You own $18,252 of Opsware, Inc., stock that has an assumed beta of 3.88. You al

Question

You own $18,252 of Opsware, Inc., stock that has an assumed beta of 3.88. You also own $29,406 of Lowe’s Companies (assumed beta = 1.58) and $3,042 of New York Times (assumed beta = 0.91). Assume that the market return will be 10 percent and the risk-free rate is 2 percent.

What is the risk premium of each stock? (Round your answers to 2 decimal places.)

What is the risk premium of the portfolio? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

You own $18,252 of Opsware, Inc., stock that has an assumed beta of 3.88. You also own $29,406 of Lowe’s Companies (assumed beta = 1.58) and $3,042 of New York Times (assumed beta = 0.91). Assume that the market return will be 10 percent and the risk-free rate is 2 percent.

Explanation / Answer

Given in the question
market return = 10%
Risk free rate i.e rf = 2%
Thus the market risk premium = market return - risk free rate
=10-2
=8%

Risk premium = calculated stock return - risk free rate
And CAPM return= rf + Beta (market risk premium)

Beta for Opsware = 3.88
Return on Opsware = 0.02 + 3.88 (0.08)
= 0.02 + 0.3104
=0.3304
=33.04%
Thus Opsware's risk premium = return - rf
=33.04% - 2% = 31.04%

Beta for Lowe = 1.58
Return on Lowe = 0.02 + 1.58 (0.08)
= 0.02 + 0.1264
=0.1464
=14.64%
Thus Lowe's risk premium = return - rf
=14.64% - 2% = 12.64%

Beta for New York Times = 0.91
Return on New York Times = 0.02 + 0.91 (0.08)
= 0.02 + 0.0728
=0.0928
=9.28%
Thus New York Times risk premium = return - rf
=9.28% - 2% = 7.28%

Total portfolio value = 18252+29406+3042=50700
Weight of Opsware = 18252/50700 = 0.36
Weight of Lowe = 29406/50700 = 0.58
Weight of New York Times = 3042/50700 = 0.06
Thus,
Total portfolio return = weights * individual returns
=0.36*33.64 + 0.58*12.64 + 0.06*7.28
=12.1104+7.3312+0.4368
=19.8784
Hence portfolio risk premium = return - rf
=19.8784 - 2
=17.8784
=17.88%

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