Extra Questions

Q1) You own a portfolio that has $3,000 invested in Stock A and $4,100 invested in Stock B. Assume the expected returns on these stocks are 10 percent and 16 percent, respectively.   What is the expected return on the portfolio?  Total value = $3,000 + 4,100 Total value = $7,100   So, the expected return of this portfolio is:    E(Rp) = ($3,000 / $7,100)(.10) + ($4,100 / $7,100)(.16) E(Rp) = .1346, or 13.46%

Q2) What is the expected return on an equally weighted portfolio of these three stocks? What is the variance of a portfolio invested 29 percent each in A and B and 42 percent in C?  State of Economy Probability Stock A Stock B Stock C Boom 0.74 12% 6% 32% Bust 0.26 21% 27% -12% To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the return of the portfolio in each state of the economy is:      Boom:Rp= (.12 + .06 + .32) / 3 Rp= .1667, or 16.67%   Bust:Rp= (.21 + .27 – .12) / 3 Rp= .1200, or 12.00%  This is equivalent to multiplying the weight of each asset (1/3 or .3333) times its expected return and summing the results, which gives:    Boom:Rp= 1/3(.12) + 1/3(.06) + 1/3(.32) Rp= .1667, or 16.67%    Bust:Rp= 1/3(.21) + 1/3(.27) + 1/3(–.12) Rp= .1200, or 12.00%   To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. Doing this, we find:     E(Rp) = .74(.1667) + .26(.1200) E(Rp) = .1545, or 15.45%    b.   This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:    Boom:Rp= .29(.12) +.29(.06) + .42(.32) Rp= .1866, or 18.66%   Bust:Rp= .29(.21) +.29(.27) + .42(–.12) Rp= .0888, or 8.88%    And the expected return of the portfolio is:    E(Rp) = .74(.1866) + .26(.0888) E(Rp) = .1612, or 16.12%    To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance. So, the variance of the portfolio is:    σp2 = .74(.1866 – .1612)2 + .26(.0888 – .1612)2 σp2 = .00184

Q3) You own a stock portfolio invested 29 percent in Stock Q, 15 percent in Stock R, 41 percent in Stock S, and 15 percent in Stock T. The betas for these four stocks are .98, 1.04, 1.44, and 1.89, respectively.   What is the portfolio beta? The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is:   βp = .29(.98) + .15(1.04) + .41(1.44) + .15(1.89) βp = 1.31

Q4) A stock has a beta of 0.9, the expected return on the market is 10 percent, and the risk-free rate is 4 percent.   What must the expected return on this stock be? The CAPM states the relationship between the risk of an asset and its expected return. The CAPM is:   E(Ri) = Rf + [E(RM) – Rf] × βi   Substituting the values we are given, we find:   E(Ri) = .04 + (.10 – .04)(0.90) E(Ri) = .058, or 5.8%

Q5) A stock has an expected return of 14.2 percent, the risk-free rate is 5.5 percent, and the market risk premium is 6.9 percent.   What must the beta of this stock be? We are given the values for the CAPM except for the β of the stock. We need to substitute these values into the CAPM, and solve for the β of the stock. One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find:   E(Ri) = Rf + [E(RM) – Rf] × βi .142 = .055 + .069βi βi = 1.261