Question

Suppose that you have $1 million and the following two opportunities from which to construct a portfolio: a. Risk-free asset earning 8% per year. b. Risky asset with expected return of 23% per year and standard deviation of 31%. If you construct a portfolio with a standard deviation of 22%, what is its expected rate of return? (Do not round your intermediate calculations. Round your answer to 1 decimal place.) Expected return on portfolio

Answer 1

Standard Deviation of a 2-asset portfolio with one being a risk-free asset is:

$\sigma$_P = [(weight of risky asset)² * ($\sigma$ of risky asset)²]^1/2

0.22 = [(wR)² * (0.31)²]^1/2

(0.22)² = (wR)² * 0.0961

0.0484 / 0.0961 = (wR)²

wR = [0.5036]^1/2 = 0.7097, or 70.97%

wRF = 1 - wR = 1 - 0.7097 = 0.2903, or 29.03%

Expected Return on Portfolio = [wRF * rRF] + [wR * rR]

= [0.2903 * 8%] + [0.7097 * 23%]

= 2.32% + 16.32% = 18.65%