In: Finance
Question 4
because there is no possibility of default, the risk of the firm’s equity does not change.”
To get the full marks of this question, you need to specify the dollar amount that you invest in the new portfolios in (i) and (ii)
As part d itself is a very big question answering part d
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%.
How do you construct a new portfolio that has a higher expected
return than your current portfolio but with the same volatility? (3
marks)
How do you construct a new portfolio that has a lower volatility
than your current portfolio but with the same expected return? (3
marks)
To get the full marks of this question, you need to specify the
dollar amount that you invest in the new portfolios in (i) and
(ii)
Answer:
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