Risk and Return
o The General Concept
§ Higher expected return requires higher risk to take in mutual funds.
§ With a complete certainty, the assets will be risk free.
§ As a degree of uncertainty increase, the expected return must also higher.
§ Intuitively investors would require a higher expected return in exchange for accepting higher risk for that particular stock or bonds or mutual funds.
§ But generally investors are risk-averse
o Volatility as a Proxy for Risk
§ Volatility is a measure of risk.
§ The amount of an assets‘s return varies through successive time periods.
§ Volatility used to call as a standard deviation of return.
§ More fluctuate the return of assets, give a greater risk.
§ Greater volatility → the potential future values of more volatile assets span a much wider range.
o Diversification and Systematic Risk
§ By diversification investors can minimize volatility
§ Only one stock, it moves simultaneously
§ More differs the stocks we have, the simultaneous moves reduce and it will reduce the volatility or the risk
§ Volatility can be reduced by spreading the same amount of money across the multiple assets → Systematic Risk → cannot be diversified away
§ This concept is called the Modern Portfolio Theory
§ Unsystematic Risk → risk that uncontrollable → can be diversified away
§ Because it has zero return, it affecting the volatility, but it can be reduced by adding more diversified portfolio
o Beta as a Measure of Systematic Risk
§ Assets exhibits both Systematic and Unsystematic Risk
§ Systematic Risk → measured by degree which its return vary relative to those of the overall market → parameter called beta
§
§ rA is the return of assets; rM is the return of the market; σ2M is the variance of the return of the market; cov(rA , rM) is covariance between the return of the market and the return of the assets
§ To determine beta → average the individual securities’ betas, weighted by the market capitalization of each security
CAPM
o Key Assumptions Drive the Formulation of the Model
§ CAPM or Capital Asset Pricing Model → quantify the relationship between beta of an assets and its corresponding expected return
§ First assumption → investors only cares about expected return and volatility → they will maximize expected return for any level of expected volatility
§ Second Assumption → investors still believe the risk and return trade off in the market
§ Third assumption → only one risk factor is common to broad-based market portfolio → and categorize as Systematic Risk
§ CAPM → if beta known, it is possible to calculate the corresponding expected return
o Logic of the Model
§ First → consider about Unsystematic Risk → categorize as risk-free rate → rf
§ Second → consider an assets that has the expected return movement inline with market movements → beta =1 → E(rA) = E(rM)
§ Last → consider an assets that has the expected return experience the bigger swings compare to market movements → beta > 1 → E(rA) > E(rM)
§ CAPM formula → E(rA) = rf + βA ( E(rM) – rf )
§ (E(rM)–rf) → Equity Risk Premium → excess return beyond the risk-free rate
§ Beta is ration between Expected return from market and the expected return from the assets
§ Beta 1.5 means that if the risk-free rate given is 10%, so the expected return of the stock will be 1.5 x 10% = 15%
o CAPM as a Tool to Evaluate Fund Managers
§ CAPM can be used also to evaluate the performance of active fund managers
§ Managers tend to predict higher return than predict the risk include
§ If realized return > predicted return → adding investment value
§ Challenge for managers is to make higher expected return in the same level of risk or even lowering the risk
§ Excess return or “α” (alpha) can used to evaluate the manager’s performance
§ If α > 0 this portfolio would lie above the SML and vice versa
o Regression Analysis
§ First Take monthly return for the stock for significant period of time
§ Second Return of overall market
§ Finally Risk-Free return on the overall market
§ rA = rf + βA ( rM – rf ) + α → rA - rf = βA ( rM – rf ) + α
o Critic of the CAPM
§ CAPM model not totally correct → questionable
§ Some other risk factors that affecting the return does not include in CAPM
o Additional Factors Increase Predictive Power
§ A bunch of risk that not include in CAPM, include bankruptcy risk, currency risk, supplier risk
§ The addition of independent variables to regression often improves the explanatory power of the model
§ That’s why some people believe that CAPM not objective enough to see the expected return because some risk factors dose not include
Fama and French and the Three Factor Model
o Size and Value Factors Create Additional Explanatory Power
§ Size and Value is two most important factors outside the market risk that can explain better to the real expected return
o The SMB and HML Factors
§ The SMB Factor → Small Minus Big
Ø Design to measure the additional return investors have historically received by invest in stocks with relatively small capitalization → Size Premium
§ The HML Factor → High Minus Low
Ø Design to measure the “value Premium” provided to investors for investing in companies with high book-to-market values
o Constructing the Three Factor Model
§ rA = rf + βA ( rM – rf ) + SASMB + hAHML
§ SA measure the level of exposure to size risk
§ HA measures the level of exposure to value risk
o SMB and HML Provide Added Descriptive Dimensions for Riskiness
§ Investors can choose to weight their portfolios such as have greater or lesser exposure to each of the specific risk factors
o Categorizing funds with the Three Factor Model
§ Classifying Funds into Style Buckets
§ Specifying Risk Factor Exposure Informs Investor Choice
o Multivariate Regression and Evaluating Managers with the Three Factor Model
§
o Fund Evaluation (Practice) – Legg Mason (Using CAPM)
o Fund Evaluation (Practice) – Legg Mason (Using the Three Factor Model)
o The General Concept
§ Higher expected return requires higher risk to take in mutual funds.
§ With a complete certainty, the assets will be risk free.
§ As a degree of uncertainty increase, the expected return must also higher.
§ Intuitively investors would require a higher expected return in exchange for accepting higher risk for that particular stock or bonds or mutual funds.
§ But generally investors are risk-averse
o Volatility as a Proxy for Risk
§ Volatility is a measure of risk.
§ The amount of an assets‘s return varies through successive time periods.
§ Volatility used to call as a standard deviation of return.
§ More fluctuate the return of assets, give a greater risk.
§ Greater volatility → the potential future values of more volatile assets span a much wider range.
o Diversification and Systematic Risk
§ By diversification investors can minimize volatility
§ Only one stock, it moves simultaneously
§ More differs the stocks we have, the simultaneous moves reduce and it will reduce the volatility or the risk
§ Volatility can be reduced by spreading the same amount of money across the multiple assets → Systematic Risk → cannot be diversified away
§ This concept is called the Modern Portfolio Theory
§ Unsystematic Risk → risk that uncontrollable → can be diversified away
§ Because it has zero return, it affecting the volatility, but it can be reduced by adding more diversified portfolio
o Beta as a Measure of Systematic Risk
§ Assets exhibits both Systematic and Unsystematic Risk
§ Systematic Risk → measured by degree which its return vary relative to those of the overall market → parameter called beta
§
§ rA is the return of assets; rM is the return of the market; σ2M is the variance of the return of the market; cov(rA , rM) is covariance between the return of the market and the return of the assets
§ To determine beta → average the individual securities’ betas, weighted by the market capitalization of each security
CAPM
o Key Assumptions Drive the Formulation of the Model
§ CAPM or Capital Asset Pricing Model → quantify the relationship between beta of an assets and its corresponding expected return
§ First assumption → investors only cares about expected return and volatility → they will maximize expected return for any level of expected volatility
§ Second Assumption → investors still believe the risk and return trade off in the market
§ Third assumption → only one risk factor is common to broad-based market portfolio → and categorize as Systematic Risk
§ CAPM → if beta known, it is possible to calculate the corresponding expected return
o Logic of the Model
§ First → consider about Unsystematic Risk → categorize as risk-free rate → rf
§ Second → consider an assets that has the expected return movement inline with market movements → beta =1 → E(rA) = E(rM)
§ Last → consider an assets that has the expected return experience the bigger swings compare to market movements → beta > 1 → E(rA) > E(rM)
§ CAPM formula → E(rA) = rf + βA ( E(rM) – rf )
§ (E(rM)–rf) → Equity Risk Premium → excess return beyond the risk-free rate
§ Beta is ration between Expected return from market and the expected return from the assets
§ Beta 1.5 means that if the risk-free rate given is 10%, so the expected return of the stock will be 1.5 x 10% = 15%
o CAPM as a Tool to Evaluate Fund Managers
§ CAPM can be used also to evaluate the performance of active fund managers
§ Managers tend to predict higher return than predict the risk include
§ If realized return > predicted return → adding investment value
§ Challenge for managers is to make higher expected return in the same level of risk or even lowering the risk
§ Excess return or “α” (alpha) can used to evaluate the manager’s performance
§ If α > 0 this portfolio would lie above the SML and vice versa
o Regression Analysis
§ First Take monthly return for the stock for significant period of time
§ Second Return of overall market
§ Finally Risk-Free return on the overall market
§ rA = rf + βA ( rM – rf ) + α → rA - rf = βA ( rM – rf ) + α
o Critic of the CAPM
§ CAPM model not totally correct → questionable
§ Some other risk factors that affecting the return does not include in CAPM
o Additional Factors Increase Predictive Power
§ A bunch of risk that not include in CAPM, include bankruptcy risk, currency risk, supplier risk
§ The addition of independent variables to regression often improves the explanatory power of the model
§ That’s why some people believe that CAPM not objective enough to see the expected return because some risk factors dose not include
Fama and French and the Three Factor Model
o Size and Value Factors Create Additional Explanatory Power
§ Size and Value is two most important factors outside the market risk that can explain better to the real expected return
o The SMB and HML Factors
§ The SMB Factor → Small Minus Big
Ø Design to measure the additional return investors have historically received by invest in stocks with relatively small capitalization → Size Premium
§ The HML Factor → High Minus Low
Ø Design to measure the “value Premium” provided to investors for investing in companies with high book-to-market values
o Constructing the Three Factor Model
§ rA = rf + βA ( rM – rf ) + SASMB + hAHML
§ SA measure the level of exposure to size risk
§ HA measures the level of exposure to value risk
o SMB and HML Provide Added Descriptive Dimensions for Riskiness
§ Investors can choose to weight their portfolios such as have greater or lesser exposure to each of the specific risk factors
o Categorizing funds with the Three Factor Model
§ Classifying Funds into Style Buckets
§ Specifying Risk Factor Exposure Informs Investor Choice
o Multivariate Regression and Evaluating Managers with the Three Factor Model
§
o Fund Evaluation (Practice) – Legg Mason (Using CAPM)
o Fund Evaluation (Practice) – Legg Mason (Using the Three Factor Model)
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