Understanding Risk and Return, the CAPM, and the Fama-French Three-Factor Model

1. Risk and Return
a. The General Concept
§ Higher expected returns require taking higher risk
§ Uncertainty ↑ - return required to justify the risk ↑ - investors’ willingness to invest ↓
§ Investor willing to sacrifice some return to reduce the risk
b. Volatility as a Proxy for Risk
§ Widely accepted measure of risk (standard deviation of risk)
§ Amount of asset’s varies through successive time period
§ Greater volatility → future values of volatile assets span a much wider range
c. Diversification and Systematic Risk
§ Individual stock’s volatility in and of itself
§ Holding two stocks → won’t experience extreme
§ Assets do not move in lock step with one another → volatility can be reduced without reducing expected returns
§ Volatility reduced by the addition of more assets to a portfolio → unsystematic risk
d. Beta as a measure of Systematic Risk
§ Systematic risk → measured by the degree to which its returns vary relative to those of the overall market
§ Beta → measure of the risk contribution of an individual security to a well diversified portfolio
§ Determining Beta → average the individual securities betas, weighted by the market capitalization of each security

2. CAPM
a. Key Assumptions Drive the Formulation of the Model
§ CAPM → quantify the relationship between the beta of an asset and its corresponding expected return
§ Assumptions:
1. Investors care only about expected returns and volatility
2. Investors have homogeneous beliefs about the risk/reward tradeoffs in the market
3. Only a risk factor is common to a broad-based market portfolio
§ If securities’ beta is known, it is possible to calculate expected returns
b. Logic of The Model: Developing Intuition
§ Consider assets has no volatility, no risk, its return do not vary with the market → Beta = 0, expected return = risk-free rate
§ Consider assets that has Beta = 1 → E(rA) = E(rM)
§ Consider assets that has Beta > 1, expect this asset to earn more return as compensation of this extra risk
§ CAPM → E(rA) = rf + ßA(E(rM) – rf)
c. The CAPM as a Tool to Evaluate Fund Managers
§ Active fund managers select stocks in portfolio based on research and informed opinions
§ Realized return > predicted return on CAPM → adding value
§ Realized return < predicted return on CAPM → just collecting fees, no investment value
§ Managers to increase expected returns → invest in positions that embody greater systematic risk
§ Difference between realized return and predicted retun on CAPM is excess return (ά)
§ ά positive, managers’ work is good
d. Regression Analysis: A Tool for Employing the CAPM
§ We need three time series of data:
1. Returns for the stocks whose beta we are calculating for a significant period of time
2. Returns on the overall market index in the same period
3. Risk free returns for the same period
§ rA = rf + ßA(rM – rf) + ά
§ We can regress the excess market return ↔excess portfolio return
e. Critique of the CAPM
§ Several key criticms:
1. CAPM true predict power is questionable
a. R2 measure only 0.85, which the maximum is 1
b. 15% of the variation is still unexplainable
2. The simplicity of CAPM’s assumption of a single risk factor explaining expected returns is still questionable
§ The predictive and explanatory power of the CAPM is bound by the structure of the model
f. Additional Factors Increase Predictive Power
§ Risk factors facing companies today: market risk, bankruptcy risk, currency risk, etc
§ Model with more than one risk give more descriptive and predictive model

3. Fama and French and Three Factor Model
a. Size and Value Factors Create Additional Explanatory Power
§ Value and size → most significant factors (besides market risks) → explaining the realized returns of publicity traded stocks

§ Two factors to represent these risks:
1. SMB to address size risk
2. HML to address value risk
b. The SMB and HML Factors
§ SMB Factor: Accounting for the Size Premium
1. Small Minus Big → measure the additional return investors have historically received by investing in stocks of companies with relatively small market capitalization
2. Average return for the smallest 30% of stocks minus average return of the largest 30% of stocks in that month
3. Positive SMB → small caps stocks outperformed large caps stocks
§ HML Factor
1. High Minus Low → measure the value premium provided to investors for investing in companies with high book-to-market values (B/M)
2. Average return for the 50% of stocks with the highest B/M ratio minus average return of 50% of stocks with the lowest B/M ratio
3. Positive HML → value stocks outperformed growth stocks
c. Interpretations of the Factors
§ SMB and HML factors first drew attention and continue to be the most commonly used simply
§ For SMB → small companies logically should be expected to be more sensitive to many risk factors → undiversified nature
§ For HML → companies need to reach a minimum size in order to execute an Initial public Offering
d. Constructing the Three Factor Model
§ Fama French Three Factor Model → describes the expected return on an asset as a result of its relationship to three risk factors: market risk, size risk, and value risk
§ rA = rf + ßA(rM – rf) + sASMB + hAHML
e. SMB and HML Provide Added descriptive Dimensions for Riskiness
§ Primary implications → investors can choose to weight their portfolios such that they have greater or lesser exposure to each risk factors → can target more precisely different levels of expected returns
f. Categorizing Funds with the Three Factor Model
§ Compelling feature → it provides a way to categorize mutual funds by the size and value risks to which its portfolio is exposed as a result of assets held
§ Two main benefits:
1. Classifying funds into style buckets
a. Compare managers → placing them in broad buckets based on the style of asset allocation they choose
b. The Morningstar (the biggest resource for mutual fund) classification of fund is often different with what the fund claims as its official strategy
2. Specifying risk factor exposure informs investor choice
a. Investors can effectively choose the amount to which they are exposed to each risk factor when investing in particular funds
g. Multivariate Regression and Evaluating Managers with the Three Factor Model
· Five time series needed:
1. Return for the stock whose beta we are calculating for a significant period of time
2. Returns on the overall market index for the same period
3. Risk free returns for the same period
4. Calculated SMB and HML for each months
§ rA – rf = ά + ßA(rM – rf) +sASMB + hAHML
§ Positive measure of alpha → the mutual fund manager is adding value to the portfolio
§ Benefits of regression with Three factor model:
1. Explain much more of the variation observed in realized returns → R2 ≥0.95
2. It exposes the fact that the positive alpha observed in CAPM regression model merely a result of exposure to either HML or SMB factors, rather than actual manager performance
h. Fund Evaluation in Practice (1) – Legg Mason (CAPM)
§ Legg Mason Value Prim fund returned 27.3% > market only 21.6
§ Evaluate funds manager: ά = 0.46%, ß = 0.93
§ CAPM only consider one-dimensional market risk → the realized returns must come from either the fund’s exposure to market risk, or the value added by the manager
§ Manager was able to add 46 basis points to the fund’s return on the monthly basis or about 5.5% per year above the return expected from a portfolio with beta of .93
T-statistic associated with alpha is 2.37, means that achieving returns without skill would be extremely unlikely probabilistic
i. Fund Evaluation in Practice (2) – Legg Mason Revisited (Three Factor Model)
§ Coefficient results: ά = 0.22, ß = 0.99, sA = 0.36, hA = 0.22
§ Manager was only able to add 22 basis points on a monthly basis
§ The high return associated with the fund’s exposure to size and value risk rather than the skill of the manager