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Understanding Asset Pricing Models: CAPM & Portfolio Performance

Explore CAPM relationship between risk and return, SML, beta analysis, assessing portfolio performance, limitations of models. Learn about multifactor pricing models, estimating beta, APT, Fama-French Three Factor Model, and new behavioral approaches to asset pricing.

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Understanding Asset Pricing Models: CAPM & Portfolio Performance

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  1. Investments: Analysis and Behavior Chapter 5- Asset Pricing Theory and Performance Evaluation

  2. Learning Objectives • Know the theory and application of the CAPM. • Learn multifactor pricing models. • Realize the limitations of asset pricing models. • Assess the performance of a portfolio. • Compute alpha, Sharpe, and Treynor measures

  3. Capital Asset Pricing Model (CAPM) • Elegant theory of the relationship between risk and return • Used for asset pricing • Risk evaluation • Assessing portfolio performance • William Sharpe won the Nobel Prize in Economics in 1990 • Empirical record is poor

  4. CAPM Basic Assumptions • Investors hold efficient portfolios—higher expected returns involve higher risk. • Unlimited borrowing and lending is possible at the risk-free rate. • Investors have homogenous expectations. • There is a one-period time horizon. • Investments are infinitely divisible. • No taxes or transaction costs exist. • Inflation is fully anticipated. • Capital markets are in equilibrium. Examine CAPM as an extension to portfolio theory:

  5. The Equation of the CML is: • Y = b + mX This leads to the Security Market Line (SML)

  6. SML: risk-return trade-off for individual securities • Individual securities have • Unsystematic risk • Volatility due to firm-specific events • Can be eliminated through diversification • Also called firm-specific risk and diversifiable risk • Systematic risk • Volatility due to the overall stock market • Since this risk cannot be eliminated through diversification, this is often called nondiversifiable risk.

  7. The equation for the SML leads to the CAPM β is a measure of relative risk • β = 1 for the overall market. • β = 2 for a security with twice the systematic risk of the overall market, • β = 0.5 for a security with one-half the systematic risk of the market.

  8. Using CAPM • Expected Return • If the market is expected to increase 10% and the risk free rate is 5%, what is the expected return of assets with beta=1.5, 0.75, and -0.5? • Beta = 1.5; E(R) = 5% + 1.5  (10% - 5%) = 12.5% • Beta = 0.75; E(R) = 5% + 0.75  (10% - 5%) = 8.75% • Beta = -0.5; E(R) = 5% + -0.5  (10% - 5%) = 2.5% • Finding Undervalued Stocks…(the SML)

  9. CAPM and Portfolios • How does adding a stock to an existing portfolio change the risk of the portfolio? • Standard Deviation as risk • Correlation of new stock to every other stock • Beta • Simple weighted average: • Existing portfolio has a beta of 1.1 • New stock has a beta of 1.5. • The new portfolio would consist of 90% of the old portfolio and 10% of the new stock • New portfolio’s beta would be 1.14 (=0.9×1.1 + 0.1×1.5)

  10. Estimating Beta • Need • Risk free rate data • Market portfolio data • S&P 500, DJIA, NASDAQ, etc. • Stock return data • Interval • Daily, monthly, annual, etc. • Length • One year, five years, ten years, etc.

  11. Market Index variations

  12. Interval variations

  13. Problems using Beta • Which market index? • Which time intervals? • Time length of data? • Non-stationary • Beta estimates of a company change over time. • How useful is the beta you estimate now for thinking about the future? • Other factors seem to have a stronger empirical relationship between risk and return than beta • Not allowed in CAPM theory • Size and B/M

  14. Multifactor models • Arbitrage Pricing Theory (APT) • Multiple risk factors, one of which may be beta • What are these factors, F1, F2, etc.? • Unexpected inflation, risk yield spread, oil prices,… • Example • Specify an APT model with three factors; the CAPM beta (F1), unexpected inflation (F2), and the risk yield spread (F3). • A company being analyzed has risk factor sensitivities of b1 = 1.2, b2 = -2.2, and b3 = 0.1. The intercept, α, was 3.5%. The risk premium on the market was 5%, unexpected inflation turned out to be +2%, and the yield spread is 4%, what risk premium should the company have earned?

  15. Multifactor models • Fama-French Three Factor Model • Beta, size, and B/M • SMB, difference in returns of portfolio of small stocks and portfolio of large stocks • HML, difference in return between low B/M portfolio and high B/M portfolio • Kenneth French keeps a web site where you can obtain historical values of the Fama-French factors, mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

  16. New Behavioral Approaches • The design of asset pricing models began using theories of rational investor behavior. • Rational investors are generally thought to be risk averse, can fully exploit all available information, and do not suffer from psychological biases. • The expected rate of return on investment for a given portfolio is solely a function of the economic risks faced. • Investors do not always act “rational • Behavioral risk factors like the reluctance to realize losses, overconfidence, and momentum might be applied to asset pricing.

  17. Add a momentum factor… • Those that follow behavioral finance might argue that the SMB factor is actually a Overreaction risk factor. • Also add a momentum factor: The UMD (up minus down) momentum factor is the return on a portfolio of the best performing stocks minus the portfolio return for the worst stocks during the preceding twelve month period.

  18. Evaluating Portfolio Performance • How well did a portfolio manager do? • Different portfolios take different levels of risk. • There they should earn different returns. • Some managers have constraints • Must invest in small cap stocks or a particular industry. • Evaluation of a portfolio’s performance should therefore include: • Risk-adjusted performance • Comparisons with similarly constrained portfolios

  19. Benchmarks • Comparing the portfolio to similar portfolios • Market benchmarks • S&P 500 Index: General market • S&P 100 Index: Large cap • S&P 400 Index: Mid cap • S&P 600 Index: Small cap • Russell 2000 • Industry benchmarks • Dow Jones US Technology Index, DJ US Financial, DJ US Health Care, … • Managed Portfolio benchmarks • Average return of all mutual funds with the same constraints • Small cap, value strategy, international, etc.

  20. Alpha • Given CAPM, a portfolio should earn the return of: E(RP) = RF+ βP(RM - RF) • So, if RF = 5%, βP = 1.2, RM = 11% • The return should be 12.2% = 5%+ 1.2×(11%-5%) • If the portfolio earned 13%, then it did well. If it earned 11.5%, it did poorly. Alpha is the difference between what it did earn and what is should have earned. αP= RP - RF- βP(RM - RF) • Positive alphas are good! • Alpha is an absolute measure of performance. • What is the source of the non-zero alpha? • Selectivity: stock picking • Market timing

  21. Table 5.2 Beta Estimation for Ten Large Mutual Funds Using the S&P 500 as a Market Index

  22. Sharpe Ratio • Reward-to-variability measure • Risk premium earned per unit of total risk: • Higher Sharpe ratio is better. • Use as a relative measure. • Portfolios are ranked by the Sharpe measure.

  23. Treynor Index • Reward-to-volatility measure • Risk premium earned per unit of systematic risk: • Higher Treynor Index is better. • Use as a relative measure.

  24. Example • A pension fund’s average monthly return for the year was 0.9% and the standard deviation was 0.5%. The fund uses an aggressive strategy as indicated by its beta of 1.7. • If the market averaged 0.7%, with a standard deviation of 0.3%, how did the pension fund perform relative to the market? • The monthly risk free rate was 0.2%. Solution: • Compute and compare the Sharpe and Treynor measures of the fund and market. • For the pension fund: • For the market: • Both the Sharpe ratio and the Treynor Index are greater for the market than for the mutual fund. Therefore, the mutual fund under-performed the market.

  25. Summary • CAPM is an elegant model • Used extensively in the industry • You can find a Beta estimate on any financial information website • Morningstar shows mutual fund risk-adjusted measures • Used in portfolio evaluation • However, there are estimation problems • Doesn’t work very well • Multifactor models work better • Portfolios should be evaluated using risk-adjusted measures and compared with benchmarks of similar characteristics

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