Question

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 10% 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:

Answer 1

risk free rate , rf = 4% = 0.04

expected return on market portfolio , rm = 10% = 0.10

let us construct a portfolio of market and risk free asset, where the weight of market portfolio = w1

and the weight of risk free asset = w2 = 1-w1

expected return of this portfolio should = expected return on google = 14%

volatility of market portfolio = 18% = 0.18

(w1*rm) + (w2*rf) = 14

(w1*10) + ((1-w1)*4) = 14

10w1 + 4 - 4w1 = 14

4+6w1 = 14

6w1 = 10

w1 = 10/6 = 1.666667

w2 = 1-w1 = 1-1.666667 = -0.666667

volatility of this portfolio = w1* volatility of market portfolio ( since volatility of risk free asset is zero)

volatility of this portfolio = 1.666667*0.18 = 0.30 or 30%