This document provides an abstract for a paper that will be presented at the 12th Pacific Rim Real Estate Society Conference from January 22-25, 2006 in Auckland, New Zealand. The paper aims to examine the relationships between size and systematic downside risk and unsystematic downside risk for Malaysian property shares. While previous studies have looked at the relationship between size and risk using variance as a risk measure, this study uses the alternative measure of downside risk. The abstract outlines the concepts of systematic and unsystematic downside risk, reviews prior literature, and previews the methodology and findings of the research.
The document summarizes a five-factor asset pricing model that augments the Fama-French three-factor model by adding profitability and investment factors.
The five-factor model is tested using portfolios sorted on size, book-to-market equity ratio, profitability, and investment to produce spreads in average returns. The results show patterns in average returns related to size, value, profitability, and investment that the five-factor model seeks to capture. Specifically, small stocks and stocks with high book-to-market ratios, profitability, or low investment tend to have higher average returns. However, the model has difficulties explaining the low returns of some small, low-profitability stocks that invest heavily.
Dividend portfolio – multi-period performance of portfolio selection based so...Bogusz Jelinski
What will happen to your investment if you ignore change of share prices while calculating both returns and risk during stocks portfolio selection? Is it profitable in long term to
sell a share when its price has started to skyrocket?
An Empirical Investigation of Fama-French-Carhart Multifactor Model: UK Evidenceiosrjce
The study employs Fama-French-Carhart Multifactor Model to investigate the significance of Firm
Size, Book-to-Market ratio and Momentum in explaining variations in returns of stocks listed on the UK equity
market using monthly stock data of 100 randomly selected UK stocks from January 1996 to December 2013
collected from DataStream 5.0. The empirical results from the Ordinary Least Square (OLS) regression analysis
of the test of the multifactor model found firm size insignificant for three of the six portfolios formed; the value
factor (book-to-market ratio) significant for all the six portfolios while the momentum factor is significant for
the three portfolios with big market capitalization stocks. Overall, the empirical results indicate the presence of
value effect among small-cap and big-cap stocks and momentum effect among big-cap stocks in the London
Stock Exchange. Firm size is not found to be a reliable significant factor in explaining stock returns in the
equity market.
Portfolio Analysis in US stock market using Markowitz modelIJASCSE
This document discusses portfolio analysis in the US stock market using the Markowitz model. It provides details on the inputs required, such as expected returns, standard deviations, and correlation coefficients between securities. An example application is presented analyzing 10 stocks from different industries over 15 years. The results show the optimal allocation across stocks based on expected returns and risks. Limitations of the mean-variance optimization approach are also noted.
Property all risk and business interruption training 1Afrianto Budi
1. The document discusses key aspects of an intermediate level all risks property insurance policy, including policy wordings, coverage details, exclusions, and claims procedures.
2. It addresses topics like different methods of determining sums insured, clauses that impact value, industrial special risk extensions, and case studies.
3. The document also provides explanations of policy conditions such as deductibles, reasonable precautions, inspection rights, subrogation, and dispute resolution options.
This document presents a detailed flowchart on the process of property development in Malaysia, from land purchase application to construction to delivery of the property to purchasers.
This document summarizes the key points of the article "Risk, Return, and Equilibrium: Empirical Tests" by Eugene F. Fama and James D. MacBeth. The article tests the relationship between average stock returns and risk using the two-parameter portfolio model. It finds that the data is consistent with investors holding efficient portfolios as the model predicts, and that stock prices fully reflect available information as implied by an efficient market. Specifically:
1) Regressions of stock returns on measures of risk find a linear relationship between risk and return as the model implies, with higher risk associated with higher return.
2) The risk measures used capture risk completely and no other risk factors are needed.
This document reviews literature on studies of mutual fund performance in the United States. It discusses seminal works that developed modern portfolio theory and the Capital Asset Pricing Model (CAPM), including works by Markowitz, Sharpe, Lintner, Treynor, Jensen, and others. The document also summarizes various studies that have examined the relationship between mutual fund performance and cash inflows, with mixed and generally insignificant results. It notes limitations of these studies, including small sample sizes and the ambiguity of measuring performance based on different market indexes.
The document summarizes a five-factor asset pricing model that augments the Fama-French three-factor model by adding profitability and investment factors.
The five-factor model is tested using portfolios sorted on size, book-to-market equity ratio, profitability, and investment to produce spreads in average returns. The results show patterns in average returns related to size, value, profitability, and investment that the five-factor model seeks to capture. Specifically, small stocks and stocks with high book-to-market ratios, profitability, or low investment tend to have higher average returns. However, the model has difficulties explaining the low returns of some small, low-profitability stocks that invest heavily.
Dividend portfolio – multi-period performance of portfolio selection based so...Bogusz Jelinski
What will happen to your investment if you ignore change of share prices while calculating both returns and risk during stocks portfolio selection? Is it profitable in long term to
sell a share when its price has started to skyrocket?
An Empirical Investigation of Fama-French-Carhart Multifactor Model: UK Evidenceiosrjce
The study employs Fama-French-Carhart Multifactor Model to investigate the significance of Firm
Size, Book-to-Market ratio and Momentum in explaining variations in returns of stocks listed on the UK equity
market using monthly stock data of 100 randomly selected UK stocks from January 1996 to December 2013
collected from DataStream 5.0. The empirical results from the Ordinary Least Square (OLS) regression analysis
of the test of the multifactor model found firm size insignificant for three of the six portfolios formed; the value
factor (book-to-market ratio) significant for all the six portfolios while the momentum factor is significant for
the three portfolios with big market capitalization stocks. Overall, the empirical results indicate the presence of
value effect among small-cap and big-cap stocks and momentum effect among big-cap stocks in the London
Stock Exchange. Firm size is not found to be a reliable significant factor in explaining stock returns in the
equity market.
Portfolio Analysis in US stock market using Markowitz modelIJASCSE
This document discusses portfolio analysis in the US stock market using the Markowitz model. It provides details on the inputs required, such as expected returns, standard deviations, and correlation coefficients between securities. An example application is presented analyzing 10 stocks from different industries over 15 years. The results show the optimal allocation across stocks based on expected returns and risks. Limitations of the mean-variance optimization approach are also noted.
Property all risk and business interruption training 1Afrianto Budi
1. The document discusses key aspects of an intermediate level all risks property insurance policy, including policy wordings, coverage details, exclusions, and claims procedures.
2. It addresses topics like different methods of determining sums insured, clauses that impact value, industrial special risk extensions, and case studies.
3. The document also provides explanations of policy conditions such as deductibles, reasonable precautions, inspection rights, subrogation, and dispute resolution options.
This document presents a detailed flowchart on the process of property development in Malaysia, from land purchase application to construction to delivery of the property to purchasers.
This document summarizes the key points of the article "Risk, Return, and Equilibrium: Empirical Tests" by Eugene F. Fama and James D. MacBeth. The article tests the relationship between average stock returns and risk using the two-parameter portfolio model. It finds that the data is consistent with investors holding efficient portfolios as the model predicts, and that stock prices fully reflect available information as implied by an efficient market. Specifically:
1) Regressions of stock returns on measures of risk find a linear relationship between risk and return as the model implies, with higher risk associated with higher return.
2) The risk measures used capture risk completely and no other risk factors are needed.
This document reviews literature on studies of mutual fund performance in the United States. It discusses seminal works that developed modern portfolio theory and the Capital Asset Pricing Model (CAPM), including works by Markowitz, Sharpe, Lintner, Treynor, Jensen, and others. The document also summarizes various studies that have examined the relationship between mutual fund performance and cash inflows, with mixed and generally insignificant results. It notes limitations of these studies, including small sample sizes and the ambiguity of measuring performance based on different market indexes.
Optimal Risky Asset Proportion in the Presence of correlated Background RriskTakafumi SHIRATORI
This study derives the optimal investment proportion for financial assets in the presence of background risk by maximization of expected utility in a single period framework. To simplify the problem, I assume that there exist only two financial assets, one risky and one risk free. The optimal proportion says that she should increase her exposure to financial risky asset when financial risky asset and background risk is negatively correlated. This paper is the first analysis to derive this surprising result. Under such a situation, to increase exposure to financial risky asset is optimal even if there exists background risk.
I obtained Master of Business Administration of Waseda University Graduated School with this study in 2012. I researched under Dr. Masayuki Ikeda.
Systemic and Systematic risk - Monica Billio, Massimiliano Caporin, Roberto Panzica, Loriana Pelizzon
SYRTO Code Workshop
Workshop on Systemic Risk Policy Issues for SYRTO (Bundesbank-ECB-ESRB)
Head Office of Deustche Bundesbank, Guest House
Frankfurt am Main - July, 2 2014
This document discusses a study on expected shortfall as a risk measure in a multi-currency environment. It begins with an introduction and literature review on expected shortfall and value-at-risk as risk measures. It discusses the advantages of expected shortfall over value-at-risk, including that it is coherent and accounts for the magnitude of losses. The document then reviews literature on risk measures in multiple currencies and discusses how expected shortfall can vary depending on the currency used for aggregation. It proposes to model expected shortfall in multiple currencies and examine the implications of currency choice and composition of risk-free assets on risk measurement.
Capital asset pricing model (capm) evidence from nigeriaAlexander Decker
This document summarizes a research study that tested the predictions of the Capital Asset Pricing Model (CAPM) using stock return data from the Nigerian stock exchange from 2007 to 2010. The study combined individual stocks into portfolios to enhance the precision of estimates. The results did not support CAPM's predictions that higher risk (higher beta) is associated with higher returns. The study also found that the slope of the Security Market Line did not equal the excess market return, further invalidating CAPM predictions for the Nigerian market. The document provides context on CAPM theory and reviews prior empirical studies that have also found poor support for CAPM predictions.
Measuring and allocating portfolio risk capital in the real worldAlexander Decker
This document discusses measuring and allocating portfolio risk capital using value-at-risk and expected shortfall. Daily stock price data from the London Stock Exchange over 3 years was used to calculate the risk measures for portfolios in different sectors. The risk capital required for each stock was determined using a fair allocation principle. The results showed that stocks with higher average returns and lower volatility required less risk capital. The portfolios with the lowest quantified risk amounts were mining, media, financial services, banks and the top 10 FTSE companies portfolios.
The document summarizes the capital asset pricing model (CAPM) and reviews early empirical tests of the model. It begins by outlining the logic and key assumptions of the CAPM, including that the market portfolio must be mean-variance efficient. However, empirical tests found problems with the CAPM's predictions about the relationship between expected returns and market betas. Specifically, cross-sectional regressions did not find intercepts equal to the risk-free rate or slopes equal to the expected market premium. To address measurement error, later tests examined portfolios rather than individual assets. In general, the early empirical evidence revealed shortcomings in the CAPM's ability to explain returns.
PROBLEMS IN SELECTION OF SECURITY PORTFOLIOS THE PERFORMANDaliaCulbertson719
PROBLEMS IN SELECTION OF SECURITY PORTFOLIOS
THE PERFORMANCE OF MUTUAL FUNDS IN THE PERIOD 1945-1964
MICHAEL C. JENSEN*
I. INTRODUCTION
A CENTRAL PROBLEM IN FINANCE (and especially portfolio management) has
been that of evaluating the "performance" of portfolios of risky investments.
The concept of portfolio "performance" has at least two distinct dimensions:
1) The ability of the portfolio manager or security analyst to increase re-
turns on the portfolio through successful prediction of future security
prices, and
2) The ability of the portfolio manager to minimize (through "efficient"
diversification) the amount of "insurable risk" born by the holders of
the portfolio.
The major difficulty encountered in attempting to evaluate the performance
of a portfolio in these two dimensions has been the lack of a thorough under-
standing of the nature and measurement of "risk." Evidence seems to indicate
a predominance of risk aversion in the capital markets, and as long as in-
vestors correctly perceive the "riskiness" of various assets this implies that
"risky" assets must on average yield higher returns than less "risky" assets.'
Hence in evaluating the "performance" of portfolios the effects of differential
degrees of risk on the returns of those portfolios must be taken into account.
Recent developments in the theory of the pricing of capital assets by
Sharpe [20], Lintner [15] and Treynor [25] allow us to formulate explicit
measures of a portfolio's performance in each of the dimensions outlined
above. These measures are derived and discussed in detail in Jensen [11].
However, we shall confine our attention here only to the problem of evaluating
a portfolio manager's predictive ability-that is his ability to earn returns
through successful prediction of security prices which are higher than those
which we could expect given the level of riskiness of his portfolio. The founda-
tions of the model and the properties of the performance measure suggested
here (which is somewhat different than that proposed in [11]) are discussed
in Section II. The model is illustrated in Section III by an application of it
to the evaluation of the performance of 115 open end mutual funds in the
period 1945-1964.
A number of people in the past have attempted to evaluate the performance
of portfolios2 (primarily mutual funds), but almost all of these authors have
* University of Rochester College of Business. This paper has benefited from comments and
criticisms by G. Benston, E. Fama, J. Keilson, H. Weingartner, and especially M. Scholes.
1. Assuming, of course, that investors' expectations are on average correct.
2. See for example [2, 3, 7, 8, 9, 10, 21, 24].
389
390 The Journal of Finance
relied heavily on relative measures of performance when what we really need
is an absolute measure of performance. That is, they have relied mainly on
procedures for ranking portfolios. For example, if there are two por ...
Traditional Risk Assessments use "heat maps", or risk matrices, to develop rankings, leading to decision making on projects, operations. Risks are ranked from larger to lower, sometimes splitting them into three or more classes of criticality.
Those approaches may be complaint with ISO31000, ONR49000, COSO, but they are not the best you can do!
As we will show in this paper, they actually lack in focus and transparency. Ingenious methods allow to reuse those data, however, and make far better decisions based on rational and sustainable rankings.
This document is an MSc finance dissertation written by XULI XIAO and supervised by Dr. Alexandra Dias. It examines applying copula theory to estimate value at risk (VaR) of a portfolio composed of Hong Kong and Taiwan market indices. Specifically, it models the marginal distributions of the index returns using ARMA-GARCH and fits various copula models including Gaussian, Gumbel, and Clayton copulas to capture the dependence structure. One-step ahead VaR is estimated using the copula-based models and backtested, finding that the models underestimate VaR during the Asian financial crisis period likely due to regime shift in the data.
The document discusses Value at Risk (VaR), a metric used to measure and manage financial risk. It provides an introduction to VaR and outlines several key concepts, including: reasons for VaR's widespread adoption; calculating VaR for single and multiple assets; assumptions underlying VaR calculations; and approaches to estimating VaR for linear and non-linear derivatives. It also covers converting daily VaR to other time periods, factors affecting portfolio risk, and stress testing as a complement to VaR analysis.
This document discusses Value at Risk (VaR) and related concepts over multiple learning outcomes (LOs). It introduces VaR and explains why it was widely adopted as a risk measure. It also defines how to calculate VaR for single and multiple assets, and how to convert between time periods. The document discusses assumptions of VaR calculations and reasons for using continuously compounded returns. It also addresses factors that affect portfolio risk and how to calculate VaR for linear and non-linear derivatives. Finally, it introduces cash flow at risk (CFaR) and how VaR and CFaR can be used to evaluate projects and allocate risk.
Questions and Answers At Least 75 Words each.Please answer th.docxmakdul
Questions and Answers: At Least 75 Words each.
Please answer the following questions.
1. What are the differences and similarities between samples and populations?
2. What are the measures of Central Tendency assumptions?
3. What are measures of Dispersion used for and what are the assumptions for each?
4. Define collaboration and how you will apply it in Statistics? (100 Words)
The Capital Asset Pricing Model:
Theory and Evidence
Eugene F. Fama and Kenneth R. French
T he capital asset pricing model (CAPM) of William Sharpe (1964) and JohnLintner (1965) marks the birth of asset pricing theory (resulting in aNobel Prize for Sharpe in 1990). Four decades later, the CAPM is still
widely used in applications, such as estimating the cost of capital for firms and
evaluating the performance of managed portfolios. It is the centerpiece of MBA
investment courses. Indeed, it is often the only asset pricing model taught in these
courses.1
The attraction of the CAPM is that it offers powerful and intuitively pleasing
predictions about how to measure risk and the relation between expected return
and risk. Unfortunately, the empirical record of the model is poor—poor enough
to invalidate the way it is used in applications. The CAPM’s empirical problems may
reflect theoretical failings, the result of many simplifying assumptions. But they may
also be caused by difficulties in implementing valid tests of the model. For example,
the CAPM says that the risk of a stock should be measured relative to a compre-
hensive “market portfolio” that in principle can include not just traded financial
assets, but also consumer durables, real estate and human capital. Even if we take
a narrow view of the model and limit its purview to traded financial assets, is it
1 Although every asset pricing model is a capital asset pricing model, the finance profession reserves the
acronym CAPM for the specific model of Sharpe (1964), Lintner (1965) and Black (1972) discussed
here. Thus, throughout the paper we refer to the Sharpe-Lintner-Black model as the CAPM.
y Eugene F. Fama is Robert R. McCormick Distinguished Service Professor of Finance,
Graduate School of Business, University of Chicago, Chicago, Illinois. Kenneth R. French is
Carl E. and Catherine M. Heidt Professor of Finance, Tuck School of Business, Dartmouth
College, Hanover, New Hampshire. Their e-mail addresses are �[email protected]
edu� and �[email protected]�, respectively.
Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004 —Pages 25– 46
legitimate to limit further the market portfolio to U.S. common stocks (a typical
choice), or should the market be expanded to include bonds, and other financial
assets, perhaps around the world? In the end, we argue that whether the model’s
problems reflect weaknesses in the theory or in its empirical implementation, the
failure of the CAPM in empirical tests implies that most applications of the model
are invalid.
We begin by outlining the logic of t ...
This document summarizes the capital asset pricing model (CAPM). It begins by outlining the logic and key assumptions of the CAPM, including that all investors hold the same market portfolio which must lie on the efficient frontier. It then states that the CAPM predicts the expected return of an asset is determined by its beta, or non-diversifiable risk relative to the market. However, the document notes that empirical tests have found the CAPM performs poorly in applications. It concludes the CAPM's failings indicate applications based on the model are invalid, challenging researchers to develop alternative models.
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Mean-variance analysis is used to identify optimal portfolios based on expected returns, variances, and covariances of asset returns. The minimum-variance frontier shows the efficient combinations of expected return and risk. The efficient frontier begins with the global minimum-variance portfolio and provides the maximum expected return for a given level of variance. The capital market line describes combinations of the risk-free asset and market portfolio. The capital asset pricing model expresses expected returns as a linear function of systematic risk measured by beta.
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Adrian, Crump, Vogt - Nonlinearity and Flight-to-Safety in the Risk-Return Tradeoff for Stocks and Bonds (wp at https://www.newyorkfed.org/research/staff_reports/sr723.html )
This document discusses a model for analyzing how network connectivity impacts asset returns and risks. The model augments a traditional multi-factor model to account for systemic links between assets represented by a network connectivity matrix. The model shows that network links inflate asset loadings to common factors, impacting expected returns and total risk decomposition into systematic and idiosyncratic components. Greater network connectivity reduces diversification benefits by slowing the decrease in portfolio idiosyncratic risk as the number of assets increases. The authors propose extending the model to incorporate heterogeneous asset responses to links and time-varying network structures.
The document summarizes a study on modeling risk aggregation and sensitivity analysis for economic capital at banks. It finds that different risk aggregation methodologies, such as historical bootstrap, normal approximation, and copula models, produce significantly different economic capital estimates ranging from 10% to 60% differences. The empirical copula approach tends to be the most conservative while normal approximation is the least conservative. The results indicate banks should take a conservative approach to quantify integrated risk and consider the impact of methodology choice and parameter uncertainty on economic capital estimates.
The document discusses capital asset pricing theory and arbitrage pricing theory. It summarizes the CAPM model and its assumptions, including that an asset's required rate of return is linearly related to its beta value. It also discusses the security market line and empirical tests of CAPM. The document then summarizes arbitrage pricing theory, including its assumptions and the arbitrage pricing equation. It notes that APT is more general than CAPM but lacks consistency in measurements. Finally, it summarizes the Sharpe index model and Markowitz portfolio theory, including calculations for portfolio return, risk, proportions and the efficient frontier.
Bba 2204 fin mgt week 8 risk and returnStephen Ong
This document discusses risk and return in financial management. It provides learning goals related to understanding risk, return, and risk preferences. It defines risk as the uncertainty of returns from an investment and return as the total gain from an investment. It discusses measuring the risk of single assets using scenarios, probabilities, standard deviation, and the coefficient of variation. It also introduces the concept of measuring the risk and return of a portfolio by considering the correlation between assets.
Nicotinergic impact on focal and non focal neuroplasticity induced by non-inv...merzak emerzak
This study investigated the effects of nicotine on neuroplasticity induced by non-invasive brain stimulation techniques. 48 healthy non-smokers received either nicotine or placebo patches combined with transcranial direct current stimulation (tDCS) or paired associative stimulation (PAS) applied to the motor cortex. Motor evoked potentials were measured as an indicator of corticospinal excitability. Nicotine abolished or reduced inhibitory neuroplasticity induced by both tDCS and PAS, but only slightly prolonged facilitatory plasticity induced by PAS. Thus, nicotine influences plasticity differently than global cholinergic enhancement, demonstrating discernible effects of activating nicotinic receptors.
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PROBLEMS IN SELECTION OF SECURITY PORTFOLIOS THE PERFORMANDaliaCulbertson719
PROBLEMS IN SELECTION OF SECURITY PORTFOLIOS
THE PERFORMANCE OF MUTUAL FUNDS IN THE PERIOD 1945-1964
MICHAEL C. JENSEN*
I. INTRODUCTION
A CENTRAL PROBLEM IN FINANCE (and especially portfolio management) has
been that of evaluating the "performance" of portfolios of risky investments.
The concept of portfolio "performance" has at least two distinct dimensions:
1) The ability of the portfolio manager or security analyst to increase re-
turns on the portfolio through successful prediction of future security
prices, and
2) The ability of the portfolio manager to minimize (through "efficient"
diversification) the amount of "insurable risk" born by the holders of
the portfolio.
The major difficulty encountered in attempting to evaluate the performance
of a portfolio in these two dimensions has been the lack of a thorough under-
standing of the nature and measurement of "risk." Evidence seems to indicate
a predominance of risk aversion in the capital markets, and as long as in-
vestors correctly perceive the "riskiness" of various assets this implies that
"risky" assets must on average yield higher returns than less "risky" assets.'
Hence in evaluating the "performance" of portfolios the effects of differential
degrees of risk on the returns of those portfolios must be taken into account.
Recent developments in the theory of the pricing of capital assets by
Sharpe [20], Lintner [15] and Treynor [25] allow us to formulate explicit
measures of a portfolio's performance in each of the dimensions outlined
above. These measures are derived and discussed in detail in Jensen [11].
However, we shall confine our attention here only to the problem of evaluating
a portfolio manager's predictive ability-that is his ability to earn returns
through successful prediction of security prices which are higher than those
which we could expect given the level of riskiness of his portfolio. The founda-
tions of the model and the properties of the performance measure suggested
here (which is somewhat different than that proposed in [11]) are discussed
in Section II. The model is illustrated in Section III by an application of it
to the evaluation of the performance of 115 open end mutual funds in the
period 1945-1964.
A number of people in the past have attempted to evaluate the performance
of portfolios2 (primarily mutual funds), but almost all of these authors have
* University of Rochester College of Business. This paper has benefited from comments and
criticisms by G. Benston, E. Fama, J. Keilson, H. Weingartner, and especially M. Scholes.
1. Assuming, of course, that investors' expectations are on average correct.
2. See for example [2, 3, 7, 8, 9, 10, 21, 24].
389
390 The Journal of Finance
relied heavily on relative measures of performance when what we really need
is an absolute measure of performance. That is, they have relied mainly on
procedures for ranking portfolios. For example, if there are two por ...
Traditional Risk Assessments use "heat maps", or risk matrices, to develop rankings, leading to decision making on projects, operations. Risks are ranked from larger to lower, sometimes splitting them into three or more classes of criticality.
Those approaches may be complaint with ISO31000, ONR49000, COSO, but they are not the best you can do!
As we will show in this paper, they actually lack in focus and transparency. Ingenious methods allow to reuse those data, however, and make far better decisions based on rational and sustainable rankings.
This document is an MSc finance dissertation written by XULI XIAO and supervised by Dr. Alexandra Dias. It examines applying copula theory to estimate value at risk (VaR) of a portfolio composed of Hong Kong and Taiwan market indices. Specifically, it models the marginal distributions of the index returns using ARMA-GARCH and fits various copula models including Gaussian, Gumbel, and Clayton copulas to capture the dependence structure. One-step ahead VaR is estimated using the copula-based models and backtested, finding that the models underestimate VaR during the Asian financial crisis period likely due to regime shift in the data.
The document discusses Value at Risk (VaR), a metric used to measure and manage financial risk. It provides an introduction to VaR and outlines several key concepts, including: reasons for VaR's widespread adoption; calculating VaR for single and multiple assets; assumptions underlying VaR calculations; and approaches to estimating VaR for linear and non-linear derivatives. It also covers converting daily VaR to other time periods, factors affecting portfolio risk, and stress testing as a complement to VaR analysis.
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Questions and Answers At Least 75 Words each.Please answer th.docxmakdul
Questions and Answers: At Least 75 Words each.
Please answer the following questions.
1. What are the differences and similarities between samples and populations?
2. What are the measures of Central Tendency assumptions?
3. What are measures of Dispersion used for and what are the assumptions for each?
4. Define collaboration and how you will apply it in Statistics? (100 Words)
The Capital Asset Pricing Model:
Theory and Evidence
Eugene F. Fama and Kenneth R. French
T he capital asset pricing model (CAPM) of William Sharpe (1964) and JohnLintner (1965) marks the birth of asset pricing theory (resulting in aNobel Prize for Sharpe in 1990). Four decades later, the CAPM is still
widely used in applications, such as estimating the cost of capital for firms and
evaluating the performance of managed portfolios. It is the centerpiece of MBA
investment courses. Indeed, it is often the only asset pricing model taught in these
courses.1
The attraction of the CAPM is that it offers powerful and intuitively pleasing
predictions about how to measure risk and the relation between expected return
and risk. Unfortunately, the empirical record of the model is poor—poor enough
to invalidate the way it is used in applications. The CAPM’s empirical problems may
reflect theoretical failings, the result of many simplifying assumptions. But they may
also be caused by difficulties in implementing valid tests of the model. For example,
the CAPM says that the risk of a stock should be measured relative to a compre-
hensive “market portfolio” that in principle can include not just traded financial
assets, but also consumer durables, real estate and human capital. Even if we take
a narrow view of the model and limit its purview to traded financial assets, is it
1 Although every asset pricing model is a capital asset pricing model, the finance profession reserves the
acronym CAPM for the specific model of Sharpe (1964), Lintner (1965) and Black (1972) discussed
here. Thus, throughout the paper we refer to the Sharpe-Lintner-Black model as the CAPM.
y Eugene F. Fama is Robert R. McCormick Distinguished Service Professor of Finance,
Graduate School of Business, University of Chicago, Chicago, Illinois. Kenneth R. French is
Carl E. and Catherine M. Heidt Professor of Finance, Tuck School of Business, Dartmouth
College, Hanover, New Hampshire. Their e-mail addresses are �[email protected]
edu� and �[email protected]�, respectively.
Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004 —Pages 25– 46
legitimate to limit further the market portfolio to U.S. common stocks (a typical
choice), or should the market be expanded to include bonds, and other financial
assets, perhaps around the world? In the end, we argue that whether the model’s
problems reflect weaknesses in the theory or in its empirical implementation, the
failure of the CAPM in empirical tests implies that most applications of the model
are invalid.
We begin by outlining the logic of t ...
This document summarizes the capital asset pricing model (CAPM). It begins by outlining the logic and key assumptions of the CAPM, including that all investors hold the same market portfolio which must lie on the efficient frontier. It then states that the CAPM predicts the expected return of an asset is determined by its beta, or non-diversifiable risk relative to the market. However, the document notes that empirical tests have found the CAPM performs poorly in applications. It concludes the CAPM's failings indicate applications based on the model are invalid, challenging researchers to develop alternative models.
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1. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
An Exploration of the Relationship between Size and Risk in a
Downside Risk Framework Applied to Malaysian Property Shares
PACIFIC RIM REAL ESTATE SOCIETY (PRRES) CONFERENCE
AUCKLAND NEW ZEALAND
Chyi Lin Lee, Jon Robinson and Richard Reed
c.lee27@pgrad.unimelb.edu.au; jrwr@unimelb.edu.au and r.reed@unimelb.edu.au
Faculty of Architecture, Building and Planning
The University of Melbourne
Melbourne 3010, Australia
Abstract
The relationship between size and risk (systematic and unsystematic risk) has received
considerable attention in recent literature. However, these studies employ variance as the
risk measure, which the appropriateness for using this risk measure is always questioned
by researchers and practitioners due to its underlying strict assumptions. Therefore, there
is crucial to adopt an alternative risk measure for ascertaining the relationships. The aim
of the study is to examine the relationships between size and systematic downside risk
and unsystematic downside risk in line with the theoretical sound of this risk measure.
The empirical evidences reveal that the size is strongly correlated with unsystematic
downside risk. While, there is a weak inverse relationship between size and systematic
downside risk.
Keywords: systematic downside risk, unsystematic downside risk, size, property shares
1. Introduction
Since the introduction of Modern Portfolio Theory by Markowitz (1952), diversification
has become the main issue for investors, particularly institutional investors, in making
investment decisions. Consequently, Sharpe (1963) proposed a linear model that provides
a better understanding for investors on risk and diversification in which the total risk of
asset i is decomposed into systematic risk and unsystematic risk. Systematic risk is an
undiversifiable risk, which is attributed with a common factor. On the other hand,
unsystematic risk is a diversifiable risk, which is also known as specific risk and it can be
totally eliminated via a well diversified portfolio (Brown & Matysiak, 2000, Hargitay &
Yu, 1993).
Recently, there have been many attempts to demonstrate the relationship between size
and risk. For instance, Conover et al. (1998) found that differences between large firms
and small firms in terms of return and risk are statistically significant. Litt et al. (1999)
1
2. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
provided a plausible explanation for this scenario, which revealed that size has a
moderate negative correlation with unsystematic risk. This is consistent with findings by
Byrne & Lee (2003), Chaudhry et al. (2004) and Malkiel & Xu (1997), who they found a
negative relationship between size and specific risk.
Conversely, Gyuorko & Nelling (1996) found a positive and statistically significant
relationship between size and systematic risk. Byrne & Lee (2003) also found a positive
and statistically significant relationship between size and systematic risk. Interestingly,
this relationship became weak and negative when investment characteristics were
controlled. Similarly, Litt et al. (1999) also found a weak negative correlation between
beta and size.
Therefore, there is no consensus for a relationship between size and systematic risk. One
of the possible explanations is that these studies employ variance as the risk measure.
Variance is currently the most widely used measure of portfolio risk and it has received
the considerable attention from researchers and practitioners (Evans, 2004). But the use
of variance as a risk measure is constrained by several strict assumptions: investors have
a constant quadratic utility function and asset return distributions are normally distributed.
Many finance and real estate literature have rejected both assumptions (Lee et al., 2005).
A survey conducted by Mao (1970) reported that investors are more concerned about the
probability of return being lower than a target rate of return. In other words, investors
dislike downside volatility and the main concern for most investors is downside risk,
which is the likelihood of returns falling below a target rate of return (Byrne & Lee,
2004). Markowitz (1959) also recognised the importance of this argument and suggested
the use of semi-variance, or lower partial moment, which is more appealing than variance.
As a result, downside risk appears to be a more robust and sensible risk measure than
variance; it is suggested that it used in portfolio analysis (Lee et al., 2005).
The appropriateness of using downside risk was also demonstrated by Hogan & Warren
(1974) and Bawa & Linderberg (1977). They generalised the downside risk (lower partial
moment) into the Capital Asset Pricing Model (CAPM) and developed a mean-lower
partial moment capital asset pricing model (D-CAPM). Nantell & Price (1979) and Price
et al., (1982) examined the difference between the systematic risks that are derived in a
downside risk framework and a mean variance framework. Their findings depicted that
systematic risk in a downside risk framework differs from systematic risk in a mean
variance framework if the return distributions are in lognormal form.
A growing body of research has also demonstrated the superiority of systematic downside
risk than traditional systematic risk. These studies also suggested the use of downside
beta (systematic downside risk) as an alternative for traditional beta in portfolio
management (Bhardwaj & Brooks, 1993, Cheng, 2005, Chiang et al., 2004, Conover et
al., 2000, Estrada, 2000, 2002, Harlow & Rao, 1989).
However, there is limited literature about the relationship between size and downside risk.
Devaney & Lee (2005) probably conducted the first study that examined the relationship
2
3. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
between real estate portfolio size and downside risk. Their study replaced variance by
downside risk due to the hypothesis that the risk for a fund manager is the risk of
underperformance of the benchmark rather than the volatility of returns of the portfolio.
They used Monte Carlo simulation and the returns from 1728 properties over the period
1995-2004 in the Investment Property Databank (IPD) database. The results indicated
that the increase in portfolio size reduced the portfolio’s downside risk (total risk).
Importantly, to date, there is no study of the implications of size in reducing systematic
risk and unsystematic risk in a downside risk framework.
The aim of this study is to examine the relationship between size and risk (systematic and
unsystematic risks) in a downside risk framework. In Sections 2 and 3, the concept of
systematic downside risk and unsystematic downside risk are provided. Section 4
discusses the data and then introduces the methodology used in this study. The next
section empirically tests the relationship between size and systematic risk and
unsystematic risk in a downside risk framework. Section 6 summarises the findings and
provides a conclusion.
2. The Concept of Systematic Downside Risk
In the Mean Variance Analysis framework, Sharpe (1964) proposed that the expected
return of asset i in CAPM is estimated as:
E ( Ri ) = R f +
COV ( Ri , Rm )
(E ( Rm − R f )) (1)
Var ( Rm )
where COV (Ri , Rm ) = Covariance of returns on the market portfolio with returns on
security i
E ( Ri ) = Expected return on asset i
E ( Rm ) = Expected return on the market portfolio
Var ( Rm ) = Variance of returns on the market portfolio
Rf = Risk free rate of return
usually simplified and presented as follow:
E ( Ri ) = R f + β i (E ( Rm − R f ) ) (2)
where β i is the beta, which is computed by using COV (Ri , Rm ) / Var ( Rm ) .1
In the downside risk framework, semivariance is used as the risk measure. Bawa &
Linderberg (1977), Harlow & Rao (1989) and Hogan & Warren (1974) generalised
1
See Elton & Gruber (1995) and Estrada (2002) for the details of beta computation.
3
4. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
downside risk into CAPM and proposed that the expected return of the asset i in Mean
Lower Partial CAPM (or D-CAPM) is estimated from the following:
(E ( R − R f ))
CVS R f ( Ri , Rm )
E ( Ri ) = R f + m (3)
SV R f ( Rm )
where CVS R f (Ri , Rm ) = Cosemivariance of returns on the market portfolio with
returns on security i
SVR f ( Rm ) = Semivariance of returns below R f on the market portfolio
CVS R f (Ri , Rm )
= Downside Beta ( β i )
D
SV R f ( Rm )
The expected return of the asset i in Equations (1) and (3) is computed in exactly in the
same way in both frameworks except for the estimation of beta. As such, beta in the
downside risk framework is defined as CVS R f ( Ri , Rm ) / SVR f ( Rm ) and Equation (3) can
be simplified as follows:
E ( Ri ) = R f + β i
D
(E ( R m − R f )) (4)
where β i is the downside beta.
D
However, Estrada (2002) highlighted the limitations of the existing estimation of
downside beta, which Bawa & Linderberg (1977), Harlow & Rao (1989) and Hogan &
Warren (1974) defined as co-semivariance as follows:
[
CVS R f ( Ri , Rm ) = E{(Ri − R f ).Min (RM − R f ),0 } ] (5)
Clearly, Equation (5) is in asymmetry form. Thus, the cosemivariance between two assets
i and M is different from the cosemivariance between asset M and i (Estrada, 2000,
2002, Lee et al., 2005, Nawrocki, 1992). As a result, Estrada (2002) proposed a
replacement of the CAPM beta by the ratio below (in symmetric form) in order to obviate
the limitations of the Equation (5):
E{Min[(Ri − µ i )]Min[(RM − µ M ),0]}
βi D =
{
E Min[(RM − µ M ),0]
2
} (6)
where Ri is return of asset i at the time t , µ i denotes the risk free rate or the rate of
return of benchmark.
4
5. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
3. The Concept of Unsystematic Downside Risk
One of the essential properties of CAPM is to facilitate risk decomposition and
quantification in which total risk can be decomposed into two orthogonal components: a
market risk and firm-specific residual. A time-series regression for CAPM is as follows:
Ri − R f = α i + β i ( R M − R f ) + ε i (7)
where Ri = return of asset i at the time t , R f = risk-free rate, α i = non-index related
return to asset i , β i = beta of asset i , RM = return to market index at the time t , ε i =
residual return of asset i at the time t .
Taking the variance of both sides; the variance of returns on asset i is shown as:
Var ( Ri ) = β i Var ( RM ) + Var (ε i )
2
(8)
where Var ( Ri ) is the variance of the asset i , Var (ε i ) is volatility measure for
unsystematic risk.2
As discussed above, the computation of CAPM and D-CAPM are the exactly same
except for beta. Therefore, the unsystematic downside risk can also be estimated by
amending Equation (8) in which total risk is substituted by total downside risk; beta is
changed to downside beta; variance of the market portfolio is replaced by semivariance
of the market portfolio and unsystematic risk is substituted by unsystematic downside
risk. The relationships between total downside risk, systematic downside risk and
unsystematic downside risk are written as follow:
D2
SVR f ( Ri ) = β i SVR f ( Rm ) + SVR f (ε i ) (9)
Where SVR f ( Ri ) = Total Downside Risk (Semivariance)
SVR f ( Rm ) = Semivariance of market portfolio
SVR f (ei ) = Unsystematic downside risk
4. Data and Methodology
4.1 Data
In this study, annual returns from Malaysian Property Shares (PSs) were utilised. As at
31st December 2003, there were 90 property companies listed on Bursa Malaysia
(formerly known as Kuala Lumpur Stock Exchange). From which 30 listed property
2
See Beckers (1996), Chaudhry et al. (2004) and Sanders et al. (2001) for the details.
5
6. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
shares have been selected in this study. The analysis spans the 1992-2003 time period in
which covers the boom (1993) and recession (1997) phases of the most recent property
shares cycle in Malaysia.
It must be noted that Bursa Malaysia experienced highly speculative activity in 1993; the
daily turnover surged to RM4.8 billion on 22 December 1993 (Central Bank of Malaysia,
1994b). There was a steep rise in share prices due to the speculative activities (Central
Bank of Malaysia, 1994a). In addition, the monthly returns for most PSs in 1993 were
exceptionally high, for example, the monthly return of AHPLANT in October 1993 at
117.54%. This affected the stabilisation of the money market and the exchange rate
(Department of Valuation and Property Services Malaysia, 1994). Hence, annual data is
utilised in this study in order to avoid the biasing effect of the speculation period for the
stock market in 1993 and better reflect the true potential performance of PSs.
Additionally, market capitalisations of individual PSs were employed as indicators of size
and Property Stock Index was used as the market benchmark. All of these data were
obtained from Bursa Malaysia. 3-month Treasury Bill (TB) was used as the risk-free rate,
which was obtained from Central Bank of Malaysia.
4.2 Methodology
As discussed above, the rationale of using variance is doubtful if the asset return
distributions are not symmetrically or normally distributed. As such, it is crucial to
examine the asset return distribution to establish whether return is normally or
asymmetrically distributed.
Several tests can be used in order to examine the normality of asset return distributions.
In this study, skewness, kurtosis and Jera-Bera Test were used for examining the PSs
return distributions. This is consistent with the methodology of Brown & Matysiak (2000)
and Kishore (2004).
Skewness
Skewness characterises the degree of asymmetry of a distribution around its mean. Zero
skewness indicates the distribution is symmetry. Whereas, positive skewness indicates a
distribution with an asymmetric tail extending toward right. Conversely, negative
skewness indicates a distribution with an asymmetric tail extending toward left.
Skewness is computed as follow:
1 T ( Ri − R) 3
S= ∑ σ3
T − 1 i =1
(10)
where Ri is the return for asset i , R is the mean return of asset i , σ is the standard
deviation of asset i and T is total number of returns.
6
7. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
Kurtosis
Kurtosis describes the degree of flatness or peakedness of an asset return distribution.
Kurtosis is estimated from the following:
1 T ( Ri − R) 4
K= ∑ σ4
T − 1 i =1
(11)
where Ri is the return for asset i , R is the mean return of asset i , σ is the standard
deviation of asset i and T is total number of returns.
Jarque-Bera Test
Jarque & Bera (1980, 1987) proposed a combination of skewness and kurtosis (is also
known as the Jarque-Bera Test) in order to examine the normality of a distribution. The
Jarque-Bera statistic is computed as follow:
n ⎡ 2 ( K − 3) 2 ⎤
JB = ⎢S + ⎥ (12)
6⎣ 4 ⎦
where S is a measure of skewness, K is a measure of kurtosis and n is the sample size.
The Jarque-Bera statistic has a chi-squared distribution with two degrees of freedom (one
for skewness, one for kurtosis).
4.3 Downside Risk
The downside risk (total risk) can be estimated by Lower Partial Moment, which is
defined by Bawa (1975) and Fishburn (1977):
τ
LPM α (τ , Ri ) = ∫ (τ − R)
α
dF ( R )
−∞
1 T
= ∑ [ Max(0, (τ − Rit ))]α
T − 1 t =1
(13)
where dF (R ) is the cumulative distribution function of the investment return R, τ is the
target return, α is the degree of the LPM, Ri is the return of asset i and T is total
number of returns.
Notably, semi-variance is a special case of the more general LPM in which the α value
is equal to 2. Thus, it can also be referred to as a target semi-variance (Harlow, 1991). In
this study, the degree of the LPM is equal to 2 in order to estimate the semivariance.
Furthermore, the τ , target rate is set as the risk-free rate.
7
8. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
4.4 Regression Model
In this study, two regression models were employed in order to ascertain the relationship
between size and systematic downside risk and unsystematic downside risk. Both
systematic downside risk and unsystematic downside risk are regressed against size. The
regression models are estimated as follows:
Log ( SystematicDownsideRisk ) = α + β i Log ( Size) + ei (14)
Log (UnsystematicDownsideRisk ) = α + β i Log ( Size) + ei (15)
where systematic downside risk ( β Di ) and unsystematic downside risk are derived from
Equation (6) and Equation (9) respectively, size is the actual size of the PSs; α , β i and
ei are estimated from the models.
5. Results and Analysis
5.1 The Distribution of the Asset
Table 1 reveals the distribution of different size groups (Small, Medium and Large) from
1992 to 2003. In general, all different PSs size groups exhibited positive skewness.
Interestingly, all individual PSs also displayed a positive skewness except SIMEPTY (-
0.04) and FIMACORP (0).3
It is not surprising that no size group revealed a kurtosis with 3; while all size groups
displayed a kurtosis of more than 3 (leptokurtosis). The heterogeneity in kurtosis was also
apparent; the Medium group showed 6.94 kurtosis; while the Large group exhibited 4.70
kurtosis. It is more noticeable for individual PSs, for example, PTGTIN had 9.37 kurtosis
whereas SIMIPTY revealed -0.71 kurtosis.
Consistently, all size groups were statistically significant in the Jarque-Bera Test. As a
result, the assumption that these size groups are normally distributed should be rejected
by the Jarque-Bera test. Surprisingly, all individual PSs were asymmetrically distributed
except FBO (1.54), SPB (2.07), BRAYA (2.74), PARAMOUNT (3.80), CRIMSON
(3.91), IGB (4.02), FIMACORP (4.60), BOLTON (4.66) and IOI (5.86).
These results are consistent with the results for developed real estate markets such as
United States (U.S.), United Kingdom (U.K.) and Australia where return distributions of
real estate (including securitised and unsecuritised real estate) are not necessarily
3
See Appendix 1 for the details of individual PSs.
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9. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
normally distributed (Graff et al., 1997, Kishore, 2004, Maitland-Smith & Brooks, 1999,
Myer & Webb, 1993, 1994, Peng, 2005, Young & Graff, 1995). In line with this, the
assumption of Mean Variance Analysis and the rationale of using variance as risk
measure are questionable.
Table 1: The Distribution of Assets (1992-2003)
Group(s)/Asset(s) Skewness Kurtosis Jarque-Bera Test
Small 1.94 5.49 17.12*
Medium 2.45 6.94 24.07*
Large 1.66 4.70 17.14*
Note: (*) significant at 5% level
5.2 Risk Analysis
According to the Figure 1, the volatilities of assets were substantially lower when
downside risk was employed. The semi deviations of all size groups were only 1/3 of the
standard deviations for corresponding size groups. These results are consistent with the
results of Peng (2005), Sing & Ong (2000) and Sivitanides (1998) in which the variance
(standard deviation) is higher significantly than the downside risk for Australian Listed
Property Trusts, Singapore real estate and U.S. REITs respectively.
Another point must be noticed is the Large group (80.42%) has a smaller volatility
compared to Medium (97.30%) and Small (103.84%). Similarly in the downside risk
framework, the semi deviation of the Large group was 29.39%, which was lower than
Medium (29.82%) and Small (34.77%). In other words, the Large PSs have lower risk
compared to smaller PSs. These results are consistent with the results from Gyourko &
Nelling (2003) for standard deviation and Devaney & Lee (2005) for semi-deviation
(total downside risk).
Figure 1: Standard Deviation and Semi-Deviation for Different Size Groups
Standard De viation and Semi-Dev iation for
Differe nt Size Groups
120.00% 97.30% 103.24%
100.00% 80.42%
Risk(%)
80.00%
Standard Deviation
60.00%
29.39% 29.82% 34.77% Semi Deviation
40.00%
20.00%
0.00%
Large Medium Small
Size Group
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10. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
5.3 Performance Analysis
Table 2 presents the performance analysis of PSs in different size groups from 1992 to
2003. Over this 12-year period, the average return of Large group (24.23%) was slightly
higher than Medium (22.61%) and Small (20.96%).
However, average return cannot simply be used for ranking purposes without pondering
risk. As a result, in this study, risk-adjusted return was used for this purpose and the risk-
adjusted returns were calculated using the Sharpe Ratio and the Sortino Ratio.4 Using the
Sharpe Ratio, it was shown that the Large group was the best performer group compared
to the Small and Medium groups on a risk-adjusted basis. Conversely, the Sortino Ratio
provided contradictory results, which the Medium group achieved the highest risk-
adjusted performance while the Small group was the worst performer.
Thus, the results from Sharpe Ratio and Sortino Ratio are always contradictory. This can
be attributed to different risk measures are employed by both ratios. Additionally, this is
consistent with the results from Ellis & Wilson (2005) and Stevenson (2001), which
Sharpe Ratio and Sortino Ratio exhibit diverge results.
Table 2: Performance Analysis (1992-2003)
Asset Average Return Sharpe Ratio Sortino Ratio
(%)
Small 20.96 0.2347 (2) 0.6970 (3)
Medium 22.61 0.2324 (3) 0.7582 (1)
Large 24.23 0.2606 (1) 0.7130 (2)
Note: Figures in parenthesis are risk-adjusted ranking.
5.4 The Downside Beta and Unsystematic Downside Risk
Table 3 presents the downside beta (systematic downside risk) and unsystematic
downside risk of PSs. The downside beta for the small size group was 1.13. This
indicates that when market return falls by 1%, this group will fall by 1.13%. Thus,
magnifying by 13% the downside swings in the market with respect to the risk free rate.
Conversely, the downside betas for Medium and Large size groups were 0.93 and 0.96
respectively. In other words, on average, both groups will fall only 0.95% with a 1% fall
in the market. Another important observation is that there is no obvious relationship
between downside beta and size. Moreover, the downside beta for various size groups did
not vary noticeably.
However, the impact of size was found affect unsystematic downside risk. The Large size
group has the lowest unsystematic downside risk (1.38%), which was around half of the
4
Sharpe Ratio employs standard deviation as the risk measure and can be estimated as: Sharpe Ratio =
(return of asset i at the time t – the risk-free rate)/standard deviation of asset i at the time t. Whereas Sortino
Ratio utilises semi deviation as the risk measure and is computed as: Sortino Ratio = (return of asset i at the
time t – the risk-free rate)/semi deviation of asset i at the time t.
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11. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
Small group (2.18%). While, the systematic downside risk for Medium group was 1.79%.
The overall picture that emerges from Table 3 is that Large PSs have a lower
unsystematic risk, but there is no similar noticeable evidence for the downside beta. The
importance of size to downside beta and unsystematic downside risk reduction are still
vague. Hence, it is essential to investigate this issue in more depth.
Table 3: Downside Beta and Unsystematic Downside Risk
Asset Downside Beta Unsystematic
Downside Risk (%)
Small 1.13 2.18
Medium 0.93 1.79
Large 0.96 1.38
5.5 The Relationship between Size and Risk (Downside Beta and Unsystematic
Downside Risk)
Table 4 illustrates the empirical relationship between size and risk. Consistent with the
results from the previous section, the regression model depicted that downside beta has
an insignificant negative relationship with size. In other words, the Large PSs have only a
slightly lower systematic downside beta. There is no considerable reduction in systematic
downside risk for investors by investing in Large PSs. This confirms the assertions of
CAPM in which only unsystematic risk can be eliminated and affected by size. Moreover,
this is also consistent with results from Litt et al. (1999) for U.S. REITs and Byrne & Lee
(2003) for U.K. property funds by controlling the investment characteristics. But, it
counters the findings from Gyuorko & Nelling (1996), which is analysed with Mean
Variance Analysis framework.
On the other hand, size has a significant negative correlation with the unsystematic
downside risk (-0.3219). This indicates that doubling the size of the PSs will lead to a
significant reduction in unsystematic downside risk of just over 32%. In other words, the
smaller PSs have larger unsystematic downside risk. This is consistent with the
contentions of CAPM and findings from Byrne & Lee (2003), Chaudhry et al. (2004),
Litt et al. (1999) and Malkiel & Xu (1997), which are analysed under the Mean Variance
Analysis framework.
Interestingly, the size coefficients for downside beta and unsystematic downside risk are
quite close with the size coefficients for beta and unsystematic risk that were found by
Litt et al. (1999) for U.S. REITs. One of the possible explanations is they employed the
Risk-Adjusted Model for their estimation.5
5
Litt et al. (1999) reported that the size coefficients with NAREIT Beta and firm-specific risk were -0.41
and -0.16 respectively.
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12. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
Table 4: The Empirical Relationship between Size and Risk
Variable Log(Downside Beta) Log(Unsystematic
Downside Risk)
Constant 1.002 0.8524
(0.9597) (2.2647)
Log(Size) -0.1191 -0.3219
(0.1113) (0.2627)
R-square 3.93% 5.09%
Note: Figures in parenthesis are Standard Errors.
6. Conclusions and Implications
This paper investigates the relationship between size and risk (systematic risk and
unsystematic risk) in a downside risk framework. Several important findings can be
drawn from the analyses. First, the Malaysian PSs return distributions are like other real
estate (securitised and unsecuritised real estate) in developed markets; they are not
necessarily normally distributed. As such, the rationale of using variance as the risk
measure is precluded if the return distributions are in asymmetric form and it strengthens
the motivation to use downside risk, particularly for emerging markets.
Second, the variance (standard deviation) exhibits higher risk for investors. This can be
attributed to the inclusion of upside potential in risk estimation under the Mean Variance
Analysis framework, which is not logical. It is not surprising that the risk of Malaysian
PSs, as an emerging market, is over-estimated considerably by using variance. In line
with this, downside risk is suggested to be used as a risk measure particularly for
emerging markets.
Third, size is negatively correlated to the unsystematic risk, while there is no similar
evidence for systematic risk in a downside risk framework. This supports the assertions
of CAPM in which investors only can diversify their unsystematic risk through size
investment strategy but would not gain any systematic downside risk reduction via this
strategy. In other words, portfolio fund managers and investors can only gain the full
unsystematic downside risk diversification benefit by investing in Large Market
Capitalisation PSs.
This probably is the first study to explore the relationship between size and risk
(systematic risk and unsystematic risk) in a downside risk framework in a real estate
context and future work is needed to confirm the relationship. Future research should be
directed to improving the model by employing more factors. Larger samples should be
employed to help researchers to more accurately assess the relationship between size and
systematic risk and unsystematic risk in a downside risk framework.
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13. 12th Pacific Rim Real Estate Society Conference 22-25 January 2006
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