Question

Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:

1. Risk-free asset earning 13% per year.

2. Risky asset with expected return of 30% per year and standard deviation of 36%.

If you construct a portfolio with a standard deviation of 28%, what is its expected rate of return? (Do not round your intermediate calculations. Round your answer to 1 decimal place.)

Answer 1

Given that a portfolio is made from following assets:

Risk-free asset earning 13% per year. Rf = 13%

Risky asset with expected return of 30% per year and standard deviation of 36%.

Rr = 30%

SD(r) = 36%

Required standard deviation of the portfolio is 28%

So, standard deviation of portfolio consisted of risk free asset and risky asset is calculate as

Weight of risky asset*standard deviation of risky asset

So here, weight of risky asset = Required standard deviation of the portfolio/standard deviation of risky asset

=> weight of risky asset Wr = 28/36 = 77.78% or 0.7778

Weight of risk free asset Wf = 1-Wr = 1-0.7778 = 0.2222 or 22.22%

Expected return of a portfolio is weighted average return of its assets

=> Expected return of this portfolio = Wf*Rf + Wr*Rr = 0.2222*13 + 0.7778*30 = 26.22%