een the returns on stocks A and BsA,B=the covariance between the returns on stocks A and B,sA=the standard deviation on stock A, andsB=the standard deviation on stock B
19 Portfolio Risk and Return The covariance between stock A and stock B is as follows:sA,B = .2( )(.5-.2) + .3( )(.3-.2) +.3( )(.1-.2) +.2( )(-.1-.2) =The correlation coefficient between stock A and stock B is as follows:-.0105rA,B = (.0512)(.2049) =
20 Portfolio Risk and Return Using either the correlation coefficient or the covariance, the Variance on a Two-Asset Portfolio can be calculated as follows:s2p = (wA)2s2A + (wB)2s2B + 2wAwBrA,B sAsBORs2p = (wA)2s2A + (wB)2s2B + 2wAwB sA,BThe Standard Deviation of the Portfolio equals the positive square root of the the variance.
21 Portfolio Risk and Return Let’s calculate the variance and standard deviation of a portfolio comprised of 75% stock A and 25% stock B:s2p =(.75)2(.0512)2+(.25)2(.2049)2+2(.75)(.25)(-1)(.0512)(.2049)=sp = = = 1.28%Notice that the portfolio formed by investing 75% in Stock A and 25% in Stock B has a lower variance and standard deviation than either Stocks A or B and the portfolio has a higher expected return than Stock A.This is the purpose of diversification; by forming portfolios, some of the risk inherent in the individual stocks can be eliminated.
22 Capital Asset Pricing Model (CAPM) If investors are mainly concerned with the risk of their portfolio rather than the risk of the individual securities in the portfolio, how should the risk of an individual stock be measured?In important tool is the CAPM.CAPM concludes that the relevant risk of an individual stock is its contribution to the risk of a well-diversified portfolio.CAPM specifies a linear relationship between risk and required return.The equation used for CAPM is as follows:Ki = Krf + bi(Km - Krf)Where:Ki = the required return for the individual securityKrf = the risk-free rate of returnbi = the beta of the individual securityKm = the expected return on the market portfolio(Km - Krf) is called the market risk premiumThis equation can be used to find any of the variables listed above, given the rest of the variables are known.
23 CAPM ExampleFind the required return on a stock given that the risk-free rate is 8%, the expected return on the market portfolio is 12%, and the beta of the stock is 2.Ki = Krf + bi(Km - Krf)Ki = 8% + 2(12% - 8%)Ki = 16%Note that you can then compare the required rate of return to the expected rate of return. You would only invest in stocks where the expected rate of return exceeded the required rate of return.
24 Another CAPM ExampleFind the beta on a stock given that its expected return is 12%, the risk-free rate is 4%, and the expected return on the market portfolio is 10%.12% = 4% + bi(10% - 4%)bi = 12% - 4%10% - 4%bi = 1.33Note that beta measures the stock’s volatility (or risk) relative to the market.