Question

BMAN23000A (16) You currently own Facebook stock. Suppose that Facebook has an expected return of 18% and a volatility of 15%. The market portfolio has an expected return of 11% and a volatility of 13%. The risk-free rate is 2%. Assuming the CAPM assumptions hold, you want to find an alternative portfolio with the lowest possible volatility and the same expected return as Facebook. The volatility of this portfolio is closest to: 13.2% Facebook 15% 18% 23.1% 17.6% subt onts solRp) x Co 10%

Answer 1

Alternate Portfolio can be created by Borrowing at risk free rate and investing such borrowed amount alongwith our own money into market portfolio. This will result in increased leverage and hence, increased return and volatility.

Expected Return = Same as Facebook = 18%

Let weight of investment be W. So weight of borrowings = 1-W

Portfolio Return = (Return on investment×Weight of Investment) + (Rate of borrowing×Weight of borrowing)

18 = (11 × W) + [2 × (1 - W)]

18 = 11W + 2 - 2W

16 = 9W

Therefore, W = Weight of Investment = 1.777 and Weight of Borrowing = 1-1.777 = -0.777

Therefore, with this Portfolio Return will be (11×1.777)+(2×-0.777) = 18%

Portfolio Volatility = (Volatility of Investment×Weight of Investment) + (Volatility of Borrowing×Weight of Borrowing)

= (13×1.777) + (0×-0.777) = 23.101%

Therefore, Correct Option is (B) 23.1%

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