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Return, Risk and the Security Market Line Systematic and Unsystematic

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Return, Risk and the Security Market Line Systematic and Unsystematic Expected and Unexpected Returns • The return on any stock traded in a Return, Risk and the Security financial market is composed of two parts. c The normal, or expected, part of the return is Market Line the return that investors predict or expect. d The uncertain, or risky, part of the return Chapter 18 comes from unexpected information revealed during the year. • Total return – Expected return = Unexpected return R – E(R) = U Systematic and Unsystematic Diversification and Risk Risk Systematic risk • In a large portfolio, some stocks will go up in value because of positive company-specific Risk that influences a large number of events, while others will go down in value assets. Also called market risk. because of negative company-specific events. Unsystematic risk • Unsystematic risk is essentially eliminated by Risk that influences a single company or diversification, so a portfolio with many assets a small group of companies. Also called has almost no unsystematic risk. unique or asset-specific risk. • Unsystematic risk is also called diversifiable risk, while systematic risk is also called nondiversifiable risk. Total risk = Systematic risk + Unsystematic risk The Systematic Risk Principle Measuring Systematic Risk • The systematic risk principle states that Beta coefficient (β) the reward for bearing risk depends only Measure of the relative systematic risk of an on the systematic risk of an investment. asset. Assets with betas larger than 1.0 • So, no matter how much total risk an asset have more systematic risk than average, has, only the systematic portion is relevant and vice versa. in determining the expected return (and • Because assets with larger betas have the risk premium) on that asset. greater systematic risks, they will have greater expected returns. • Note that not all betas are created equal. 1 Measuring Systematic Risk Portfolio Betas • The riskiness of a portfolio has no simple relation to the risks of the assets in the portfolio. • In contrast, a portfolio beta can be calculated just like the expected return of a portfolio. – In general, you can multiply each asset’s beta by its portfolio weight and then add the results to get the portfolio’s beta. The Reward-to-Risk Ratio Implications • Notice that all the combinations of portfolio In general … expected returns and betas fall on a • The reward-to-risk ratio must be the same for all straight line. assets in a competitive financial market. E()R − R 20% −8% • If one asset has twice as much systematic risk • Slope = A f = = 7.50% β 1.6 as another asset, its risk premium will simply be A twice as large. • What this tells us is that asset A offers a • Because the reward-to-risk ratio must be the reward-to-risk ratio of 7.50%. In other same, all assets in the market must plot on the words, asset A has a risk premium of same line. 7.50% per “unit” of systematic risk. The Fundamental Result The Security Market Line Security market line (SML) Graphical representation of the linear relationship between systematic risk and expected return in financial markets. • For a market portfolio, E(R )− R E(R )− R SML slope = M f = M f β M 1 = E()RM − R f 2 The Security Market Line The Security Market Line • The term E(RM) – Rf is often called the Capital asset pricing model (CAPM) market risk premium because it is the risk A theory of risk and return for securities premium on a market portfolio. on a competitive capital market. E(Ri ) = R f + [E(RM )− R f ]×β i • The CAPM shows that E(Ri) depends on c Rf, the pure time value of money. d E(RM) – Rf, the reward for bearing systematic risk. e βi, the amount of systematic risk. The Security Market Line Where Do Betas Come From? • A security’s beta depends on c how closely correlated the security’s return is with the overall market’s return, and d how volatile the security is relative to the market. • A security’s beta is equal to the correlation multiplied by the ratio of the standard deviations. σ i β i = Corr()Ri , RM × σ m Why Do Betas Differ? • Betas are estimated from actual data. Different sources estimate differently, possibly using different data. – For data, the most common choices are three to five years of monthly data, or a single year of weekly data. – To measure the overall market, the S&P 500 stock market index is commonly used. – The calculated betas may be adjusted for various statistical reasons. 3.
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