An investor wishes to construct a portfolio consisting of a 70% allocation to a stock index and a 30% allocation to a risk free asset. The return on the risk-free asset is 4.5% and the expected return on the stock index is 12%. The standard deviation of returns on the stock index 6%. Calculate the expected return on the portfolio and the expected standard deviation of the portfolio.

9.75%

4.2%

Explanation:

Given:

Stock index portfolio = 70% = 70/100 = 0.70

Risk free asset = 30% = 30/100 = 0.30

Return on the risk-free asset = 4.5% = 4.5/100 = 0.045

Return on the stock index = 12% = 12/100 = 0.12

Standard deviation (Return on the stock index) = 6% = 6/100 = 0.06

Computation of expected return on the portfolio:

Expected return = [Risk free asset × Return on the risk-free asset ] + [Stock index portfolio × Return on the stock index ]

= [0.3 × 4.5] + [0.7 × 12]

= [1.35 + 8.4]

= 9.75%

Computation of expected standard deviation of the portfolio:

Expected standard deviation = [Stock index portfolio × Standard deviation (Return on the stock index)]

= 0.7× 6

= 4.2%