assets due to diversification.
- Important portfolio theory concepts like the efficient frontier and capital market line that show the tradeoff between risk and return for efficient portfolios.
Performance Of Fo F Do Experience And Size Matterchardingsmith
This summary provides the key information from the document in 3 sentences:
The document discusses the performance of funds of hedge funds (FHFs), analyzing whether experience and size impact performance. It uses quantile regression to study the effect of these factors on various return levels rather than just average return. The empirical results suggest that experience and size have a negative effect on performance at higher quantiles, but size has a positive effect at lower quantiles, with both factors showing no significant effect at the median.
This document summarizes a research paper that examines how financial distress affects the cross-section of equity returns. The paper develops a simple model that considers financial leverage in equity valuation and the potential for shareholder recovery during financial distress. The model shows that the possibility of shareholder recovery can reduce equity risk for highly distressed stocks. This helps explain various empirical patterns, such as lower returns for distressed stocks, stronger value effects for high default risk firms, and momentum profits concentrated in low credit quality stocks. The model predicts a hump-shaped relationship between value premiums and default probability, as well as stronger momentum profits for nearly distressed firms with higher potential recovery. Empirical tests on market data generally confirm these predictions.
Superior performance by combining Rsik Parity with Momentum?Wilhelm Fritsche
This document examines different strategies for global asset allocation between equities, bonds, commodities and real estate. It finds that applying trend following rules substantially improves risk-adjusted performance compared to traditional buy-and-hold portfolios. It also finds trend following to be superior to risk parity approaches. Combining momentum strategies with trend following further improves returns while reducing volatility and drawdowns. A flexible approach that allocates capital based on volatility-weighted momentum rankings of 95 markets produces attractive, consistent risk-adjusted returns.
Measurement of Risk and Calculation of Portfolio RiskDhrumil Shah
This document discusses measuring risk and calculating portfolio risk. It defines risk as the probability of loss and explains that higher investment means higher risk but also higher potential return. It then discusses measuring the risk of individual assets using variance and standard deviation calculated from the asset's probability distribution of returns. The document also explains how to calculate the expected return, variance and standard deviation of a portfolio by taking the weighted average of the individual assets. Diversifying a portfolio can reduce overall risk since the returns on different assets may not move in the same direction.
Lodging REIT Analysis - Keynote Presentation for Research Committee by Brad K...Brad Kuskin
Although numerous studies examine REIT performance over extended periods of time, many online and data-driven investment tools do not adequately provide existing and prospective investors with the tools necessary to extract business management risk out of lodging REIT returns. Given investors' current reliance on technology and graphic-oriented return analysis, it is critical that lodging REIT shareholders understand that not all equity REITs are equal. Typically, investors govern by a combination of return on capital and diversification. However, lodging REITs are inherently misleading due to their "equity REIT" classification.
As lodging REITs expand to encompass a vast portion of the hospitality industry, particularly marquis lodging assets in primary metropolitan markets, an accurate comprehension of inherent risks is critical for any investor considering deploying capital into a lodging REIT.
Managerial Finance. "Risk and Return". Types of risk. Required return. Correlation. Diversification. Beta coefficient. Risk of a portfolio. Capital Asset Pricing Model. Security Market Line.
The document discusses risk and return in investing. It explains that equity investments like stocks historically have higher average returns of over 10% compared to debt investments like bonds that return 3-4%, but stocks are also more volatile. It defines risk as the variability of returns, and introduces the concepts of systematic risk that affects all stocks equally and unsystematic risk that is specific to individual stocks. Diversification can reduce unsystematic risk but not systematic risk. It also discusses measuring market risk through a stock's beta value, which represents its volatility relative to the overall market.
This document discusses the myth of diversification and correlation asymmetries between asset classes. It finds that empirical correlations are often asymmetric, with higher correlations during downturns when diversification is needed most. Through an analysis of various equity, style, size, hedge fund, and fixed income indices, it shows exceedance correlations are generally higher on the downside and lower on the upside compared to theoretical normal distributions. This suggests diversification works best during good times but fails when markets decline.
This document summarizes a paper that explores how actuaries can apply techniques from financial economics in their work. It presents several case studies using concepts like risk discount rates, locking-in adjustments, and risk neutral methodologies. The case studies value a personal equity plan and examine asset-liability studies and capital adequacy from the perspective of financial economics. It includes computer code with examples to demonstrate stochastic modeling and valuation. The paper aims to bring these new techniques into the actuarial profession for discussion and potential wider application.
- Direct real estate outperformed other asset classes on a risk-adjusted basis based on summary statistics of returns from 1987-1999 in the UK. Bonds also outperformed equities during this period.
- Direct real estate had a negative correlation with other asset classes, providing diversification benefits, while indirect real estate was strongly positively correlated with equities.
- During an economic downturn from 1993-1995 in the UK, direct real estate increased while other asset classes declined, demonstrating its diversification properties.
- A mean variance analysis found that an optimal portfolio allocated 57% to direct real estate, 41% to bonds, 2% to equities, and 0% to indirect real estate, achieving the highest risk
Diversification and portfolio analysis@ bec domsBabasab Patil
- Diversification reduces risk by combining assets whose returns are not perfectly positively correlated, thereby lowering portfolio risk without reducing expected returns. Markowitz diversification is more analytical than simple diversification by considering assets' correlations.
- Portfolio analysis involves calculating a portfolio's expected return and risk. The expected return is a weighted average of assets' individual expected returns, while risk is measured by portfolio standard deviation rather than a simple weighted average of individual risks. Correlations between assets are important for determining portfolio risk.
- The efficient frontier shows the set of optimal portfolios that offer the maximum expected return for a given level of risk. Individual investors will select different portfolios on the efficient frontier depending on their unique risk tolerances and utility
These Lecture series are relating the use R language software, its interface and functions required to evaluate financial risk models. Furthermore, R software applications relating financial market data, measuring risk, modern portfolio theory, risk modeling relating returns generalized hyperbolic and lambda distributions, Value at Risk (VaR) modelling, extreme value methods and models, the class of ARCH models, GARCH risk models and portfolio optimization approaches.
This document introduces a new measure called Active Share to quantify active portfolio management. Active Share describes the percentage of portfolio holdings that differ from the portfolio's benchmark index. It argues that Active Share, combined with tracking error, provides a comprehensive picture of a fund's active management approach. The authors apply this two-dimensional framework to analyze mutual funds, finding that the most active stock pickers outperform, while closet indexers and funds focusing on factor bets underperform after fees.
The Markowitz Model assists investors in selecting efficient portfolios by analyzing possible combinations of securities. It helps reduce risk through diversification by choosing securities whose price movements are not perfectly correlated. The model determines the efficient set of portfolios and allows investors to select the optimal portfolio based on their preferred risk-return tradeoff. Markowitz introduced diversification and showed holding multiple lower-risk securities can reduce overall portfolio risk compared to a single higher-risk security. The model calculates expected returns, variances, and correlations between securities to determine the minimum risk portfolio for a given level of return.
This report analyzes liability-driven investment strategies to hedge risks for pension funds. It first discusses the pension crisis and identifies key risks like shifting demographics, market volatility, and interest rates. It then models pension liabilities using actuarial assumptions and cash flow projections. Several hedging strategies are proposed, including duration matching with futures. Back-testing finds that combining corporate bond and long-term Treasury futures best hedges risks. The results suggest heavier weighting of corporate bonds and stocks for underfunded plans.
This document summarizes a student paper on the low-volatility anomaly. The paper examines whether low-volatility stocks achieve higher risk-adjusted returns compared to predictions of CAPM and MPT. It reviews literature explaining the anomaly through various behavioral biases. The paper tests the anomaly using 30 S&P 500 stocks over 20 years. Regression analysis finds no significant relationship between past stock volatility and future returns, providing no support for either CAPM or the low-volatility anomaly based on the sample. Statistical tests confirm the results and inability to reject the null hypothesis of no relationship between risk and return.
Measuring luck in estimated alphas barras scailletbfmresearch
This paper develops a new technique to account for "false discoveries" or luck-driven significant performance estimates when evaluating the abilities of multiple mutual fund managers simultaneously. The technique estimates the proportion of funds with true zero alphas, without alphas, and with positive alphas. Applying this to a large dataset of US equity mutual funds, the analysis finds that 75.4% of funds have zero true alpha, 24.0% have negative alphas, and only 0.6% have positive alphas, suggesting very few truly skilled managers despite some funds appearing successful due to luck. This challenges previous work suggesting more widespread manager skill.
Performance persistence of fixed income funds dromsbfmresearch
This study examines the performance persistence of fixed income mutual funds between 1990 and 1999. It uses a methodology that ranks funds based on their annual returns, with the top 50% labeled as "winners" and bottom 50% labeled as "losers". It then analyzes whether winners and losers in one period remain winners or losers in the next period. The study finds some evidence of short-term persistence in fund performance driven by changes in interest rates, with statistical significance and consistency between the direction of persistence and bond returns. However, the nature of persistence is shown to be dependent on shifts in interest rates over time.
This document summarizes a study that examines whether mutual fund managers can pick stocks by analyzing the performance of stocks that funds buy and sell around subsequent quarterly earnings announcements. The study finds:
1) On average, stocks that mutual funds buy outperform stocks they sell by about 10 basis points in the 3 days around the next earnings announcement.
2) This performance persists after benchmarking against stocks with similar characteristics, and funds that perform best tend to have a growth style.
3) Mutual fund trades forecast future earnings surprises, indicating managers can predict fundamentals.
4) Abnormal returns around earnings announcements account for 18-51% of total abnormal returns to stocks funds trade.
This study examines persistence in mutual fund performance over 1962-1993 using a survivorship-bias-free database. The author finds:
1) Common factors in stock returns and differences in mutual fund expenses explain almost all persistence in mutual fund returns, with the exception of strong underperformance by the worst-performing funds.
2) The "hot hands effect" documented in prior literature is driven by the one-year momentum effect in stock returns, but individual funds do not earn higher returns from actively following momentum strategies after accounting for costs.
3) Expenses have a negative impact on performance of at least one-for-one, and higher turnover also negatively impacts performance, reducing returns by around 0.95
This document provides an extensive literature review of studies examining performance persistence in mutual funds. The review summarizes findings from early studies in the 1960s-1980s that used long time periods of 10-15 years and generally found some evidence of performance persistence, especially for inferior performers. However, later studies using shorter time periods found more inconsistent results and that persistence was strongly dependent on the sample and methodology used. The review concludes that while short-term persistence is sometimes found, past performance is not a reliable predictor of future returns due to biases in conventional testing procedures. Results are often sensitive to the specific measures and time periods examined, especially for equity funds.
The document discusses China's transition to a consumer-driven economy. It provides analysis from CLSA China Macro Strategist Andy Rothman on trends in China's economy including the declining importance of exports, strong growth in domestic consumption, increasing incomes driving spending, and continued growth in infrastructure investment. The analysis suggests China's economy remains healthy and growing despite slowing external demand.
Fis group study on emerging managers performance drivers 2007bfmresearch
This study examined the performance of emerging investment managers over three years ending in 2006. It found that:
1) For large cap managers, increased firm assets were negatively correlated with risk-adjusted returns for core and growth strategies, but not for value. This may be because increased assets led to less concentrated core portfolios, lowering returns.
2) For small cap managers, risk-adjusted returns were highest for firms with less than $500 million in assets, possibly due to added resources like analysts. Returns leveled off between $500 million and $1 billion, and declined above $1 billion.
3) Having more research analysts was consistently positively correlated with higher risk-adjusted returns across strategies, while the impact
The document discusses quantitative research on the prospects for a large cap comeback. It finds that large cap stocks have underperformed small caps for years and currently trade at large discounts based on various valuation metrics. Some factors that have contributed to this include the growth of ETFs which benefited small and mid caps, an increased focus on risk that favored higher beta small caps, and increased hedging and shorting that particularly impacted large liquid stocks. The research argues these valuation differences and factors favor a potential comeback by large caps.
This document provides a 3-sentence summary of a research paper that develops a multifactor model to forecast the 1-year returns of actively managed equity mutual funds. The model uses forecasts of a fund's manager skill, style (based on factors like market, size, value, and momentum), and expected factor returns. When tested on German equity funds, the multifactor model substantially improved forecasts compared to a naive model, reducing the mean squared error by up to 30% and yielding returns over 200 basis points higher for top-decile funds.
Short term persistence in mutual fund performance(12)bfmresearch
This study examines the short-term persistence of mutual fund performance using daily returns data over quarterly periods. The researchers estimate stock selection and market timing models for mutual funds and rank funds into deciles based on their estimated abnormal returns each quarter. They then measure the average abnormal return of each decile in the following quarter. They find that the top-performing decile in a given quarter generates a statistically significant average abnormal return of 25-39 basis points in the subsequent quarter, providing evidence of short-term persistence in performance. However, this persistence disappears when funds are evaluated over longer periods using a concatenated time series approach.
This document discusses a research paper that investigates why mutual fund performance does not persist over the long run. It finds that fund flows and manager changes act as mechanisms that prevent persistent outperformance or underperformance. For winner funds, high inflows reduce future performance, and losing a top manager also lowers returns. However, winner funds not experiencing high inflows or a manager change outperform those facing both by 3.6% annually. For loser funds, internal governance through manager replacement is more important than external governance from outflows. Firing an underperforming manager and experiencing outflows together improves future performance more than the individual effects alone.
This report provides an analysis of defined contribution retirement plans based on 2010 Vanguard recordkeeping data. Some key findings include:
- Median and average account balances reached their highest levels since tracking began in 1999, recovering from market declines.
- Use of target-date funds as investment options and default investments continues to grow significantly, with 42% of participants using them and 20% wholly invested in a single target-date fund.
- Professionally managed investment options like target-date funds are being used by an increasing number of participants, with 29% solely invested in an automatic investment program in 2010 compared to just 9% in 2005.
Prior performance and risk chen and pennacchibfmresearch
This document summarizes a research paper that models how a mutual fund manager's choice of portfolio risk is affected by the fund's prior performance and the manager's compensation structure. The model shows that when compensation cannot fall to zero, managers take on more tracking error risk (deviation from the benchmark portfolio) as performance declines. However, increased total return volatility is not necessarily predicted. Empirical tests on over 6,000 funds from 1962-2006 find evidence managers increase tracking error, but not return, volatility during poor performance, especially longer-tenured managers. This adds new insights to research on risk-shifting incentives in mutual fund tournaments.
The document presents a model showing that mutual fund managers have an incentive to distort new investments toward stocks their fund already holds large positions in near the end of quarters. This increases the fund's reported returns and attracts more inflows, allowing for greater distortion next quarter. However, the price impact is temporary, so each quarter starts with a larger return deficit until it cannot be overcome, explaining the empirical evidence of short-term persistence and long-term reversal in fund performance. The model also provides insights into why some funds underperform and explains behaviors of smaller and younger funds.
1) Selecting good mutual funds is difficult as only 20% outperform over the long run and 40% of funds from 10 years ago are no longer in existence.
2) Both qualitative and quantitative factors must be analyzed to pick funds, including the people and investment process, fees, performance history, and consistency with the stated investment strategy.
3) A disciplined due diligence process considers the experience, philosophy, ownership structure, incentives, and research capabilities of the fund managers as well as the quantitative metrics of costs, returns, risk levels, and turnover of the fund.
- Investors spend an estimated 0.67% of the total value of the US stock market each year on active investing strategies seeking returns above the market.
- This amounts to at least a 10% capitalized cost of the current market value to facilitate price discovery through active investing.
- Under reasonable assumptions, a typical investor could increase average annual returns by 67 basis points over 1980-2006 by switching to a passive market portfolio instead of active strategies.
Performance changes and mgmt turnover khoranabfmresearch
This document summarizes a study examining the impact of mutual fund manager replacements on subsequent fund performance. The key findings are:
1) Funds with negative pre-replacement performance continue to underperform benchmarks post-replacement, but see improved relative performance compared to pre-replacement.
2) Replacing outperforming managers results in deteriorating post-replacement performance relative to pre-replacement.
3) Funds with poor pre-replacement performance see significantly declining asset inflows pre-replacement, providing evidence that manager replacements are important for advisors to reverse declining inflows.
This study examines whether the ownership stakes of directors in mutual funds are related to fund performance. The researchers collected data on the ownership of independent and non-independent directors of large equity mutual funds. They found that funds with low director ownership, or "skin in the game", significantly underperformed peers. This underperformance was both statistically significant and economically large. Further analysis showed fees only explained a small part of the underperformance, suggesting director oversight impacts more than just fee negotiations. The study aimed to distinguish between directors having private information on future performance versus a lack of incentive alignment causing the underperformance, finding evidence supported the latter explanation.
The document discusses how beliefs systems influence investment decisions and strategies in important ways. It provides two examples: 1) How beliefs about economic versus accounting frames of reference led to divergent views on liability-driven investing. 2) How the use of style boxes to classify investment managers can create incentives for managers to conform to consultant definitions of style over pursuing returns. The document argues that unpacking unconscious beliefs and their cultural influences is important for improving investment judgment and evaluating investment managers.
The document discusses using the information ratio to measure the performance of mutual funds relative to a benchmark. It defines the information ratio as the excess return of a portfolio over the benchmark return, divided by the tracking error. A higher information ratio means a fund's performance is more consistent relative to the benchmark. The document also notes limitations of the information ratio include needing substantial data and being sensitive to the chosen benchmark.
This document introduces the Two Sigma Factor Lens, which is a framework for constructing a parsimonious set of risk factors that individually describe independent risks across many asset classes yet collectively explain much of the risk in typical institutional investor portfolios. The lens is intended to capture the majority of risk in a holistic yet concise manner so that changes to factor exposures can easily translate to asset allocation changes. The document discusses how analyzing portfolios through a risk factor lens allows investors to better understand overlapping risk sources across asset classes and more efficiently manage portfolio risk.
The Market’s Reaction to Corporate Diversification: What Deserves More Punish...RyanMHolcomb
The document summarizes a paper that examines whether the market rewards or punishes corporate diversification. It begins by reviewing relevant investment theory and prior studies. Lang and Stulz (1993) found a negative relationship between diversification and Tobin's Q, but the authors aim to examine if this relationship holds in 2009 using different diversification measures. They hypothesize firms will be "punished more" for unrelated diversification. The document defines key terms like the Herfindahl-Hirschman Index and Tobin's Q that will be used in the analysis. Prior literature presented mixed views on the costs and benefits of diversification.
This document discusses a new measure of portfolio diversification called Effective Portfolio Dimensionality (EPD). EPD aims to quantify diversification in a single number by assessing the number of independent dimensions of risk in a portfolio. The EPD divides portfolio correlations into perfect positive correlation, perfect negative correlation, and zero correlation, with zero correlation representing true diversification. The EPD is compared for different portfolio construction techniques using real-world asset categories, showing intuitive results. Portfolios with higher EPD scores are generally considered to be more diversified.
Information ratio mgrevaluation_bossertbfmresearch
This document discusses using the Information Ratio (IR) to evaluate mutual fund managers. The IR measures excess return over a benchmark relative to excess return volatility. While commonly used, the IR has limitations that depend on benchmark choice, data frequency, and fund return distributions. The document aims to empirically analyze IR characteristics across different asset classes and countries to determine if it is a reliable performance measure or if guidelines are needed for its use.
Risk Factors as Building Blocks for Portfolio DiversificationCallan
Author: Eugene Podkaminer
Asset classes can be broken down into building blocks, or factors, that explain the majority of the assets’ risk and return characteristics. A factor-based investment approach enables the investor theoretically to remix the factors into portfolios that are better diversified and more efficient than traditional portfolios.
Seemingly diverse asset classes can have unexpectedly high correlations—a result of the significant overlap in their underlying common risk factor exposures. These high correlations caused many portfolios to exhibit poor diversification in the recent market downturn, and investors can use risk factors to view their portfolios and assess risk.
Although constructing ex ante optimized portfolios using risk factor inputs is possible, there are significant challenges to overcome, including the need for active, frequent rebalancing; creation of forward-looking assumptions; and the use of derivatives and short positions. However, key elements of factor-based methodologies can be integrated in multiple ways into traditional asset allocation structures to enhance portfolio construction, illuminate sources of risk, and inform manager structure.
Mercer Capital | Valuation Insight | Corporate Finance in 30 Minutes Mercer Capital
This document provides a primer on corporate finance for directors and shareholders. It summarizes key concepts in three areas: capital structure, capital budgeting, and dividend policy. For capital structure, it discusses the tradeoff between debt and equity and how the optimal structure minimizes overall cost of capital. For capital budgeting, it outlines how management should select projects with expected returns exceeding the cost of capital. For dividend policy, it addresses shareholders' preferences for income versus growth and how these fit a company's strategic position. The goal is to give directors and shareholders a framework to meaningfully contribute to major financial decisions.
These documents summarize several academic studies on hedge fund performance and investor returns:
1) One study finds that annualized returns for hedge fund investors are 3-7% lower than buy-and-hold returns for the same funds, due to poor timing of capital flows. Risk-adjusted returns are close to zero.
2) Another examines how fund life cycles are affected by flows, size, competition and performance. It finds increasing competition in a category decreases fund survival probabilities.
3) A third study finds macroeconomic risk explains a significant portion of hedge fund return dispersion, but not for mutual funds. Higher macroeconomic risk is positively related to future hedge fund returns.
TO STUDY THE OPTIMIZATION OF PORTFOLIO RISK AND RETURNPriyansh Kesarwani
Vijay Shankar Singh presented on optimizing portfolio risk and return. The presentation covered introducing portfolio theory, constructing three portfolios of public, private and foreign companies, evaluating their risk-adjusted returns over three years using Sharpe's and Treynor's measures. Portfolio III of foreign collaboration securities performed best with the highest three-year return of 52.57% and outperforming on risk-adjusted measures. The presentation recommended investing in portfolio III for long-run gains due to its diversification and correlation with the market index.
This document summarizes research on index effects that occur around index rebalancing dates. It discusses the growth of passive investing, hypotheses for why abnormal returns may occur on additions and deletions from indexes, and evaluates whether an index effect exists in the S&P/TSX Composite index in Canada. The methodology examines stock returns around rebalancing dates to identify any cumulative abnormal returns.
This document analyzes different categories of active mutual fund management based on measures of Active Share and tracking error. It finds that the most active stock pickers have outperformed their benchmarks after fees, while closet indexers and funds focusing on factor bets have underperformed after fees. Performance patterns were similar during the 2008-2009 financial crisis. Closet indexing has become more popular recently. Fund performance can be predicted by cross-sectional stock return dispersion, favoring active stock pickers when dispersion is higher.
This document analyzes different categories of active mutual fund management based on measures of Active Share and tracking error. It finds that the most active stock pickers have outperformed their benchmarks after fees, while closet indexers and funds focusing on factor bets have underperformed after fees. Performance patterns were similar during the 2008-2009 financial crisis. Closet indexing has become more popular recently. Fund performance can be predicted by cross-sectional stock return dispersion, favoring active stock pickers when dispersion is higher.
This study examines how hedge fund manager characteristics impact fund performance. The authors analyze data on over 1,000 hedge fund managers, including SAT scores, education levels, work experience, and age. They find managers from higher-SAT undergraduate institutions tend to have higher raw and risk-adjusted returns, more inflows, and take less risk. Unlike mutual funds, the study also finds hedge fund flows do not negatively impact future performance.
This document summarizes a study on the determinants of capital structure in Thailand. The study analyzed data on 144 Thai listed companies from 2000 to 2011 to examine how firm-specific factors like size, profitability, asset tangibility, growth opportunities, and volatility influence a company's leverage ratios. The results showed that leverage ratios increased significantly with firm size but decreased significantly with profitability, in line with trade-off and pecking order theories. However, tangibility, growth, and volatility did not have significant relationships with leverage ratios. Therefore, the study concluded that firm size and profitability are the main determinants of capital structure for companies in Thailand.
This paper examines the relationship between mutual fund manager ownership stakes in the funds they manage and the performance of those funds. The author hypothesizes that greater manager ownership will be positively associated with fund returns and negatively associated with fund turnover, as higher ownership would better align manager and shareholder interests by reducing agency costs. Using a dataset of manager ownership disclosures from 2004-2005, the author finds that funds with higher manager ownership had higher returns and lower turnover, supporting the hypotheses. However, manager ownership was not related to a fund's tax burden.
Mercer Capital - Corporate Finance in 30 Minutes Whitepaper.pdfMercer Capital
Corporate finance does not need to be a mystery. In this whitepaper, we distill the
fundamental principles of corporate finance into an accessible and non-technical
primer. Structured around the three key decisions of capital structure, capital
budgeting, and distribution policy, the guide is designed to assist family business directors and shareholders without a finance background make relevant and
meaningful contributions to the most consequential financial decisions all companies must make. Our goal with this whitepaper is to give family business directors
and shareholders a vocabulary and conceptual framework for thinking about strategic corporate finance decisions, allowing them to bring their perspectives and
expertise to the discussion.
This document discusses the risks inherent in hedge fund strategies and argues that the 49% capital requirement under Solvency II does not properly reflect these risks. It analyzes hedge fund strategies using both holdings-based and returns-based approaches. Based on applying an internal model to hedge fund indices over a period including the financial crisis, it concludes that a 25% capital requirement would be more appropriate for a well-diversified hedge fund allocation. The document aims to show that hedge funds can offer capital efficiency and risk-adjusted returns for insurance companies under Solvency II regulations.
This document discusses using fuzzy logic and genetic algorithms to optimize investment portfolio selection. It begins with an overview of traditional portfolio management approaches and their limitations. It then introduces using fuzzy logic to better represent uncertain information from financial markets. Trapezoidal fuzzy numbers are proposed to model variables like expected asset returns. Genetic algorithms are described as an optimization tool inspired by natural selection, and their application to the portfolio selection problem is discussed. The selection process would use fuzzy logic to rank investments based on financial indicators. The genetic algorithm would then operate on a population of portfolio solutions to maximize expected returns based on the fuzzy representations of the variables.
AIAR Winter 2015 - Henry Ma Adaptive Invest ApproachHenry Ma
This document discusses the shortcomings of modern portfolio theory and the efficient market hypothesis. It introduces an alternative framework called adaptive investment which adjusts portfolios based on changing economic and market conditions. Specifically, it discusses how the risk/return relationship breaks down when including more asset classes, how average returns and other parameters are unstable over time. It also discusses how traditional investment practices like buy-and-hold and benchmark-centric investing led to suboptimal outcomes for investors. The document proposes that an adaptive investment approach which adjusts to different market regimes may better help investors achieve their goals.
Collateralized Fund Obligations MSc thesis Executive SummaryNICOLA Padovani
This dissertation analyzes Collateralized Fund Obligations (CFOs), which issue securitized tranches backed by pools of hedge funds. The author aims to explain the limited success of CFOs compared to expectations.
The paper reviews hedge fund investment vehicles and risks. It identifies clusters of correlated hedge fund strategies using indices. It models pools of strategies using multivariate Archimedean copulas to account for joint extreme returns.
The paper analyzes how CFOs apply techniques from Collateralized Debt Obligations, like credit support and diversification covenants. It proposes a modeling and pricing approach using copulas to simulate joint distributions and calculate tranche spreads. Hypothetical CFOs are priced using
Similar to 2010 09 the empirical law of active management (20)
This document summarizes a study examining 125 equity mutual funds that closed to new investment between 1993 and 2004. The study tests three hypotheses about why funds close: 1) The "good steward" hypothesis argues funds close to restrict inflows and maintain performance, and will perform well after reopening. 2) The "cheap talk" hypothesis posits closing has no real cost if fees increase and existing investors contribute, compensating managers. 3) The "family spillover" hypothesis claims closing diverts attention to other funds in the same family. The study finds little support for good steward performance, but evidence managers raise fees consistent with cheap talk, and little family benefit except briefly around closure.
Standard & poor's 16768282 fund-factors-2009 jan1bfmresearch
This document summarizes a study by Standard & Poor's on factors that predict investment fund performance. The study analyzed both qualitative factors like fund size, expenses, and age as well as quantitative metrics like Jensen's alpha and information ratio. The key findings were:
- For developed markets, larger funds with lower expenses tended to outperform. But for emerging markets, smaller funds did better due to differences in liquidity.
- Jensen's alpha and information ratio best predicted future performance of developed market equity funds over shorter time periods.
- Past performance was informative over 2 years but less so over 1 year due to noise. Fund selection should focus on factors predicting shorter term outperformance.
Performance emergingfixedincomemanagers joi_is age just a numberbfmresearch
1) Younger fixed-income managers tend to outperform older, more established managers in terms of gross returns. Returns are significantly higher for emerging managers in their first year and first five years compared to later years.
2) The study examines 54 fixed-income managers formed since 1985 that had majority employee ownership. Most were formed before 2000, when barriers to entry increased.
3) Business risk is low for emerging managers, as only 6.8% of the 88 examined managers are no longer in business. Higher first-year and early-period returns for emerging managers indicate they provide alpha during their hungry startup phase.
The document summarizes findings from the Standard & Poor's Indices Versus Active Funds (SPIVA) Scorecard, which compares the performance of actively managed mutual funds to relevant benchmarks. Some key points:
- Over the past 3 years, the majority (over 50%) of actively managed large-cap, mid-cap, small-cap, global, international, and emerging market funds underperformed their benchmarks.
- Over the past 5 years, indices outperformed a majority of active managers in nearly all major domestic and international equity categories based on equal-weighted returns. Asset-weighted averages also showed underperformance in 11 out of 18 domestic categories.
- For fixed income funds, over 50% under
This document summarizes research on the relationship between portfolio turnover and investment performance. Recent studies have found no evidence that higher portfolio turnover leads to lower returns, as was previously thought. Trading costs have declined over time, and portfolio turnover is not a good proxy for actual trading costs, which depend more on trade size and type of security traded. A 2007 study directly estimated trading costs and found no clear correlation between costs and returns. The author's own analysis of mutual funds from 2007-2008 also found little relationship between turnover and performance. Therefore, advisors should not assume higher turnover means lower returns.
This document discusses using active share and tracking error as measures of portfolio manager skill. It defines active share as the percentage of a fund's portfolio that differs from its benchmark index. Tracking error measures systematic factor risk by capturing how much a fund's returns vary from its benchmark. Research shows funds with high active share and moderate tracking error tend to outperform on average. The document examines how active share and tracking error can help identify skillful managers by focusing on their portfolio construction process rather than just past returns.
This document is a guide to the markets published by JPMorgan that provides data and analysis across various asset classes including equities, fixed income, international markets, and the economy. It includes sections on returns by investment style and sector for equities, economic indicators and drivers, interest rates and other data for fixed income, international market returns and valuations, and asset class performance and correlations. The guide contains over 60 charts and analyses global and domestic financial trends and investment opportunities.
The document discusses whether the concept of "Alpha" is a useful performance metric for investors. It makes two main arguments:
1) Alpha alone does not determine if a portfolio has superior risk-adjusted returns, as portfolio volatility and correlation to benchmarks also influence risk-adjusted returns.
2) Alpha is dependent on leverage - a higher reported Alpha could simply be due to using leverage rather than superior investment skill.
The document concludes that Alpha is a misleading performance measure and not suitable as the sole metric, especially for investors concerned with total risk and returns rather than just a single return component.
The document discusses Barclays' process for evaluating and selecting investment managers. It states that identifying the right asset allocation and implementing it properly are both important for achieving investment goals. The process involves both science, through a formal and structured methodology, and art, by applying judgment and philosophy. Barclays aims to identify managers most likely to perform well through rigorous due diligence and ongoing monitoring. The paper will explain Barclays' comprehensive approach to manager analysis, selection, and review.
Active managementmostlyefficientmarkets fajbfmresearch
This survey of literature on active vs passive management shows:
1) On average, actively managed funds do not outperform the market after accounting for fees and expenses, though a minority do add value.
2) Studies suggest some investors may be able to identify superior active managers in advance using public information.
3) Investors who identify superior active managers could improve their risk-adjusted returns by including some exposure to active strategies.
This document summarizes recent academic research on active equity managers who deliver persistent outperformance. It discusses studies finding that:
1) While the average equity manager underperforms after fees, a minority of managers have demonstrated persistent outperformance that cannot be attributed to chance alone.
2) Managers with higher "active share" (the degree to which their portfolio composition differs from the benchmark) tend to generate greater risk-adjusted returns.
3) Managers with lower portfolio turnover and a focus on strong stock selection, rather than market timing, are more likely to outperform over time.
The document evaluates how Brown Advisory's investment approach aligns with the characteristics identified in these studies as being associated with persistent
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This document summarizes a study comparing the performance of mutual funds managed by individual managers versus teams of managers. The study finds that funds managed by teams have similar risk-adjusted performance to individually-managed funds, despite team-managed funds growing at a faster rate. Additionally, team-managed funds have significantly lower risk, lower cross-sectional performance differences, lower expenses, and lower portfolio factor loadings than individually-managed funds. The study uses a large sample of domestic and international mutual funds to test these findings.
This document discusses returns-based style analysis (RBSA), a technique developed by William Sharpe to determine the style of a portfolio or mutual fund using only returns data. The document provides an overview of RBSA and compares it to holdings-based style analysis. It then describes how to implement RBSA using Excel by constructing a portfolio of indices to minimize the tracking error between the returns of the portfolio being analyzed and the index portfolio returns. The document concludes by providing an example RBSA using the Dodge & Cox Balanced Fund to illustrate the technique.
1) The study investigates how fund size affects performance in the active money management industry. Specifically, it analyzes whether fund returns decline as fund size increases.
2) The results show that both gross and net fund returns decline as lagged fund size increases, even after accounting for various performance benchmarks and fund characteristics. This suggests that larger fund size erodes performance.
3) However, controlling for its own size, a fund's performance does not deteriorate as the size of the family it belongs to increases. This indicates that scale itself does not necessarily harm performance, depending on how the fund is organized.
Examination of hedged mutual funds agarwalbfmresearch
Hedge funds have traditionally only been available to accredited investors while providing lighter regulation and stronger performance incentives compared to mutual funds. Recently, some mutual funds have adopted hedge fund-like strategies but remain subject to tighter regulation. This study examines the performance of these "hedged mutual funds" relative to both hedge funds and traditional mutual funds. It finds that despite using similar strategies as hedge funds, hedged mutual funds underperform due to their tighter regulation and weaker incentives. However, hedged mutual funds outperform traditional mutual funds, with the superior performance driven by those with managers having hedge fund experience.
Morningstar ratings and fund performance blake moreybfmresearch
This study examines the ability of Morningstar ratings to predict the future performance of mutual funds compared to alternative predictors. The authors analyze two samples of US equity funds: seasoned funds from 1992-1997 and complete funds from 1993. They assess predictive ability using out-of-sample performance over 1, 3, and 5 year horizons, adjusting for loads and styles. The results indicate that low Morningstar ratings generally predict relatively poor future performance, but there is little evidence that top-rated funds outperform similar funds. Morningstar ratings do only slightly better than alternative predictors in forecasting future fund performance.
Fund returnsandperformanceevaluationtechniques grinblattbfmresearch
This paper empirically compares three techniques for evaluating mutual fund performance: the Jensen Measure, the Positive Period Weighting Measure, and the Treynor-Mazuy Measure of Total Performance. It does so using a sample of 279 mutual funds and 109 passive portfolios constructed from firm characteristics and industries. The study finds that 1) the performance measures can yield different inferences depending on the benchmark used, 2) measures may detect timing ability differently, and 3) cross-sectional regressions of performance on fund characteristics may provide insights even when individual performance measures lack statistical power.
This study analyzes the trading behaviors of 155 mutual funds between 1975 and 1984 to determine if they exhibited momentum investing and herding behaviors. The researchers find that 77% of funds were "momentum investors," buying stocks that had outperformed in the past, though most did not systematically sell past underperformers. Funds exhibiting momentum behaviors on average realized significantly better risk-adjusted returns than other funds. The study also finds weak evidence that funds tended to buy and sell the same stocks at the same time, known as herding behavior.
Performance of trades and stocks of fund managers pinnuckbfmresearch
This document summarizes a study that examines the performance of stock holdings and trades of Australian fund managers. The study finds:
1) The stocks held by fund managers realize abnormal returns on average, consistent with some stock selection ability.
2) Stocks purchased by fund managers realize abnormal returns on average, while stocks they sell do not, supporting the idea that fund managers have superior information.
3) Large stocks are more likely to benefit from fund managers' superior information than small stocks.
However, the superior returns from stock holdings are not delivered to unit holders, possibly due to fees and poor market timing. The results provide out-of-sample support for recent U.S. studies finding fund managers
[4:55 p.m.] Bryan Oates
OJPs are becoming a critical resource for policy-makers and researchers who study the labour market. LMIC continues to work with Vicinity Jobs’ data on OJPs, which can be explored in our Canadian Job Trends Dashboard. Valuable insights have been gained through our analysis of OJP data, including LMIC research lead
Suzanne Spiteri’s recent report on improving the quality and accessibility of job postings to reduce employment barriers for neurodivergent people.
Decoding job postings: Improving accessibility for neurodivergent job seekers
Improving the quality and accessibility of job postings is one way to reduce employment barriers for neurodivergent people.
A toxic combination of 15 years of low growth, and four decades of high inequality, has left Britain poorer and falling behind its peers. Productivity growth is weak and public investment is low, while wages today are no higher than they were before the financial crisis. Britain needs a new economic strategy to lift itself out of stagnation.
Scotland is in many ways a microcosm of this challenge. It has become a hub for creative industries, is home to several world-class universities and a thriving community of businesses – strengths that need to be harness and leveraged. But it also has high levels of deprivation, with homelessness reaching a record high and nearly half a million people living in very deep poverty last year. Scotland won’t be truly thriving unless it finds ways to ensure that all its inhabitants benefit from growth and investment. This is the central challenge facing policy makers both in Holyrood and Westminster.
What should a new national economic strategy for Scotland include? What would the pursuit of stronger economic growth mean for local, national and UK-wide policy makers? How will economic change affect the jobs we do, the places we live and the businesses we work for? And what are the prospects for cities like Glasgow, and nations like Scotland, in rising to these challenges?
Economic Risk Factor Update: June 2024 [SlideShare]Commonwealth
May’s reports showed signs of continued economic growth, said Sam Millette, director, fixed income, in his latest Economic Risk Factor Update.
For more market updates, subscribe to The Independent Market Observer at https://blog.commonwealth.com/independent-market-observer.
In a tight labour market, job-seekers gain bargaining power and leverage it into greater job quality—at least, that’s the conventional wisdom.
Michael, LMIC Economist, presented findings that reveal a weakened relationship between labour market tightness and job quality indicators following the pandemic. Labour market tightness coincided with growth in real wages for only a portion of workers: those in low-wage jobs requiring little education. Several factors—including labour market composition, worker and employer behaviour, and labour market practices—have contributed to the absence of worker benefits. These will be investigated further in future work.
Dr. Alyce Su Cover Story - China's Investment Leadermsthrill
In World Expo 2010 Shanghai – the most visited Expo in the World History
https://www.britannica.com/event/Expo-Shanghai-2010
China’s official organizer of the Expo, CCPIT (China Council for the Promotion of International Trade https://en.ccpit.org/) has chosen Dr. Alyce Su as the Cover Person with Cover Story, in the Expo’s official magazine distributed throughout the Expo, showcasing China’s New Generation of Leaders to the World.
TEST BANK Principles of cost accounting 17th edition edward j vanderbeck mari...Donc Test
TEST BANK Principles of cost accounting 17th edition edward j vanderbeck maria r mitchell.docx
TEST BANK Principles of cost accounting 17th edition edward j vanderbeck maria r mitchell.docx
TEST BANK Principles of cost accounting 17th edition edward j vanderbeck maria r mitchell.docx
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
New Visa Rules for Tourists and Students in Thailand | Amit Kakkar Easy VisaAmit Kakkar
Discover essential details about Thailand's recent visa policy changes, tailored for tourists and students. Amit Kakkar Easy Visa provides a comprehensive overview of new requirements, application processes, and tips to ensure a smooth transition for all travelers.
Vicinity Jobs’ data includes more than three million 2023 OJPs and thousands of skills. Most skills appear in less than 0.02% of job postings, so most postings rely on a small subset of commonly used terms, like teamwork.
Laura Adkins-Hackett, Economist, LMIC, and Sukriti Trehan, Data Scientist, LMIC, presented their research exploring trends in the skills listed in OJPs to develop a deeper understanding of in-demand skills. This research project uses pointwise mutual information and other methods to extract more information about common skills from the relationships between skills, occupations and regions.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
2. The Fundamental Law of Active Management says that the information ratio of a portfolio is the
product of the skill of the manager in selecting securities and the breadth of the strategy. In this
construct, “skill” is measured by the correlation between the manager’s expected and realized
returns, and “breadth” is the square-root of the number of independent positions in the portfolio.
Grinold and Kahn [1999] state: “The Fundamental Law is designed to give us insight into active
management. It isn’t an operational tool.” nevertheless, the usefulness of these insights has led
practitioners to seek to make it an operational tool. The main advance in this direction were brought
by Clarke, de Silva and Thorley [2002], who introduced the concept of transfer coefficient1 to account
for the constraints that a manager faces when implementing a particular strategy. They also worked
out the application of the Fundamental Law to ex-post performance attribution. However, despite
these advances, the practical application of the Fundamental Law of Active Management remains
difficult.
Firstly, one needs to have access to the manager’s return expectations, which are hard to obtain. For
qualitatively-oriented managers, return expectations are not formalized in a way that allows the
2
computation of an information coefficient. Often quantitative managers will not make this
information available to external investors in order to avoid potential reverse engineering of the
manager’s investment process. Moreover, when assessing a manager, using information that can be
independently verified is always preferable.
Secondly, the Fundamental Law relies heavily on the assumption that managers follow the precepts of
the active portfolio management theory developed in Grinold and Kahn [1999]. Hence, applications of
the Fundamental Law to managers that do not follow these precepts will lead to questionable results.
Finally, by seeking to transform the Fundamental Law into an operational tool, researchers have also
made it more complex and difficult to interpret (See Clarke, de Silva and Thorley [2006] or Buckle
[2004]). One of the key advantages of the analytical framework proposed in this paper is the simplicity
1
The transfer coefficient is the correlation between optimal unconstrained portfolio weights and actual portfolio weights
2
The information coefficient is the correlation between the manager expected returns and realized returns
September, 2010 2
3. of its application. This approach only requires portfolio holdings and realized returns to analyze how
the breadth of the portfolio and the skill of a manager contribute to the information ratio of the
portfolio. It does not require any information regarding the manager’s expected returns or assumptions
with respect to the manager’s investment process.
A New Approach to Estimating Breadth: The Diversification Factor
The fact that the Fundamental Law is difficult to apply to many portfolios does not mean that it does
not apply. Indeed, the risk adjusted returns of a portfolio, no matter what the investment process is,
will always be a function of a manager’s skill and a strategy’s breadth. In order to apply the
Fundamental Law to a wider range of strategies, we sidestep the issues outlined in the introduction by
starting from portfolio weights rather than the manager’s expected alphas. The cornerstone of this
approach consists of computing what would be the information ratio (IR) of the portfolio if there were
no diversification benefits (i.e. if all positions in the portfolio were perfectly correlated). The
difference between the IR computed assuming that all positions are perfectly correlated and the actual
IR represents the benefits from diversification. On the other hand, the IR of the portfolio in the
absence of diversification benefits represents the skill of the manager.
If there were no benefit from portfolio diversification, the active risk of the portfolio would be the
position-weighted mean active volatility of the assets included in the portfolio3:
wi i
i
Where wi is the weight of asset i and i is the active volatility of asset i. The asset active volatility is
defined as the volatility of the return difference between the benchmark and the asset. Hence the
impact of diversification on the active risk of the portfolio can be measured by the ratio of the
position-weighted mean volatility ( ) and the actual portfolio active risk( ). The higher the
3
See appendix 1 for proof
September, 2010 3
4. ratio is, the larger the impact of diversification. Hence, we define the diversification factor (DI) as
follows:
DI=
As a result, the active risk of a portfolio can be written as:
DI
There are three elements that will affect the diversification of the portfolio: the number of positions,
the correlation between these positions and the concentration of assets’ weights and assets’
volatilities. The first element is fairly straightforward. More positions mean more diversification.
However, not all positions bring the same level of diversification. Adding highly correlated positions to
the portfolio creates little diversification. Hence, the second element that impacts the diversification
of the portfolio is the level of correlation among the positions in the portfolio. The concentration of
the weights in the portfolio will also impact the diversification factor. Indeed, if we consider a
portfolio where one position’s weight is 20 times the weight of all the other positions, the
diversification of this portfolio will be lower than that of a similar portfolio where all positions are
equally weighted. The same logic applies to volatilities. If one asset’s volatility is 20 times that of the
other assets, the portfolio return will be highly dependent on the outcome of this one bet and its
diversification will be lower than if all volatilities were equal. Concentration of positions’ weights and
concentration of positions’ volatilities have the same impact on diversification. They both reduce it by
making the portfolio more dependent on fewer positions. We regroup these two variables into one
variable, the concentration of the risk-weights (where risk-weights for position i is equal to ( wi i ) ).
We show in appendix 1 that the portfolio diversification can be written as a function of these three
factors:
DI=
1 (Equation 1)
1
n (i )
n
September, 2010 4
5. Where:
n is the number of positions in the portfolio
is roughly a risk-weighted average correlation among the positions in the portfolios4
i is the risk-weight of position i, (i.e. i (wi i ) )
(i ) is the standard deviation of the risk weights across the portfolio, measuring the
concentration in the portfolio.
The diversification factor can be interpreted as a number of positions. Let’s illustrate this point with
the example of a portfolio that contains ten positions, where the active returns of these positions are
independent and each position has an equal risk-weight of 10%. In this example, = ( ) =0 and
therefore it follows from equation (1) that the diversification of the portfolio is 10. Hence, for any
portfolio, diversification represents the equivalent number of independent positions with equal risk-
weights.
A New Approach to Estimating Skill
To assess the impact of diversification on the risk-adjusted returns of a portfolio, we need to divide the
numerator and the denominator of the information ration by :
IR * DI
Where is the active return of the portfolio. Then we define the quantity as the skill (SK) of the
manager which yields:
IR SK * DI
4
see exact formula in appendix 1
September, 2010 5
6. The Empirical Law of Active Management expresses exactly the same fact as the Fundamental Law,
namely, that IR is a product of skill and diversification. However, using the Empirical Law, we do not
need to make any assumptions about the way in which the portfolio is constructed. The only
information that is required to analyze the skill and diversification of the manager is a portfolio’s
holdings and realized returns.
Skill in the context of the Empirical Law represents the ability of the manager to allocate its risk-
capital to securities with high risk-adjusted returns. To demonstrate this point, we need to observe
that the portfolio alpha is also the weighted average alpha of each security in the portfolio (i.e.
wi i ). Then we can express skill as the risk-weighted average of the information ratios of the
i
individual positions in the portfolio:
i
w i i
SK i i
i IRi
i
Where IRi is the information ratio of position i and i its risk-weight. In this framework, skill
represents the ability of the manager to select securities that have a strong information ratio on a
stand-alone basis. In other words, it is a measure of the manager’s ability to maximize the risk-
adjusted returns of the portfolio without using the benefit of risk diversification. It is important to note
that in the Empirical Law, the skill coefficient is defined more broadly than the information coefficient
of the Fundamental Law. Whereas the information coefficient measures the pure stock picking ability
of the manager, the skill factor, in addition to stock picking, also incorporates the impact of portfolio
concentration and the size of the manager’s opportunity. We can illustrate this point by examining the
covariance between the risk-weights and the information ratio:5
~ ~ 1
n i
~ ~ 1
n i
~ 1
Cov , IR ~ i * IRi ~ i * ~ IRi
n i
~
5
Note that this decomposition was inspired by Andrew Lo’s AP decomposition. See proposition 1 in Lo [2007]
September, 2010 6
7. ~ ~
Where i and IRi are the risk weights and information ratios of each of the securities in the
manager’s investment universe and ~
n is the number of securities in the investment universe. We
define investment universe as the entire set of securities in which the manager can invest. (The ~
denotes that the variable covers the entire universe as opposed to securities included in the portfolio
only.) By including all the securities in the manager’s universe in our covariance computation, we can
fully capture the relation between risk-weights and information ratios. Indeed, securities that are in
the manager universe but not in the portfolio do not directly contribute to the risk adjusted return of
the portfolio; however, they do contain information with respect to the manager’s stock-picking skill.
IR 0 .
~
Given that the universe is a passive and information-less portfolio, we can assume that i
i
* IR is our skill factor.
~ ~
The expectation of the risk-weights and information ratio products: i i
i
Hence, we can re-write the skill of the manager in function of the covariance between securities risk
weights and information ratios: ~ ~ ~
SK n Cov( , IR
~ ~
Finally, if n is large enough so that IR ) 1, we obtain:
~ ~ ~ ~
SK ( , IR n )
This decomposition of the skill factor is helpful to understand the three elements that are important in
determining the skill of a manager:
~ ~
( , IR : The correlation between risk-weights and securities information ratios is
similar to the information coefficient in the Fundamental Law; it represents the ability of
the manager to pick-securities.
~
n : The size of the universe of securities that the manager will analyze. It represents the
opportunity set from which the manager can create value added for his clients.
~
) : A measure of the portfolio concentration. This parameter illustrates the fact that
a more concentrated portfolio will better leverage the manager’s stock picking ability.
September, 2010 7
8. This last point illustrates the fact that diversification also forces managers to go down the list of their
investment ideas and implement positions with less expected return.
Comparison of the Fundamental and Empirical Laws
The Empirical Law and Fundamental Law possess two key differences. First, the Empirical Law side
steps the concepts of information coefficient and transfer coefficient. The skill of a manager depends
on the relation between risk-weight and risk-adjusted performance (see Exhibit 1). As we discussed in
the introduction, for manager-of-managers, the information necessary to compute a transfer
coefficient or information coefficient is not available. In practice, fundamental managers cannot
cleanly separate transfer coefficient and breadth. The concept of TC makes sense for quantitative
managers using models that provide expected returns on wide ranges of securities irrespective of
whether they can be implemented or not. On the other hand, given the cost of bottom-up research,
fundamental analysts focus on trades that can be implemented. In an investment firm that runs long
only portfolios, one rarely sees analysts spending much time on overvalued assets. This makes the
distinction between transfer coefficient and diversification less meaningful for fundamental managers.
Exhibit 1: Information Triangle
Fundamental Law
Empirical Law
Manager Proprietary Information
Ex‐ante Alphas
Information Transfer
Coefficient Coefficient
Performance SK Portfolio Positions
(or Risk –Weights)
Public Information for
Traditional Funds
This diagram is inspired from Figure 1 of Clarke de Silva Thorley (2002).
September, 2010 8
9. Therefore, the Empirical Law does not distinguish between the two. If a position is not in the portfolio,
we do not seek to know if this is due to lack of breadth or poor transfer coefficient. However, given
access to the unconstrained optimal weights of a quantitative manager, we have the flexibility to
reintroduce the concept of transfer coefficient. By recomputing the manager IR, DI and SK with these
optimal weights (noted IR*, DI* and SK*), we can define our transfer coefficient as:6
IR
TC , which yields IR TC * SK * DI
* *
*
IR
The second key difference between the two approaches is that the Fundamental Law makes the
assumption that the portfolio manager uses a mean variance optimization to construct the portfolio.
The Empirical Law does not rely on any formal assumption regarding the manager’s portfolio
construction process, and uses the fund’s IR as the yardstick of a manager’s success.
Can you get indigestion from the diversification free lunch?
Warren Buffett has observed that “Diversification is a protection against ignorance. It makes very little
sense for those who know what they're doing.”7 Indeed, diversification forces the skilled manager to
reduce the portfolio’s concentration in the positions with the highest expected return in order to
reduce risk. If one has perfect foresight there is no risk, and there is little to be gained in reducing risk
through diversification. However, for investment managers with less than perfect foresight
diversification makes a lot of sense. As we noted previously, while diversification also forces portfolio
managers to add to the portfolio positions with decreasing risk-adjusted return.
Moreover, bottom-up stock picking requires specialized knowledge in the securities being analyzed.
Thus far, we have implicitly assumed that skill is a fixed quantity that is inherent to the investment
process and can be leveraged into as many trades as one can implement. While this somewhat reflects
6
Note than in theory this TC can be greater than one. Since the objective function that produces the optimal weights of the
manager is not necessarily the IR, it is conceivable that the constrained IR be greater than the unconstrained IR.
7
Source: http://en.wikiquote.org/wiki/Warren_Buffett
September, 2010 9
10. the way quantitative managers create value, for fundamental managers more diversification means less
depth of research. Therefore, a fixed SK coefficient does not reflect the tradeoff between quality of
coverage (or depth) and breadth of coverage, which fundamental managers do face. Fundamental
managers could leverage their SK factor across other trades only if they hire more analysts of the same
quality; however, producing a good analyst is costly and/or time-consuming. In the long term, it is
feasible to grow a research team, but there are usually increased inefficiencies that come with larger
organizations.8
Concentration also has negative consequences for risk adjusted returns. The most obvious disadvantage
of concentration is that it will result in a higher risk. Hence, the optimal balance between
diversification and skill also depends on the client ability to take risk and to diversify this risk. For
institutional investors with long investment horizons and the resources to effectively detect skillful
managers, diversification is relatively cheap to obtain. In theory, such investors should seek
concentrated portfolios where skill is not diluted by diversification. For retail investors who have to
support higher transaction costs and cannot perform extensive due diligence, investing in few
diversified portfolios makes more sense. For a given fund size, more concentration will automatically
result in less liquid positions, which, everything else being equal, will have a negative impact on
performance.9
Empirical Analysis of the Relation between Diversification and Skill
Two empirical studies have found that mutual funds with high levels of concentration tend to
outperform funds with lower levels of concentration. Kacperczyk et al.[2005, 2007] found that small-
8
Chen et al. [2004], find results consistent with this view. They observe that small sized funds outperform large sized funds and
argue that part of this difference in performance is due to organizational diseconomies related to hierarchy costs.
9
See Becker and Vaughan [2001] for illustration of this point, see also Chen et al. [2004] who find that a key variable to explain
difference in performance between small funds and large funds is liquidity.
September, 2010 10
11. cap funds with higher levels of industry concentration were generating greater alpha than funds with
lower levels of industry concentration. Cremers and Petajisto [2008] measured the fund concentration
with its active share and found that funds with high concentration outperformed funds with low
concentration. The measures of concentration used in these two studies focus on the concentration of
portfolio weights. Unlike the DI coefficient these measures of concentration do not capture the impact
10
of concentration in positions’ volatilities and correlations among positions.
In order to understand the relation between portfolio diversification and skill, we applied the Empirical
Law of Active Management to a universe of 2,798 U.S. mutual funds invested in domestic equities from
1980 to 2006. The first obstacle we faced in assessing the skill of a manager was defining the
benchmark. While the concept of benchmark is ubiquitous in today’s asset management industry, it
was not the case in the 80’s and early 90’s. Hence, finding an accurate and consistent definition of a
fund’s benchmark across all periods is difficult. Moreover, the active returns of a fund measured
against its stated benchmark often contain common factor bets such as value, size or momentum that
can distort the active returns coming purely from stock picking skills. For these reasons, we used factor
models to determine the appropriate benchmark. We labeled as alpha or active return any returns that
could not be explained by the factors of the model we used. Therefore, the choice of model and the
factors that we included in the model were critical. Our objective was to assess the stock-picking skill
of a manager, as a result all known “priced factors” should be included in our model and excluded from
the manager’s alpha. “Priced factors” are factors for which empirical studies have demonstrated the
existence of positive risk adjusted returns; namely: market, value, size and momentum. To assess a
fund’s exposure to these factors, we used the same four-factor model as Carhart [1997]. In order to
ensure that our results were not dependent on the model, we also used two alternative models that
are based on similar factors but that use different techniques to assess the exposures. The first
w
10
Kacperczyk et al. define as industry concentration as: portfolio
wimarket portfolio
2 (where wi is the weight of industry i in the
i
i
portfolio and in the market portfolio). Cremers and Petajisto use active share, which, is the sum of the absolute deviations of the
portfolio weights from the benchmark weights. Active Share w i
i
portfolio
wibenchmark
September, 2010 11
12. alternative model is based on the characteristic based benchmarks developed by Daniel et al. [1997].
11
The second alternative model is based on the 25 Fama-French portfolios sorted on value and size.
(See appendix 2 for a more precise description of the models and the data).
Exhibit 2 shows the average alpha, skill, diversification and number of securities per fund across each
of the periods we examined. Alpha and skill are net of the funds’ expenses ratios. The decline in
mutual fund alphas that we observed in this table was very important. The average mutual fund in our
universe went from generating a 29 bps positive alpha in the first part of the a 90’s to a negative 1.3%
alpha in the second part of the 90’s. This trend is consistent with the four-factor alphas reported by
Kosowski et al. [2006] for similar periods and is also reported by Fama and French [2009]. Such
variations in the average alpha and skill of mutual fund managers are surprising considering that since
the 1990’s, the Investment Company Institute (ICI) has reported a decline in U.S. mutual fund expense
ratios.12 The second interesting trend that we observed in Exhibit 2 was a general increase in the
13
number of positions per portfolio and therefore in the diversification of the funds. This increase in
portfolio diversification among mutual fund managers is consistent with the inroads that modern
portfolio theory made during the 80’s and 90’s among practitioners and the development of passive
mutual funds. In addition, this period also witnessed a significant development of information
technology solutions that drastically reduced the operational costs of running portfolios with a large
number of positions.
Exhibit 2: Number of Funds, Mean Alpha, Skill, Diversification and number of positions per
portfolio for each Period.
The benchmark of each portfolio is estimated with the
Carhart [1997] model.
11
See Daniel et al. [1997] and Wermers [2004] for more details on DGTW portfolio. The DGTW benchmarks are available via
http://www.smith.umd.edu/faculty/rwermers/ftpsite/Dgtw/coverpage.htm. The Fama-French portfolio are available via:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
12
See: Investment Company Institute Research Department Staff [2009] and Collins [2009]
13
Cremers and Petajisto [2009] report similar results using active share.
September, 2010 12
13. Number of Number of
Period Funds Alpha SK DI Positions
1980‐1984 137 0.58% 0.007 36 71
1985‐1989 270 0.43% 0.004 45 84
1990‐1994 588 0.29% 0.001 62 96
1995‐1999 1519 ‐1.28% ‐0.013 65 125
2000‐2006 2378 ‐1.28% ‐0.008 70 148
1980‐2006 2798 ‐0.84% ‐0.007 63 135
We see two non-exclusive explanations for the decline in skill that we observed among equity mutual
funds. First, mutual fund managers were victims of their own success. The net asset value of equity
mutual funds as a percentage of the capitalization of the U.S. stock market increased from 3% to 40%
between 1980 and 200814. If mutual fund managers are a representative sample of the equity market
investors, Sharpe’s [1991] arithmetic of active management entails that as a whole, mutual fund
managers should have a negative alpha roughly equal to the fees they charge. As the industry grows
closer to representing the U.S. stock market, it is more difficult for the industry as a whole to
outperform the market.
The second explanation for this phenomenon is that the quality of U.S. Equity mutual funds has
declined. The industry would have responded to the increase in demand for mutual funds that took
place during the 80’s and 90’s by creating sub-par products. The market for asset management
services, like the Lemons market described by Akerlof [1970], is characterized by an asymmetry of
information.15 Since it is difficult for investors to distinguish a skilled from an unskilled manager, there
is a large incentive for unskilled managers to flood the market and distribute low cost investment
strategies that add no value while charging active management fees. This incentive is even greater
when demand expands and new customers with less financial acumen enter the market. Under such
circumstances, unskilled managers, or “closet indexers”, will want to take the minimum level of risk
that allows them to charge active management fees. On the other hand, skilled managers have an
incentive to take relatively more concentrated positions. Such situations should result in a positive
14
To compute these percentages, we used net asset value of equity mutual funds reported in the 2009 Investment Company Fact
Book (Investment Company Institute Research Department Staff [2009]) and the Wilshire 5000 index capitalization as a proxy for
the capitalization of the U.S. stock market.
15
See Foster and Young [2008]
September, 2010 13
14. skew in the distribution of alphas because skilled managers with concentrated portfolios will generate
high alphas, while unskilled managers will generate moderate negative alphas. Under this hypothesis,
the industry responded to an increasing demand for mutual funds by increasing its “lemon” production
and crafting strategies with little information content and with the look and feel of effective active
investment strategies. In order to assess this hypothesis, we examined the cross-sectional relation
between skill and diversification by splitting our universe of mutual funds into quintiles of
diversification and compared the skill of the funds located in each quintile.
Exhibit 3: Alpha and Skill by Quintiles of Diversification
The benchmark of each portfolio is estimated with the Carhart [1997] model.
Skill by Diversification(DI) Quintile (1980‐2006)
Quintile 1: Quintile 5:
Low DI Quintile 2 Quintile 3 Quintile 4 High DI
Mean 0.004 ‐0.007 ‐0.011 ‐0.011 ‐0.011
T‐stat (Mean Skill) 2.02 ‐6.34 ‐10.77 ‐11.98 ‐14.50
Skill Difference : Quintile 1 ‐ Quintile 2,3,4 or 5 0.012 0.016 0.015 0.015
T‐stat (Skill Difference) 4.78 6.45 6.50 6.51
Standard Deviation 0.05 0.03 0.02 0.02 0.02
Skewness 0.97 ‐0.21 0.15 ‐0.51 ‐0.62
Kurtosis 7.06 5.03 5.17 4.46 4.98
Number of Observations 560 559 560 559 560
In Exhibit 3, we observe that funds located in the first diversification quintile did exhibit significantly
more skill than any of the other quintiles. On average, the skill of these funds was greater than zero
while the skill in all the other quintiles of the distribution was significantly less than zero. All the
differences in skill between quintile 1 and each of the four other quintiles are statistically significant.
Exhibit 3 also indicates a positive skew in the distribution of the skill of low diversification portfolio
managers. This fact indicates that our result could be explained by survivorship bias. Less
diversification implies more risk. Since we required at least 36 months of returns to include a fund in
our analysis, it is possible that the low diversification funds that severely underperformed rapidly lost
their clients and did not survive long enough to be included in our analysis. Note that the positive skew
in the distribution of alpha can be explained by factors other than survivorship bias. As we observed
earlier, the presence of closet indexers or “lemons” in the mutual fund market is consistent with such
distribution of alphas.
September, 2010 14
15. In order to test the impact of a possible survivorship bias on our results, we created an artificial bias
against the top performing funds by eliminating funds in the right tail of the alpha distribution in order
to have a symmetric distribution. We removed from our analysis all funds whose alpha was greater than
the absolute value of the first percentile of the alpha distribution.
After removing these funds, the skew of the distribution became slightly negative; however, the skill
difference between the first quintile of managers and the rest of the universe remained strongly
significant (see top-panel of exhibit 4). In order to further test the robustness of our results, we
designed a more conservative artificial survivorship bias, where we removed all funds with alpha
greater than the absolute value of the fifth percentile of the alpha distribution. Under this definition of
the artificial survivorship bias, we eliminated from our sample all the funds with annualized alpha
greater than 6.7% per annum. Nevertheless, the bottom panel of exhibit 4 shows that low
diversification funds still exhibited significantly higher skill under both definitions of the artificial
survivorship bias. Hence, the relationship that we observed between skill and diversification cannot be
explained away by survivorship bias.
Exhibit 4: Alpha and Skill by Diversification Quintiles From 1980 to 2006 Excluding top Performing
Funds
Out-performing funds are funds with an alpha greater than the absolute value of the first or fifth percentile of the alpha
distribution. The benchmark of each portfolio is estimated with the Carhart model.
Skill by Diversification(DI) Quintile (1980‐2006) Excluding Top‐
Performing Funds
Quintile 1: Quintile 5:
Low DI Quintile 2 Quintile 3 Quintile 4 High DI
Mean ‐0.001 ‐0.009 ‐0.011 ‐0.011 ‐0.010
Absolute Value of 1st
T‐stat (Mean Skill) ‐0.48 ‐7.55 ‐11.27 ‐12.40 ‐14.27
Skill Difference : Quintile 1 ‐ Quintile 2,3,4 or 5 0.008 0.011 0.010 0.010
Percentile Alpha
Alpha less than
T‐stat (Skill Difference) 3.61 5.10 5.18 4.94
Standard Deviation 0.04 0.03 0.02 0.02 0.02
Skewness ‐0.04 ‐0.46 ‐0.18 ‐0.54 ‐0.63
Kurtosis 5.35 4.62 3.97 4.43 5.00
Number of Observations 554 554 554 554 554
Mean ‐0.007 ‐0.01 ‐0.012 ‐0.011 ‐0.011
Absolute Value of 5th
T‐stat (Mean Skill) ‐4.08 ‐9.28 ‐11.62 ‐12.62 ‐14.53
Skill Difference : Quintile 1 ‐ Quintile 2,3,4 or 5 0.003 0.005 0.005 0.004
Percentile Alpha
Alpha less than
T‐stat (Skill Difference) 1.80 2.73 2.58 2.31
Standard Deviation 0.04 0.03 0.02 0.02 0.02
Skewness ‐0.59 ‐0.60 ‐0.27 ‐0.55 ‐0.84
Kurtosis 5.53 4.31 3.85 4.42 4.49
Number of Observations 543 542 543 542 543
September, 2010 15
16. The relation between skill and diversification also held across the three different types of models that
we used to define the alpha for the 1980-2006 period. Exhibit 5 also shows strongly significant results if
we use the characteristic based benchmarks or the 25 Fama-French portfolios to establish the alpha of
each fund. However, the relationship between skill and diversification was not consistent across
periods. Breaking up the 1980-2006 periods into 5 distinct sub-periods, we did not find that low
diversification funds outperformed in each sub-period (see exhibit 5). We did not find any significant
relation between diversification and skill during the eighties and the early nineties.
Exhibit 5: Relation between Skill and Diversification across periods and models
For each period and each model, we show the mean of the t-stats for the differences in skill between quintile one and quintiles
two to five (Mean t-stat). We also show the smallest of the four t-stats (Min t-stat). For the Carhart model in the period 1980-
2006, we can read from table 3 that the four t-stats are 4.78, 6.45, 6.50 and 6.51. The mean of these four t-stats: 6.06 and
minimum: 4.78 are displayed in the top left cell of table 5. FF-25 denotes the results that we obtained with the 25 Fama-French
portfolios, DGTW indicate that we used the characteristic based benchmarks of Daniel et al. [1997]
1980 2000 1995 1990 1985 1980
to to to to to to
Periods: 2006 2006 1999 1994 1989 1984
Mean t‐stat 6.06 7.46 2.11 ‐0.40 0.68 ‐0.28
Carhart Min t‐stat 4.78 6.90 1.84 ‐0.64 0.07 ‐0.71
Mean t‐stat 3.59 2.23 4.08 0.86 ‐0.57 ‐1.52
DGTW Min t‐stat 1.95 1.78 2.54 0.50 ‐2.26 ‐1.98
Mean t‐stat 4.29 3.15 5.33 0.91 1.15 ‐1.03
FF‐25 Min t‐stat 3.66 1.75 4.50 0.04 0.20 ‐1.25
Number of Observations per Quintile 559.6 475.6 303.8 117.6 54 27.6
Since we could not find a significant relation between diversification and skill in every sub-period, we
found it difficult to conclude that concentrated managers had an intrinsic advantage over less
concentrated managers. Instead, the result of this study is better interpreted using Lo’s [2004]
Adaptative Market Hypothesis. The ability of U.S. mutual funds to beat the market evolved through
time under the influence of the structure of the U.S. market for mutual funds. Our interpretation of
these results is based on two elements. First, concentration among mutual fund managers has
decreased since the 80’s. Second, our analysis shows that since the mid-90’s, skill was more likely to
be found in more concentrated portfolios. These two points taken together indicated that as the
demand for mutual funds increased, the industry responded by producing funds with higher
diversification but lower information content, also known as “closet-indexers.” As a result, the average
September, 2010 16
17. skill and alpha of U.S. equity mutual funds decreased. In most industries, increases in demand are met
by increases in price; however, no such price increase took place in the asset management industry
during the 90’s.16 We infer from our data that the asset management industry took advantage of this
increase in demand by cutting the information content of its products while leaving its management
fees unchanged.
Conclusion
The Fundamental Law of Active Management played a very important role in the development of
quantitative asset management. The application of this law was designed by quantitative investment
managers for quantitative investment managers, and is difficult to apply to other types of processes.
However, the result of the Fundamental Law of Active Management applies to all investment managers.
The Empirical Law of Asset Management presented in this paper seeks to generalize and extend this
tool to a wider range of portfolios while conserving the key insights that made this concept a success.
The application of this analytical framework to U.S. equity mutual funds reveals a general decline in
skill. We found two explanations for this decrease in skill. Firstly, the mutual fund industry was a
victim of its own success, as mutual funds represent a greater share of the market capitalization. It is
now close to impossible for the industry as a whole to outperform the market. Secondly, the decrease
in skill was accompanied by an increase in diversification. Since the mid-90’s, we also observe an
inverse relationship between skill and diversification. We suggest that the increase in diversification
does reflect a decrease in the quality of the information content of U.S. mutual funds.
16
See: Investment Company Institute Research Department Staff [2009]
September, 2010 17
18. References:
Akerlof, George. “The Market for "Lemons": Quality Uncertainty and the Market Mechanism.” The
Quarterly Journal of Economics, Vol. 84, No. 3 (1970), pp. 488-500.
Beckers, Stan, G. Vaughan. “Small is Beautiful.” Journal of Portfolio Management, Vol. 27, No. 4
(2001), pp. 9-17.
Berk, Jonathan, R. Green. “Mutual Fund Flows and Performance in Rational Markets.” Journal of
Political Economy, Vol. 112, No. 6 (2004), pp. 1269-1295.
Buckle, David. “How to calculate breadth: An evolution of the Fundamental Law of Active
Management.” Journal of Asset Management, Vol. 4, No. 6 (2004), pp. 393-405.
Daniel, Kent, M. Grinblatt, S. Titman and R. Wermers. “Measuring Mutual Fund Performance with
Characteristic Based Benchmarks.” The Journal of Finance, Vol. 52, No. 3 (1997), pp. 1035-1058.
Carhart, Mark M. “On Persistence in Mutual Fund Performance.” The Journal of Finance, Vol. 52, No. 1
(1997), pp. 57-82.
Chen, Joseph, H. Hong, M. Huang and J. Kubik. “Does Fund Size Erode Mutual Fund Performance? The
Role of Liquidity and Organization.” The American Economic Review, Vol. 94, No. 5 (2004), pp. 1276-
1302.
Clarke, Roger, H. de Silva, S. Thorley. “Portfolio Constraints and the Fundamental Law of Active
Management.” Financial Analysts Journal, September/October 2002, Vol. 58, No. 5 (2002), pp. 48-66.
“The Fundamental Law of Active Portfolio Management.” Journal of Investment Management, Vol. 4,
No. 3 (2006), pp. 54–72.
Collins, Sean. “Trends in the Fees and Expenses of Mutual Funds, 2008.” Investment Company Institute
Research Fundamentals, Vol. 18, No. 3 (April 2009)
Cremers, Martjin, A. Petajisto “How Active is Your Fund Manager? A New Measure that Predicts
Performance.” Review of Financial Studies, Vol. 22, No. 9 (September 2009), pp. 3329-3365.
Foster, Dean, P. Young. “The Hedge Fund Game: Incentives, Excess Returns, and Performance Mimics.”
University of Oxford, Discussion Paper Series (2008).
Grinold, Richard C. “The Fundamental Law of Active Management.” The Journal of Portfolio
Management, Vol. 15, No. 3 (Spring 1989), pp. 30-37.
Grinold, Richard C., R. Kahn. Active Portfolio Management: A Quantitative Approach for Producing
Superior Returns and Controlling Risk, 2nd ed. McGraw-Hill, 1999.
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Edition, (2009).
Kacperczyk, Marcin T., C. Sialm, L. Zheng. “On Industry concentration of Actively Managed Equity
Mutual Funds.” The Journal of Finance, 60 (2005), pp. 1983-2012.
Kacperczyk, Marcin T., C. Sialm, L. Zheng. “Industry Concentration and Mutual Fund Performance.”
Journal of Investment Management, Vol. 5, No. 1 (2007)
Kosowski, Robert, A. Timmermann, R. Wermers, A. White. “Can Mutual fund “Stars” Really Pick Stocks?
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September, 2010 18
19. Fama, Eugene, K. French. “Luck versus Skill in the Cross Section of Mutual Fund Alpha Estimates.”
working paper (2009)
Lo, Andrew. “Risk management for hedge funds: introduction and overview.” Financial Analysts
Journal, Vol. 57, No. 6 (November/December 2001), pp.16-33.
“The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective.” Journal of
Portfolio Management, 30 (2004), pp. 15-29.
“Where Do Alphas Come From?: A New Measure of the Value of Active Investment Management.”
Journal of Investment Management, forthcoming.
Sharpe, William. “The Arithmetic of Active Management” Financial Analysts Journal, Vol. 47, No. 1
(January/February 1991), pp. 7-9.
Shleifer, Andrei, R. Vishny. “The Limits of Arbitrage.” The Journal of Finance, Vol. 52, No. 1 (1997),
pp. 35-55.
Pollet, Joshua, M. Wilson. “How Does Size Affect Fund Behavior?” working paper (2007).
Van Nieuwerburgh, Stijn, L. Veldkamp. “Information Acquisition and Under-Diversification.” working
paper (2008).
Wermers, Russ. “Are Mutual Fund Shareholders Compensated for Active Management "Bets"?” working
paper (2003).
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and Performance Persistence.” working paper (2004).
September, 2010 19
20. Appendix 1: derivation of the Empirical Law of Active Management
wi is the weight of security i in the portfolio
w is the vector of all the securities weights in the portfolio.
is the covariance matrix of the securities’ active return. If V is a classic covariance matrix of assets
returns of size (n x n), and B is a (n x n) matrix which contains n times the (n x1) vector of benchmark
weights and I is the identity matrix then can be obtained in the following way: ( I B)'V ( I B)
. 17 The active variance of the portfolio ( w' w ) can be decomposed into the risk of the portfolio if all
securities were perfectly correlated and a second term which represents the benefits from
diversification.
w' w wi2 i2 wi w j i j i , j
i i j i
w' w w wi w j i j (1 i , j 1)
2
i i
2
i i j i
2
w' w wi i wi w j i j (1 i , j )
i i j i
We separated the risk of the portfolio into two parts: First, the average volatility, which is the risk if
all positions were perfectly correlated. And second, the diversification benefits, which is the decrease
in risk due to positions in the portfolio being less than perfectly correlated.
Let’s note the average risk of a position in the portfolio as:
17
The I B matrix contains n columns of active weights for n portfolios that are fully invested in one and only one asset:
1 0 ... 0 w1b w1b ... w1b
0 b b
1 ... 0 w2
b
w2 ... w2
I B w1active w2 ... wn
active active
... ... ... ... ... ... ... ...
b b
0 0 ... 1 wn wn ... wn
b
September, 2010 20
21. wi i
i
wi i
Let’s note risk weights: i with these notations the active variance of a portfolio is:
2
w' w i 2 i j ( i , j 1)
i i j i
We can re-write the active variance of the portfolio in the following way:
w' w 2 2 i j i , j i j
i j i i j i
Or:
w' w 2 1 i j i , j i j
i j i i j i
The term
i j i
i j i , j i j can be broken down into two components:
i j i
- the product of the risk weights =
i j i
i j (Equation 1)
- risk weighted correlation =
i j i
i j i, j (Equation 2)
We can rewrite equation 1 as: 1
i j i
i j
i
i
j i
j
i
i i which can be expressed in
function of the variance of the risk weights:
2
1 1
i j i i2 i i
i j i i i n n
2
1 1 1 1
i i j 1 n 2 i n 2 n i n
i j i i
i
September, 2010 21
22. 2
1 1
i i j 1 n i n
i j i
n 1
i j i
i j
n
n * Variance(i )
Hence the concentration of the risk weights is a direct function of the variance of the risk weights:
n 1
i j nVar ( i )
i j i n
The higher the dispersion of the risk weights (that is the dispersion of portfolio weights and
volatilities), the higher the active risk of the portfolio. The second element of this diversification term
is the correlations among the positions of the portfolio (equation 2).
i j i
i j i, j i j i, j
i j i
We note i the average correlation of asset i with the other assets in the portfolio, weighted by the
18
risk-weight of each asset in the portfolio.
i j i , j hence we obtain: i j i , j i i
~
j i i j i i
We call this quantity the risk weighted correlation:
i
i i
i j i
i j i, j
If we put everything back together:
n2 1 1
w' w 2 1 nVar ( )
2 nVar ( )
n n
18
Note that the sum of the risk-weights excluding asset i does not add-up to one. The correct weighted average should be:
i
j
i , j The correlation term becomes: (1 )
i i i
j i (1 i ) i
September, 2010 22
23. The diversification factor of the portfolio is defined as:
1
DI
1 ~
nVar ( i )
n
Appendix 2:
The mutual funds quarterly holdings were obtained from the Thomson-Reuters mutual fund database.
The funds monthly returns were gathered from the CRSP mutual fund database and the securities’
returns were obtained from the CRSP U.S. Stock database. We used the MF Link mapping developed by
Russ Wermers to map funds in the Thomson-Reuters database to funds in the CRSP database.
We examined separately 6 periods: 1980-1984, 1985-1989, 1990-1994, 1995-1999, 2000-2006 and 1980-
2006. To be included in the analysis of a period a fund should have at least 36 months of returns during
that period. For each period, we used the following steps to compute the diversification and skill
factors. First we computed the return of each fund by taking the asset-weighted average return of all
share-classes. If a share-class asset value was missing on a given date, we took the equal-weighted
average return of all the share classes.
Second, we assessed the fund benchmark using each of the following three pricing models: the four-
factor model used by Carhart [1997] (henceforth: “Carhart”); a second pricing model based on the
Daniel, Grinblatt, Titman and Wermers characteristic based benchmarks (“DGTW”); and a third pricing
model based on the 25 Fama-French portfolios sorted on Value and Size (“FF-25”). 19
For the Carhart model, we performed a regression of the fund returns on the four factors of the model
(market, value, size and momentum). The exposure to the four factors resulting from this regression
defined the benchmark of the fund. As a result, the active return of the fund was equal to the alpha of
the fund computed with the Carhart model.
19
See Daniel et al. [1997] and Wermers [2004] for more details on DGTW portfolio. The DGTW benchmarks are available via
http://www.smith.umd.edu/faculty/rwermers/ftpsite/Dgtw/coverpage.htm. The Fama-French portfolio are available via:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
September, 2010 23
24. For DGTW, we performed a regression of the fund returns on the market portfolio and one of the 125
characteristic based benchmarks and the market factor. The DGTW benchmarks are the result of a sort
of U.S. stocks on value, size and momentum exposures. We choose a unique DGTW benchmark which,
when combined with the market portfolio, maximizes the variance explained by the regression. The
market portfolio that we used with each of these models was the value-weighted return on all NYSE,
AMEX, and NASDAQ stocks (from CRSP), minus the one-month Treasury bill rate. We followed the same
procedure for the FF-25 portfolios.
For each period we computed the historical active volatility of each asset in each fund using the
securities monthly returns. Asset active volatility is the standard deviation of the difference between
the asset returns and the benchmark returns. If a security does not have at least 24 months of returns,
we set its active volatility to the equal weighted average volatility of the fund’s assets with more than
24 months of returns. Every quarter, we compute the mean weighted volatility. The fund mean
weighted volatility for a period is the mean of each of the quarterly mean weighted volatility during
that period.
For a quarterly observation of the portfolio to be included in our analysis, we required that at least 75%
of the assets in the portfolio be recognized in the CRSP U.S. Stock database. For a fund to be included
in the analysis of a period, we required at least 8 valid quarters. In addition, we excluded from the
analysis, funds that had an average across all quarters of a period more than 5% of assets not
recognized in the CRSP U.S. Stock database. We excluded funds that, on average across all quarters of
a given period, had fewer than 10 positions, or less than 15 million dollars of asset under management.
Using the three models, we computed alpha (active return) and residual risk (active risk) during each of
the periods we analyzed. We then computed the weighted mean asset volatility of each portfolio using
the monthly historical return of each asset in the fund.
Finally, we took the mean of these quarterly volatilities across the entire period to obtain a proxy for
the fund asset weighted volatility ( ) for the period and used the following decomposition to compute
the fund’s skill and diversification.
September, 2010 24
25.
DI= and SK
Model Choices
While the Carhart model is the standard pricing model used in the literature, the findings of Cremers
and Petajisto [2009] raised questions about the suitability of this model to establish a pertinent
performance benchmark. Unlike Cremers and Patajisto, we obtained strongly significant results with
the Carhart model. However, we still wanted to ensure that our results were not dependent on the
type of model we were using, so we recomputed our results with two alternative models. The DGTW
benchmarks offer a very granular classification of U.S. stocks into benchmarks based on their value,
size and momentum characteristics. These DGTW benchmarks have fewer stocks than a typical
benchmark and therefore more idiosyncratic risk. We also used a coarser asset classification
framework: the 25 Fama-French value and size sorted portfolios. The disadvantage of the Fama-French
portfolio is that we did not account for the funds’ momentum exposure. Using these three models, we
computed alpha (or active return), residual risk (or active risk), skill and diversification of each
portfolio during each of the periods we analyzed.
In theory, we should also have excluded from the active returns the returns due all non-priced factors
to which the funds are systematically exposed. However, there is an infinite set of non-priced factors
that could be included in the benchmark definition. Therefore, using non-priced factors was not
practical. Since exposures are computed based on the historical co-movement of the fund’s returns and
the factor returns, we would have picked up spurious relations between the funds’ returns and the
factors if we used a larger number of non-priced factors. As a result, we would have obtained a very
narrow definition of the fund’s alpha.
September, 2010 25