Problem 1- Table below shows the historical returns for Companies A, B and C
|
Year
|
Company A
|
Company B
|
Company C
|
|
1
|
30%
|
26%
|
47%
|
|
2
|
7%
|
15%
|
-54%
|
|
3
|
18%
|
-14%
|
15%
|
|
4
|
-22%
|
-15%
|
7%
|
|
5
|
-14%
|
2%
|
-28%
|
|
6
|
10%
|
-18%
|
40%
|
|
7
|
26%
|
42%
|
17%
|
|
8
|
-10%
|
30%
|
-23%
|
|
9
|
-3%
|
-32%
|
-4%
|
|
10
|
38%
|
28%
|
75%
|
- Estimate the average return and standard deviation of each company.
- Estimate the correlations between Company A and B, A and C, as well as B and C.
Problem 2
Table below shows the historical returns for Companies A, B and C
|
Year
|
Company A
|
Company B
|
Company C
|
|
1
|
30%
|
26%
|
47%
|
|
2
|
7%
|
15%
|
-54%
|
|
3
|
18%
|
-14%
|
15%
|
|
4
|
-22%
|
-15%
|
7%
|
|
5
|
-14%
|
2%
|
-28%
|
|
6
|
10%
|
-18%
|
40%
|
|
7
|
26%
|
42%
|
17%
|
|
8
|
-10%
|
30%
|
-23%
|
|
9
|
-3%
|
-32%
|
-4%
|
|
10
|
38%
|
28%
|
75%
|
1. If one investor has a portfolio consisting of 50% Company A and 50% Company B, what are the average portfolio return and standard deviation? What is Sharpe ratio if the risk- free rate is 3.8%?
2. If another investor has a portfolio consisting of 1/3 Company A, 1/3 Company B and 1/3 Company C, what are the average portfolio return and standard deviation? What is Sharpe ratio if the risk-free rate is 3.8%?
Problem 3
What would happen to the portfolio risk if more and more randomly selected stocks were added?
Problem 4
You currently have $300,000. You want to invest it in the following three assets: 10-year US Treasury bond with coupon rate 3.8%, Blandy and Gourmange stocks below:
|
Year
|
Blandy
|
Gourmange
|
| |
|
|
|
Average annual return
|
6.4%
|
9.2%
|
|
Standard deviation of annual return
|
25.2%
|
38.6%
|
| |
|
|
|
Correlation between Blandy and Gourmange
|
0.11
|
|
Your goal is to have the expected return of 6.8% with a minimum portfolio risk. How much money should you allocate to these three assets?
Problem 5
Given the following information:
|
Year
|
Market
|
Blandy
|
Gourmange
|
|
1
|
30%
|
26%
|
47%
|
|
2
|
7%
|
15%
|
-54%
|
|
3
|
18%
|
-14%
|
15%
|
|
4
|
-22%
|
-15%
|
7%
|
|
5
|
-14%
|
2%
|
-28%
|
|
6
|
10%
|
-18%
|
40%
|
|
7
|
26%
|
42%
|
17%
|
|
8
|
-10%
|
30%
|
-23%
|
|
9
|
-3%
|
-32%
|
-4%
|
|
10
|
38%
|
28%
|
75%
|
- Estimate the betas for Blandy and Gourmange companies?
- If you have a portfolio of 25% Blandy and 75% Gourmange, what is the beta for your portfolio?
Problem 6
Based on the Capital Asset Pricing Model (CAPM) and the diagram below, what is the return of the stock if its beta is 1.2 or 0.8?
