Question

In the next year, there is a 40% chance of a bear market, and a 60% change of a bull market. Over the next year:

Debt will realize a 0% return in a bear market, and a 6% return in a bull market.

Equity will realize a -10% return in a bear market, and a 20% return in a bull market.

1.What is the volatility of the debt instrument? (%, in 2 decimal places )

2.What is the covariance of debt and equity? (decimal number, 4 decimal places)

3.What is the correlation of debt and equity? (decimal number, 3 decimal places)

4.What is the expected return of a portfolio made up of 95% debt and 5% equity? (% 2 decimal places)

5.What is the volatility of a portfolio made up of 95% debt and 5% equity? (% 2 decimal places)

6.Is this portfolio more or less volatile than a portfolio made up of 100% debt? (write ‘more’ or ‘less')

7.Which portfolio has a higher Sharpe ratio: the portfolio of all debt, or the portfolio that has a mixture of 95% debt and 5% equity? (hint: how can you answer this question without knowing the risk-free rate? write ‘debt’ or ‘mix’ )

Answer 1

1.
=sqrt(40%*(0%-(40%*0%+60%*6%))^2+60%*(6%-(40%*0%+60%*6%))^2)=2.94%

2.
=40%*(0%-(40%*0%+60%*6%))*(-10%-(40%*(-10%)+60%*20%))+60%*(6%-(40%*0%+60%*6%))*(20%-(40%*(-10%)+60%*20%))=0.0043

3.
=0.0043/(2.9394%*sqrt(40%*(-10%-(40%*(-10%)+60%*20%))^2+60%*(20%-(40%*(-10%)+60%*20%))^2))=0.995366202

4.
=95%*(40%*0%+60%*6%)+5%*(40%*(-10%)+60%*20%)=3.820%

P.S.: I am not allowed to answer more than 4 questions