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The Capital Asset Pricing Model Prof. Chen Xue Carl H. Lindner School of Business University of Cincinnati FIN 7041: Investments Overview The Capital Asset Pricing Model (CAPM) The CAPM determines expected returns of individual securities by combining portfolio choices of all investors in the economy Applications: I Benchmark returns for constructing investment strategies I Benchmark hurdle rates for capital budgeting I An educated guess for the expected returns on assets that have not yet been traded (e.g. IPOs) I A benchmark for evaluating mutual fund performance Outline Securities Returns in an Equilibrium Expected Return and Risk of Individual Securities Application: Measuring Mutual Fund Performance Equilibrium Assumptions 1. Individual investors are price takers 2. Single-period investment horizon 3. Investments are limited to traded nancial assets 4. No taxes and transaction costs 5. Investors are rational mean-variance optimizers 6. Information is costless and available to all investors 7. There are homogeneous expectations 8. Lending and borrowing at a single risk-free rate Equilibrium Basic insights Each investor holds the same tangent portfolio of risky assets I Only dier in the degree of lending/borrowing For all investors to hold the same tangent portfolio of risky assets (demand), it must be the market portfolio of all risky assets (supply) I The market portfolio, M. contains all securities and the proportion of each security is its market value as a percentage of total market value The market portfolio is the optimal risky portfolio with the highest Sharpe ratio Equilibrium Determinants of the market risk premium The risk premium on the market portfolio depends on the average risk aversion of all investors and the risk of the whole economy Recall: for optimal asset allocation, y * = [ E ( r P )-r f ] / [ A 2 P ]. In equilibrium, the aggregate position of all investors has to be the market portfolio, since total lending cancels total borrowing That is, y * = 1, and we have: E ( r M )-r f = A 2 M I What happens to the market risk premium when an average investor becomes more risk averse? I What happens when market volatility goes up? Equilibrium Example: market risk premium and risk aversion In the last eight decades, the S&P 500 yields an average excess return of 7. 9 % with a standard deviation of 23.2% (a) To the extent that these averages approximated investor expectations for the period, what must have been the average coecient of risk aversion? A = E ( r M )-r f 2 M =. 079. 232 2 = 1. 47 (b) If the coecient of risk aversion were actually 3.5, what risk premium would have been consistent with the markets historical standard deviation. View Full Document