Question

You currently have $100,000 invested in a portfolio that has an expected return of 12% and a volatility of 8%. Suppose the risk-free rate is 5%, and there is another portfolio that has an expected return of 20% and a volatility of 12%. For this question, you need to specify the dollar amount that you invest in the new portfolios in (i) and (ii)

(i)How do you construct a new portfolio that has a higher expected return than your current portfolio but with the same volatility?

(ii)How do you construct a new portfolio that has a lower volatility than your current portfolio but with the same expected return?

Answer 1

1.
Let w be the weight invested in new portfolio and 1-w be the weight in risk free rate
w*12%=8%
=>w=8%/12%=0.666666667

Expected return=0.666666667*20%+(1-0.666666667)*5%=15.0000%

This has higher expected return

Amount in new portfolio=0.666666667*100000=66666.6667
Amount in risk free rate=100000-66666.6667=33333.3333

2.
Let w be the weight invested in new portfolio and 1-w be the weight in risk free rate

w*20%+(1-w)*5%=12%
=>w=(12%-5%)/(20%-5%)=0.466666667

Volatility=Standard deviation=0.466666667*12%=5.6000%

This has lower volatility

Amount in new portfolio=0.466666667*100000=46666.6667

Amount in risk free rate=100000-46666.6667=53333.3333