Question

Mary has $100 to invest in either a risky stock or a risk-free treasury bill. The table below shows the expected return and risks for each. Expected return for stock is 30% and risk is 40. Expected return for treasury bills is 3% and the risk is 0.
a. Assume Mary’s overall portfolio risk is 30. i. What is her expected return for her portfolio. ii. What proportion of her overall money does she invest in stocks? b. What if her portfolio’s expected return is 15%. i. What is her overall portfolio risk? ii. What proportion of her overall money does she invest in stocks?

Answer 1

Mary has $100 with her to invest either in risky assets or riskfree asset.

E(Return)=30% and Variance is 40

Now Mary's Portfolio Risk is 30 that means

30=w(40)+(1-w)(0) which is w% weight for risky asset and 1-w weight for risk free asset

30=40w

w=0.75=75%

She invests 75%$100=$75 in stocks

Expected Return then will be

75%(30%)+25%(3%)=22.5+7.5%=30% over this portfolio

Answer for b)

IF Expected Return is 15%

then 15%=w(30%)+(1-w)3%=27%w+3%

12%=27%w

w=12/27=44.44% to be invested in stocks in this case and remaining in risk free assets

Overall portfolio risk

0.4444(40)+0.5556(0)=17.77