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.
Global Value Equity Portfolio (March 2011)Trading Floor
This month we have adjusted our Global Value Equity Portfolio to include the reinvestment of gross dividends and introduced dynamic weights for the constituents. This reduces transaction costs, enhances excess return and makes the portfolio easier to replicate for investors.
Global Value Equity Portfolio (March 2011)Trading Floor
This month we have adjusted our Global Value Equity Portfolio to include the reinvestment of gross dividends and introduced dynamic weights for the constituents. This reduces transaction costs, enhances excess return and makes the portfolio easier to replicate for investors.
An absolute return strategy aiming to profit from divergences in sector performance at different phases of the growth cycle. The approach combines a strong focus on industry and stock fundamentals with an appreciation of the macroeconomic environment.
Determinants of the implied equity risk premium in BrazilFGV Brazil
This paper proposes and tests market determinants of the equity risk premium (ERP) in Brazil. We use implied ERP, based on the Elton (1999) critique. The ultimate goal of this exercise is to demonstrate that the calculation of implied, as opposed to historical ERP makes sense, because it varies, in the expected direction, with changes in fundamental market indicators. The ERP for Brazil is calculated as a mean of large samples of individual stock prices in each month in the January, 1995 to September, 2015 period, using the “implied risk premium” approach. As determinants of changes in the ERP we obtain, as significant, and in the expected direction: changes in the CDI rate, in the country debt risk spread, in the US market liquidity premium and in the level of the S&P500. The influence of the proposed determining factors is tested with the use of time series regression analysis. The possibility of a change in that relationship with the 2008 crisis was also tested, and the results indicate that the global financial crisis had no significant impact on the nature of the relationship between the ERP and its determining factors. For comparison purposes, we also consider the same variables as determinants of the ERP calculated with average historical returns, as is common in professional practice. First, the constructed series does not exhibit any relationship to known market-events. Second, the variables found to be significantly associated with historical ERP do not exhibit any intuitive relationship with compensation for market risk.
Authors:
Sanvicente, Antonio Zoratto
Carvalho, Mauricio Rocha de
FGV's Sao Paulo School of Economics (EESP)
How Investment Analysis & Portfolio Management greatly focuses on portfolio c...QUESTJOURNAL
Abstract: Portfolio Construction is a capstone elective that draws on previously studied investment principles, theories and techniques. Its enable synthesize that acquired financial theories and knowledge in the context of portfolio construction and asset allocation. It focuses on gaps in theory and how they can be managed in practice.
Through examining their nature and mechanisms, identifying their spin-offs and analyzing their performance, this presentation is designed to discuss what to look out for when conduct due diligence on different hedge fund strategies.
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.
An absolute return strategy aiming to profit from divergences in sector performance at different phases of the growth cycle. The approach combines a strong focus on industry and stock fundamentals with an appreciation of the macroeconomic environment.
Determinants of the implied equity risk premium in BrazilFGV Brazil
This paper proposes and tests market determinants of the equity risk premium (ERP) in Brazil. We use implied ERP, based on the Elton (1999) critique. The ultimate goal of this exercise is to demonstrate that the calculation of implied, as opposed to historical ERP makes sense, because it varies, in the expected direction, with changes in fundamental market indicators. The ERP for Brazil is calculated as a mean of large samples of individual stock prices in each month in the January, 1995 to September, 2015 period, using the “implied risk premium” approach. As determinants of changes in the ERP we obtain, as significant, and in the expected direction: changes in the CDI rate, in the country debt risk spread, in the US market liquidity premium and in the level of the S&P500. The influence of the proposed determining factors is tested with the use of time series regression analysis. The possibility of a change in that relationship with the 2008 crisis was also tested, and the results indicate that the global financial crisis had no significant impact on the nature of the relationship between the ERP and its determining factors. For comparison purposes, we also consider the same variables as determinants of the ERP calculated with average historical returns, as is common in professional practice. First, the constructed series does not exhibit any relationship to known market-events. Second, the variables found to be significantly associated with historical ERP do not exhibit any intuitive relationship with compensation for market risk.
Authors:
Sanvicente, Antonio Zoratto
Carvalho, Mauricio Rocha de
FGV's Sao Paulo School of Economics (EESP)
How Investment Analysis & Portfolio Management greatly focuses on portfolio c...QUESTJOURNAL
Abstract: Portfolio Construction is a capstone elective that draws on previously studied investment principles, theories and techniques. Its enable synthesize that acquired financial theories and knowledge in the context of portfolio construction and asset allocation. It focuses on gaps in theory and how they can be managed in practice.
Through examining their nature and mechanisms, identifying their spin-offs and analyzing their performance, this presentation is designed to discuss what to look out for when conduct due diligence on different hedge fund strategies.
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.
Are simple indexes cost effective while trying to remain diversified with exposure to various asset classes? This short piece discusses the various costs of indexing using funds that are restricted to different indexes.
DSP US Flexible Equity Fund - An Open Ended Fund Of Funds Scheme Investing in a US Equity Fund
*The term “Flexible” in the name of the Scheme signifies that the Investment Manager of the Underlying Fund can invest either in growth or value investment characteristic securities placing an emphasis as the market outlook warrants.
This Open-ended Fund of Funds Scheme is suitable for investors who are seeking*:
1. Long-term capital growth
2. Investment in units of overseas funds which invest primarily in equity and equity related securities of companies domiciled in, or exercising the predominant part of their economic activity in the USA
3. High risk (Brown)
*Investors should consult their financial advisors if in doubt about whether the Scheme is suitable for them.
Note : Risk may be represented as :
(Blue) : Investors understand that their principal will be at low risk
(Yellow) : Investors understand that their principal will be at medium risk
(Brown) : Investors understand that their principal will be at high risk
significance of market timing and stock selection ability of mutual fund mana...professionalpanorama
A Mutual Fund is a trust that pools the savings of a number of investors
who share a common financial goal. The money thus collected is invested
by the fund manager in different types of securities depending upon the
objectives of the scheme. Mutual funds cannot guarantee a fixed rate of
return. It depends on the market condition. If a particular scheme is
performing well then more return can be expected. It also depends on the
fund managers’ expertise and knowledge. The present study is aimed to
examine the performance of mutual fund managers on the basis of
selectivity and market timing abilities in security market. However, the
majority of the selected mutual fund managers do not possess market
timing ability rather they are relying a little bit on stock selection.
Significance of market timing and stock selection ability of mutual fund mana...Tapasya123
A Mutual Fund is a trust that pools the savings of a number of investors
who share a common financial goal. The money thus collected is invested
by the fund manager in different types of securities depending upon the
objectives of the scheme. Mutual funds cannot guarantee a fixed rate of
return. It depends on the market condition. If a particular scheme is
performing well then more return can be expected. It also depends on the
fund managers’ expertise and knowledge. The present study is aimed to
examine the performance of mutual fund managers on the basis of
selectivity and market timing abilities in security market. However, the
majority of the selected mutual fund managers do not possess market
timing ability rather they are relying a little bit on stock selection.
Similar to Returns basedstyleanalysisinexcel mcdermott (20)
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what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
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how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
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Introduction to Indian Financial System ()Avanish Goel
The financial system of a country is an important tool for economic development of the country, as it helps in creation of wealth by linking savings with investments.
It facilitates the flow of funds form the households (savers) to business firms (investors) to aid in wealth creation and development of both the parties
Resume
• Real GDP growth slowed down due to problems with access to electricity caused by the destruction of manoeuvrable electricity generation by Russian drones and missiles.
• Exports and imports continued growing due to better logistics through the Ukrainian sea corridor and road. Polish farmers and drivers stopped blocking borders at the end of April.
• In April, both the Tax and Customs Services over-executed the revenue plan. Moreover, the NBU transferred twice the planned profit to the budget.
• The European side approved the Ukraine Plan, which the government adopted to determine indicators for the Ukraine Facility. That approval will allow Ukraine to receive a EUR 1.9 bn loan from the EU in May. At the same time, the EU provided Ukraine with a EUR 1.5 bn loan in April, as the government fulfilled five indicators under the Ukraine Plan.
• The USA has finally approved an aid package for Ukraine, which includes USD 7.8 bn of budget support; however, the conditions and timing of the assistance are still unknown.
• As in March, annual consumer inflation amounted to 3.2% yoy in April.
• At the April monetary policy meeting, the NBU again reduced the key policy rate from 14.5% to 13.5% per annum.
• Over the past four weeks, the hryvnia exchange rate has stabilized in the UAH 39-40 per USD range.
Latino Buying Power - May 2024 Presentation for Latino CaucusDanay Escanaverino
Unlock the potential of Latino Buying Power with this in-depth SlideShare presentation. Explore how the Latino consumer market is transforming the American economy, driven by their significant buying power, entrepreneurial contributions, and growing influence across various sectors.
**Key Sections Covered:**
1. **Economic Impact:** Understand the profound economic impact of Latino consumers on the U.S. economy. Discover how their increasing purchasing power is fueling growth in key industries and contributing to national economic prosperity.
2. **Buying Power:** Dive into detailed analyses of Latino buying power, including its growth trends, key drivers, and projections for the future. Learn how this influential group’s spending habits are shaping market dynamics and creating opportunities for businesses.
3. **Entrepreneurial Contributions:** Explore the entrepreneurial spirit within the Latino community. Examine how Latino-owned businesses are thriving and contributing to job creation, innovation, and economic diversification.
4. **Workforce Statistics:** Gain insights into the role of Latino workers in the American labor market. Review statistics on employment rates, occupational distribution, and the economic contributions of Latino professionals across various industries.
5. **Media Consumption:** Understand the media consumption habits of Latino audiences. Discover their preferences for digital platforms, television, radio, and social media. Learn how these consumption patterns are influencing advertising strategies and media content.
6. **Education:** Examine the educational achievements and challenges within the Latino community. Review statistics on enrollment, graduation rates, and fields of study. Understand the implications of education on economic mobility and workforce readiness.
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This SlideShare provides valuable insights for marketers, business owners, policymakers, and anyone interested in the economic influence of the Latino community. By understanding the various facets of Latino buying power, you can effectively engage with this dynamic and growing market segment.
Equip yourself with the knowledge to leverage Latino buying power, tap into their entrepreneurial spirit, and connect with their unique cultural and consumer preferences. Drive your business success by embracing the economic potential of Latino consumers.
**Keywords:** Latino buying power, economic impact, entrepreneurial contributions, workforce statistics, media consumption, education, home ownership, Latino market, Hispanic buying power, Latino purchasing power.
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
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USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
Greek trade a pillar of dynamic economic growth - European Business Review
Returns basedstyleanalysisinexcel mcdermott
1. JOURNAL OF EDUCATION FOR BUSINESS, 85: 107–113, 2010
Copyright C Heldref Publications
ISSN: 0883-2323
DOI: 10.1080/08832320903258592
Returns-Based Style Analysis: An Excel-Based
Classroom Exercise
John McDermott
Fairfield University, Fairfield, Connecticut, USA
W. Sharpe’s (1988, 1992) returns-based style analysis provides an excellent opportunity to use
a sophisticated portfolio-analysis tool in the classroom to help illustrate important topics in
investment and operations research courses. Students can perform classic returns-based style
analysis by creating a spreadsheet model and using the Solver add-in in Microsoft Excel.
The technique can also be used to supplement classroom units on performance measurement
and style drift in investment courses or to illustrate a finance application in an introductory
operations research course. An example analysis using a popular mutual fund is provided as
well as the accompanying Excel model.
Keywords: Analysis, Fund, Mutual fund, Performance, Style analysis
There are many methods available to financial analysts to are normally hired to manage a particular asset class (e.g.,
conduct a style analysis of a portfolio or mutual fund. Two U.S. Small value) in a portfolio. Style determination is also
potential methods are holdings-based style analysis popular- important in manager performance measurement when the
ized by Morningstar and Sharpe’s returns-based style analy- aim is to separate true alpha from beta. The selection of a
sis (RBSA). RBSA was introduced by Sharpe (1988, 1992) benchmark index is often based on style determination.
and is a powerful analytical tool that is used to capture the
style of a portfolio or mutual fund using only returns data.
Holdings-Based Style Analysis
Specifically, RBSA uses nonlinear optimization to construct
a portfolio of indices to minimize the tracking error with the In holdings-based style analysis, the actual holdings (e.g.,
portfolio being analyzed. RBSA is widely used and accepted individual stocks, mutual funds, exchange-traded funds
in the investment community and forms the basis for the pop- [ETFs]) in the portfolio are disaggregated and then classi-
ular investment analysis software Zephyr StyleADVISOR. fied into general categories based on asset classes, geogra-
The objective of this teaching note and the accompanying phy, or industry classification. Morningstar also classifies the
classroom exercise is to provide students with exposure to a portfolio into one of nine style boxes based on the portfolio’s
powerful analytical technique and also provide some work in general size (large cap, mid cap, small cap) and value–growth
building an Excel model and using the Solver add-in to con- orientation. Kaplan (2003) provided a detailed discussion of
duct nonlinear optimization. I use a well-known mutual fund, Morningstar’s style classification methodology.1
the Dodge and Cox Balanced Fund (DODBX), to illustrate A major drawback of holdings-based analysis is that an
the technique. individual or mutual fund’s holdings may vary, perhaps sig-
nificantly, through time. A snapshot of a portfolio’s holdings
one day, especially in the case of a portfolio comprised of
STYLE ANALYSIS
actively managed funds or individual stocks, may not be at
all representative of the history of the fund or of its holdings
Analysts and researchers may desire to determine the style of
in the future. Portfolio holdings are, in general, self-reported
a particular fund manager. The issue of style is particularly
and therefore subject to manipulation. For example, a port-
relevant in institutional money management when managers
folio manager may engage in window dressing, which is the
practice of altering the holdings just prior to reporting to
Correspondence should be addressed to John McDermott, Fairfield Uni-
make the portfolio look better to investors.2 In contrast with
versity, Finance Department, 1073 North Benson Road, Fairfield, CT 06824, self-reported holdings, realized returns are objective and ex-
USA. E-mail: jmcdermott@mail.fairfield.edu ternal, not subjective and internal.
2. 108 J. MCDERMOTT
The reported holdings of a portfolio may also lead to incor- to Minimize TE
rect conclusions about a portfolio’s true asset class exposure subject to
and the extent of its diversification. For example, consider
wi ≥ 0
a position in a large foreign-based multinational company n
i=1 wi = 1
(e.g., Honda Motor) that does a much of its business in the
United States and also trades as an American Depository
Receipt (ADR)on the New York Stock Exchange. Similarly, The constrained quadratic minimization described previ-
what about a large U.S. multinational (e.g., Exxon) that does ously is the essence of RBSA. The minimization can also
a much of its business internationally? What exactly is the be solved by numerical methods in a number of software
nature of these holdings in a portfolio? Holdings-based anal- programs including Solver in Excel.4
ysis is not and cannot be precise on this issue; it most likely To implement RBSA, the selected indices should ideally
would classify Honda as an international and Exxon as a be mutually exclusive (i.e., they do not overlap) and nearly
U.S. holding. The stock returns, however, may be telling a exhaustive5 (i.e., they cover the investable universe). The
very different story. RBSA is purposely agnostic to the de- popular indices I have used successfully are the following:6
bate about how a particular firm should be classified; it is
only interested in how the stock behaves in the context of Fixed Income Indices:
characterizing the overall portfolio’s returns. Citigroup 3-month T-Bill
Lehman U.S. Aggregate Bond
Returns-Based Style Analysis Lehman U.S. Corporate High Yield
Lehman Global (ex U.S.) Treasury
Given the potential shortcomings of holdings-based analysis,
the attention turns to returns-based style analysis. RBSA U.S. Equity Indices:
compares the returns of a stock portfolio or mutual fund Dow Wilshire Large Growth
against the returns of a tracking portfolio of indices that Dow Wilshire Large Value
represent the various equity and fixed income asset classes. Dow Wilshire Small Growth
The analysis defines a mix of the indices that would have best Dow Wilshire Small Value
explained the behavior of the returns of the portfolio being Dow Wilshire Micro Cap
analyzed. Technically speaking, RBSA determines a long- International Equity Indices:
only portfolio of mutually exclusive and exhaustive indices MSCI EAFE
that minimizes the variance of the tracking error relative to MSCI Emerging Markets
the portfolio being analyzed.
Beginning with the historical returns (typically the last 60 Normally, it is preferable to use at least the last 36 months
months) of a portfolio or mutual fund, I denote the client’s of returns data available to conduct the RBSA—obviously
portfolio total return in month t as Rt. Next, I choose a set of the need for a longer time horizon increases with the number
n mutually exclusive and exhaustive indices to create a port- of indices used in the analysis. Monthly returns data for
folio that as closely as possible mimics the client’s portfolio mutual funds and indices are available in many financial
returns. The monthly return on index i in period t is denoted databases and can also be obtained from public websites such
as Ii,t . as Yahoo Finance. Dow Wilshire Style Indices are available
The difference between the client’s portfolio returns and to download at www.wilshire.com.
the return on a mix of the n indices in month t is defined as
as εt . Further, the tracking error (TE) is defined as variance
AN ILLUSTRATION OF RETURNS-BASED
of this difference over the t time periods. Specifically,
STYLE ANALYSIS
εt = Rt − w1 I1,t + w2 I2,t + . . . . . . + wn In,t
T E = V ar [εt ] The DODBX is a very large7 actively managed mutual fund
where wi , equals the weight on index i. The term in brack- that was just recently reopened (in February 2008) to new
ets is return on a portfolio of the indices. The weights are investors.8 An excerpt from the holding-based analysis of
constrained to be nonnegative and to sum to 1.3 DODBX from Morningstar is shown in the Appendix.9 Morn-
ingstar classifies the fund’s U.S. equity holdings as large
wi ≥ 0 value and its fixed income holdings as high quality and inter-
n
i=1 wi = 1 mediate maturity. The DODBX is a large balanced fund with
It is important to choose the set of index weights so that the low turnover; I expect these characteristics to minimize the
tracking error between the portfolio and the mix of indices is differences between returns-based and holding-based analy-
as small as possible. Specifically, the problem is: ses in order to illustrate the legitimacy and power of RBSA
to infer style as well as equity and fixed income from returns
Choose wi for i = 1, n data only.
3. RETURNS-BASED STYLE ANALYSIS 109
FIGURE 1 Excel spreadsheet model set-up.
The Excel spreadsheet model set-up and Solver dialog The key to interpreting RBSA is to understand that the
box used to conduct the RBSA are presented in Figures 1 and provided mix of the indices creates a portfolio that most
2.10 Normally, I would provide the monthly returns data to closely tracks the analyzed portfolio; the technique, despite
my students in an Excel spreadsheet and have them structure its pedigree and sophistication, does not reveal the true allo-
the model, define the optimization in Solver, and interpret the cations! First, it is important to recognize that the precision of
results. The results of conducting the RBSA for the 60-month neither holdings-based analysis nor RBSA is perfect. RBSA
period January 2002 through December 2007 are presented looks at the average asset exposures over the course of the
in Figure 3.11 entire period of the analysis, whereas holdings-based pro-
The portfolio of indices generated by the RBSA is referred vides only a snapshot in time. In fact, we should not be
to as the custom benchmark. How well does the custom surprised to see that returns based in some cases provides a
benchmark track the DODBX? The answer is actually quite very different picture than holdings based. Differences be-
well. Figure 4 provides a comparison of growth of a dollar tween the returns and holdings-based style analyses can be
for the DODBX and the custom benchmark. Further, the R2 attributed to a variety of factors. Consider that the RBSA
of a simple linear regression of the fund’s monthly returns
on the custom benchmark’s monthly returns is 0.93.
FIGURE 3 Dodge and Cox Balanced Fund returns-based style analysis,
FIGURE 2 Solver dialog box. January 2002 to December 2007.
4. 110 J. MCDERMOTT
FIGURE 4 Growth of $1, January 2002 to December 2007.
FIGURE 5 Returns-based style analysis, a 36-month rolling analysis of the Dodge and Cox Balanced Fund.
5. RETURNS-BASED STYLE ANALYSIS 111
has no prior knowledge of the allocation by name; it is infer- International Equity
ring an allocation for the historical returns of the portfolio. In
In contrast to international equity, RBSA indicates the
some cases, the RBSA may attribute the influence of some of
U.S.equity position is much greater (i.e., 53.8% U.S.vs. 7.6%
the holdings in one category into another category, if the re-
International); the mutual fund exhibits zero exposure to
turns of those holdings behave more like the second category.
emerging markets and only 2.5% to international developed
Considering a portfolio comprised of entirely U.S. stocks, it
markets. Although the fund does hold some large interna-
might be surprising to see RBSA indicates an exposure to
tional developed market stocks (e.g., Sony, Sanofi-Aventis,
emerging markets. But on closer inspection, it is noticeable
Novartis) that trade as ADRs, RBSA evidences the fund as
that the U.S.holdings consist of several large multinational
overwhelmingly an investment in U.S.equity.
corporations with a significant presence in emerging markets
economies. For example, a RBSA of Exxon allocates 51% to
MSCI Emerging Markets Index in its custom benchmark.12 Performance Measurement
RBSA can provide insights into the true nature of a portfolio,
Sharpe (1988; 1992) suggested that the mean of the track-
insight that holdings-based analysis cannot. I now provide a
ing error can be used as a performance measure. Ter Horst,
brief interpretation of the RBSA of the DODBX by major
Nijman, and de Roon (2004) suggested the use of RBSA to
asset class.
predict future performance. Alternatively, it is possible to use
tracking portfolio as a customized benchmark and compute
Fixed Income alpha relative to the benchmark. Ben Dor, Budinger, Dynkin,
The DODBX’s fact sheetat www.dodgeandcox.com states: and Leech (2008) suggested the use of RBSA in construct-
ing performance benchmarks. In this case, the mean of the
The Fund primarily invests in a diversified portfolio of pri- tracking error is 4.62 bps (SD = 46.21 bps) per month (55.6
marily investment-grade fixed income securities, including: bps annualized). In comparison, the alpha of the fund relative
U.S. government obligations, mortgage and asset-backed se- to the customized benchmark is 60 bps (t = 0.73, df = 59).
curities, corporate bonds, collateralized mortgage obligations As previously mentioned, the R2 of the fund regressed on the
and others. To a lesser extent, the fund may also invest in be- customized benchmark is 0.93.
low investment-grade fixed income securities.
The RBSA presented in Figure 4 reveals, as expected, a Style Drift
high-quality and short-term bond strategy as the benchmark The classroom assignment could be extended to determine
portfolio allocates 27% to T-Bills, 9% to the Lehman Aggre- the extent of style drift in the portfolio or mutual fund.14 This
gate Index, 2% to Global Treasury bonds and no weight to could be accomplished by using subperiods and comparing
U.S. high-yield bonds. the results or by conducting rolling period analysis (e.g.,
The RBSA reveals the average equity–fixed income split using rolling 36-month windows) to examine the changes in
of the DODBX as 62–38. A holdings-based analysis or a weights over time. An example of a rolling-period analysis is
review of the fund’s prospectus would be obscure or even in- illustrated in Figure 5. The analysis reveals a fairly consistent
accurate on this point. For example, the fund literature states style over time.
only that “Under normal circumstances the Fund will hold
no more than 75% of its total assets in stocks.”13Although
as of June 30, 2007, the fund reported that it held 69.2% in
equities. CONCLUSION
U.S. Equity My example is a simple one by design. The DODBX strategy
is well known and its equity style has been consistent (i.e.,
The large weight (41.3%) on the DJ Wilshire Large Value U.S. Large Value) through time. The fund is very large, held
index in the custom benchmark reveals the equity side of the 84 different stocks on March 31, 2008, concentrated mostly
DODBX as primarily a U.S.Large Cap Value strategy. A look in the U.S., and its turnover is quite low (27%) for an actively
at the top 10 holdings of the fund as of March 31, 2008, lists managed fund. Therefore, I would expect a holdings-based
large U.S.companies such as Comcast, Wal-Mart, Hewlett- analysis to confirm the RBSA and it does, perhaps convinc-
Packard, confirming this finding. The RBSA also shows ex- ing the students of its validity and power. In contrast, con-
posure to U.S.Small Value (5.0%) and U.S.Microcap (7.5%). sider a complicated portfolio of stocks, bonds, ETFs, and
Note the weight on both U.S. Growth indices (Large and actively managed funds. Conducting a holdings-based anal-
Small Growth) are both zero in the style benchmark suggest- ysis is fraught with potential problems for more complicated
ing no or little exposure to this asset class. In sum, the RBSA and dynamic portfolios. It is precisely this situation in which
suggests the fund’s U.S.equity strategy has been primarily RBSA is most useful as a complement to holdings-based
large value and secondarily small value and microcap. analysis.15
6. 112 J. MCDERMOTT
I believe an introduction to RBSA has a place in upper- through 1000. The Dow Wilshire large-cap indices
level undergraduate course and introductory MBA courses contain the 750 largest stocks in the U.S., whereas
in investments, and certainly in courses in portfolio analy- small-cap indices capture stocks 751 through 2,500
sis. I have used the topic as part of a larger case study on and the microcap has 2,500 through approximately
performance evaluation in a senior-level undergraduate fi- 4,000.
nance capstone course. It could be, however, structured as 6. Thanks to Jim Davis of Dimensional Fund Advisors
a stand alone assignment on style analysis and performance for suggesting this set of indices.
measurement. For example, “Conduct a style analysis of Mu- 7. As of December 31, 2007, DODBX had over $28
tual Fund X using Sharpe’s returns-based style techniques. billion in assets.
Compare and contrast the results with Morningstar’s holding- 8. See www.dodgeandcox.com.
based style analysis” or “Construct a custom benchmark for 9. See www.morningstar.com.
Mutual Fund X using Sharpe’s returns-based style analysis. 10. Please contact the author for the Excel workbook.
How has the fund performed? Compare your result to a sin- 11. See Lobosco and Di Bartolomeo (1997) for calculat-
gle (or multi-) factor model alpha. To what do you attribute ing approximate confidence intervals.
the differences?” 12. A caution is necessary; the style benchmark can only
I believe the topic is also well suited to an introduc- explain about 41% of the variation in Exxon’s monthly
tory course in operations research to illustrate a real-world returns for the past five years ending in December
application of mathematics science tools, Excel modeling, 2007. This highlights the use of RBSA as a tool for
and the use of Solver to conduct nonlinear optimization. analyzing portfolios.
An assignment built on RBSA provides the students with 13. See www.dodgeandcox.com/balancedfund.asp
an opportunity to develop an Excel model to do sophis- 14. Chan, Chen, and Lakonishok (2002) analyze style
ticated quantitative analysis and to explore a widely ac- drift in mutual funds.
cepted tool in industry to complement holdings-based style 15. For example, Brown and Goetzmann (2001) used
analysis. RBSA in analyzing the performance of hedge funds.
NOTES REFERENCES
1. Available for download at: http://corporate. Ben Dor, A., Budinger, V., Dynkin, L., & K. Leech (2008). Constructing peer
morningstar.com/UK/html/pdf.htm?../documents/M- benchmarks for mutual funds: A style analysis-based approach. Journal
ethodologyDocuments/ResearchPapers/Holdings- of Portfolio Management, 34(2), 65–77.
Brown, S., & Goetzmann, W. (2001). Hedge funds with style (NBER Work-
basedAndReturns-basedStyleModels PK.pdf
ing Paper 8173). Cambridge, MA: National Bureau of Economic Re-
2. There is an extensive literature on window dress- search.
ing. Influential research includes Grinblatt and Tit- Chan, L., Chen H., & Lakonishok, J. (2003). On mutual fund investment
man (1993), Grinblatt, Titman, and Wermers (1995), styles (2002). Review of Financial Studies, 15, 1407–1437.
and Wermers (2002). Grinblatt, M., & Titman, S. (1993). Performance measurement without
benchmarks: An examination of mutual fund returns. Journal of Busi-
3. The nonnegativity constraint on the weights can be ness, 66(1), 47–68.
relaxed when appropriate. For example, when analyz- Grinblatt, M., Titman, S., & Wermers, R. (1995). Momentum investment
ing a portfolio that uses derivatives, short positions, strategies, portfolio performance, and herding: A study of mutual fund
or leverage. behavior. American Economic Review, 85, 1088–1105.
4. I find it instructive to run an ordinary least squares Kaplan, P. (2003, June). Holdings based and returns based style models.
New York: Morningstar Research.
(OLS) regression with the mutual fund’s monthly re- Lobosco, A., & Bartolomeo, D. (1997). Approximating the confidence inter-
turns as the dependant variable and the monthly re- vals for Sharpe style weights. Financial Analysts Journal, 53(4), 80–85.
turns of the indices as the independent variables. The Sharpe, W. (1988). Determining a fund’s effective asset mix. Investment
OLS results can be contrasted with the RBSA results Management Review, 2, 59–69.
specifically highlighting the natural interpretation of Sharpe, W. (1992). Asset allocation: Management style and performance
measurement. Journal of Portfolio Management, 18, 7–19.
the RBSA slopes as portfolio weights. Ter Horst, J., Nijman, T., & de Roon, F. (2004), Evaluating style analysis.
5. You may be wondering about U.S. midcap stocks. Journal of Empirical Finance, 11(1), 29–53.
They are split between the large and small-cap DJ Wermers, R. (2002). Mutual fund herding and the impact on stock prices.
Wilshire indices. S&P midcap indices use stocks 501 Journal of Finance, 54, 581–622.
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