Find the following ex-post measures:

 

1. Arithmetic average return of Firm A
2. Geometric average return of Firm A
3. Expected return of Firm A
4. Variance of Firm A's returns
5. Standard deviation of Firm A's returns
6. 95.44% of the time, the stock's return will vary between _______% and ________%
7. Find the covariance between Firm A and Firm B's returns
8. Find the coefficient of correlation between the two stocks
9. What is the expected return of the risky portfolio, if you invest 20% in Firm A and the remaining 80% in Firm B?
10. What is the risk (as measured by st. dev.) of the risky portfolio, P?
11. What is the expected return on the complete portfolio, C, if you decide to invest 30% of your money into a risk-free asset offering 5% return, and the remaining 70% into the risky portfolio, P?
12. What is the risk (as measured by st. dev.) of the complete portfolio?
13. What is the Sharpe ratio of the Complete portfolio?
14. What is the Treynor ratio of Firm A if its beta is 0.92?

 

Suppose you have sample historical information for two firms: Year 2019 2020 2021 2022 Firm A historical return, Ra -1% 9% 20% 14% Firm B historical return, Rb 6% 19% 12% 7%