Review Risk and Return

r = expected rate of return. ^

stand-alone risk An asset’s risk can be analyzed in two ways: (1) on a stand-alone basis, where the asset is considered in isolation, and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio. Thus, an asset’s stand-alone risk is the risk an investor would face if he or she held only this one asset.

Probability distribution Rate of return (%) Stock X Stock Y Which stock is riskier? Why? 30

Measuring Stand-Alone Risk: Standard deviation σ 1- Standard deviation σ ( absolute mean of risk) Standard deviation measures the stand- alone risk of an investment. The larger the standard deviation, the higher the probability that returns will be far below the expected return.

Standard deviation σ

Measuring Stand-Alone Risk: The Coefficient of Variation 2- The coefficient of variation CV (an alternative measure of stand-alone risk.) CV = σ/ r^ It shows the risk per unit of return It provide a more meaningful basis for comparison When the expected return on two alternatives are not the same.

Portfolio Return, rp ^ ^^ r p =   w i r i  n i = 1

Two-Stock Portfolios Two stocks can be combined to form a riskless portfolio if  = Risk is not reduced at all if the two stocks have  = In general, stocks have   0.65, so risk is lowered but not eliminated. Investors typically hold many stocks. What happens when  = 0?

Type of Risk Systematic Risk No diversifiable Risk = Market Risk war, inflation, recessions, and high interest rates. Since most stocks are negatively affected by these factors, market risk cannot be eliminated by diversification.

Type of Risk Unsystematic Risk diversifiable Risk Caused by such random events as lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm.

Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification. Stand-alone Market Diversifiable risk risk risk = +.

Capital Asset Pricing Model (CAPM) an important tool used to analyze the relationship between risk and rates of return. The primary conclusion of the CAPM is this : The relevant risk of an individual stock is its contribution to the risk of a well-diversified portfolio The risk that remains after diversifying is market risk, or the risk that is inherent in the market, and it can be measured by the degree to which a given stock tends to move up or down with the market.

Capital Asset Pricing Model (CAPM) ri expected rate of return on the ith stock. ri required rate of return on the ith stock. r RF risk-free rate of return. In this context, r RF is generally measured by the return on long-term U.S. Treasury bonds. bi beta coefficient of the ith stock. The beta of an average stock is b A = 1.0 ^

Capital Asset Pricing Model (CAPM) r M required rate of return on a portfolio consisting of all stocks, which is called the market portfolio. r M is also the required rate of return on an average ( b A = 1.0) stock. R PM = ( r M - r RF ) risk premium on “the market,” and also on an average ( b = 1.0) stock. R Pi = ( r M - r RF ) bi = (R PM )bi

Security Market Line (SML) Required return = Risk-free return + Premium for risk. the relationship between the required return and risk is called the Security Market Line (SML).