Question

A portfolio consists of two securities: a 90-day T-bill and the S&P/TSX Composite. The expected return on the T-bill is 4.5 percent. The expected return on the S&P/TSX Composite is 12 percent with a standard deviation of 20 percent. What is the portfolio standard deviation if the expected return for this portfolio is 15 percent?

a) 8.13%

b) 12.00%

c) 16.80%

d) 28.00%

Answer 1

Correct Answer is D 28%

Let the weight of 90 day T-Bill in portfolio be A

Then the weight of S & P/ TSX composite will be 1-A

Return on Portfolio will be weighted average return of individual stock.

Therefore, Return on Portfolio = Weight in TBill X Return from TBill + Weight in S&P/TSX Composite X Return from S&P/TSX Composite

15 = 4.4 x A + 12 (1-A)

15=4.4A +12 -12A

Therefore, A= -40% and 1-A = 140%

Thus weight in 90 day T-Bill is -40% and S&P/TSX Composite is 140%.

Standard Deviation of Tbill is Zero (0).

Therefore, Standard Deviation of portfolio will be Standard Deviation of S&P/TSP Composite X Weight of S&P/TSX Composite

Thus, Standard Deviation of Portfolio = 20% X 140% =28%