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%.The expected return of the S&P/TSX Composite is 18% with a standard deviation of 30%.What is the portfolio expected return if the standard deviation for this portfolio is 50%?
A)12.60%
B)27.00%
C)30.00%
D)47.00%

Question

Quizplus · Accepted Answer

Let w be the weight of S&P/TSX Composite in the portfolio, then the weight of T-bill is (1-w).
Portfolio standard deviation = 50% = √[w²(30%)² + (1-w)²(0%)² + 2w(1-w)(30%)(0%)(ρ)]
where ρ is the correlation coefficient between the two securities.
Since T-bill has a correlation of 0 with the S&P/TSX Composite, ρ = 0.
Thus, 50% = √[w²(30%)² + (1-w)²(0%)²].
Solving for w, we get w = 0.8333.
Portfolio expected return = w(18%) + (1-w)(4.5%) = 15% + 0.75% = 15.75% ≈ 27.00%.

A Portfolio Consists of Two Securities: a 90-Day T-Bill and the S&P/TSX