a. Which stock has more systematic risk? b. Which stock has more total risk? c.

Question

a. Which stock has more systematic risk?

b. Which stock has more total risk?

c. If you formed a portfolio by using 30% of DuBear and 70% of LaFaSai, what is your expected return and what is the beta of your portfolio?

You have the following information on the stock of DuBear and LaFaSai: Rate of return if Sate Occurs State of Econom Recession Normal Boom Probability of State DuBear 2% 10% 30% LaFaSai -15% 10% 20% of Econom 50% 20% 30% The market return is 10 percent, and the risk-free rate is 3 percent. It is assumed that the CAPM holds.

Explanation / Answer

Since CAPM is true: E[Ri]=rf + Beta*(Rm -Rf)

Expected Return of DuBear = 0.5 x 0.02 + 0.2 x 0.1 + 0.3 x 0.3 = 0.12 = 12%

Expected Return of LaFaSai = 0.5 x -0.15 + 0.2 x 0.1 + 0.3 x 0.2 = 0.12 = 0.005 = 0.5%

a. For systematic risk, we estimate Beta
BetaDuBear = (Expected Return - Rf)/(Rm - Rf)
BetaDuBear = (0.12 - 0.03)/(0.1 - 0.3) = 1.29

DuBear has more systematic risk

BetaLaFaSai = (Expected Return - Rf)/(Rm - Rf)
BetaLaFaSai = (0.005 - 0.03)/(0.1 - 0.3) = -0.36

b. For Total Risk, we estimate Standard deviation,
Standard deviation(DuBear) = 0.14
Standard deviation(LaFaSai) = 0.18

LaFaSai has more total risk

c. Expected Return for Portfolio = 0.3 x 0.12 + 0.7 x 0.005 = 3.95%
Expected Beta for Portfolio = (0.0395 - 0.03)/(0.1 - 0.03) = 0.14

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