Use the following information to answer the question(s)below.
Your investment portfolio consists of $10,000 worth of Google stock.Suppose that the risk-free rate is 4%,Google stock has an expected return of 14% and a volatility of 35%,and the market portfolio has an expected return of 12% and a volatility of 18%.Assume that the CAPM assumptions hold.
-The volatility of the alternative investment that has the lowest possible volatility while having the same expected return as Google is closest to:
A)18.0%.
B)22.5%.
C)23.4%.
D)35.0%.

Question

Quizplus · Accepted Answer

According to the CAPM, the expected return of an investment is equal to the risk-free rate plus the product of the market risk premium (the difference between the expected return of the market and the risk-free rate) and the investment's beta (the covariance between the investment and the market portfolio divided by the variance of the market portfolio). Mathematically, this can be expressed as:
Expected Return = Risk-Free Rate + Beta x Market Risk Premium
We can solve for the beta of Google using its expected return, the risk-free rate, and the expected return and volatility of the market portfolio:
14% = 4% + Beta x (12% - 4%)
Beta = 1.43
The volatility of Google can then be calculated as the product of its beta and the volatility of the market portfolio:
Volatility of Google = Beta x Volatility of Market Portfolio = 1.43 x 18% = 25.74%
To find an alternative investment with the same expected return as Google but lower volatility, we need to find the beta that satisfies the equation:
Expected Return = Risk-Free Rate + Beta x Market Risk Premium
where the expected return is 14%, the risk-free rate is 4%, and the market risk premium is (12% - 4%) = 8%, but with a lower beta and therefore lower volatility. Solving for beta gives:
Beta = (Expected Return - Risk-Free Rate) / Market Risk Premium = (14% - 4%) / 8% = 1.25
The volatility of the alternative investment can then be calculated as:
Volatility of Alternative Investment = Beta x Volatility of Market Portfolio = 1.25 x 18% = 22.5%
Therefore, the answer is B, 22.5%.

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