Stock and Market Portfolio
Monique L. Palmer
FIN :534 Financial management
Final Exam.
13December2010
Solve the following problem showing all the necessary steps and computations.
1. Using the data in the following table, estimate (a) the average return and volatility for each stock, (b) the covariance between the stocks, and (c) the correlation between these two stocks.
A.
Stock A
-10+20+5-5+9/6 = 3.5%
Stock B
21+30+7-3-8+25/6 = 12%
B.
Covariance = 1/5 (-0.1-0.035)(0.21-0.04) + (0.2-0.035)(0.3-0.12) + (0.05-0.035)(0.07-0.12) + (-0.05-0.035)(-0.03-0.12) + (0.02-0.035)(-0.08-.012) + (0.09-0.035)(0.25-.012) = 0.00794
Variance of A = 1/5 (-0.1-0.035)2 + (0.2-0.08)2 + (0105 – 0.035)2 + (-0.05-0.035)2 + (0.02-0.035)2 + (0.09-0.035)2 = 0.01123
Variance of B = 1/5 (0.21-0.12)2 + (0.3-0.12)2 + (0.07-0.12)2 + (-0.03-0.12)2 (-0.08-0.12)2 + (0.25-0.12)2 = 0.02448
C. Correlation = 0.00794/(0.01123) (0.02448) = 0.479
12-4. Suppose all possible investment opportunities in the world are limited to the five stocks listed in the table below.
What does the market portfolio consist of (what are the portfolio weights)?
The market portfolio consists of the market values (share price x number of shares) of ALL assets:
A: $10 x 10m = $100m and weight 100/1314 = 7.61%
B: $20 x 12m = $240m and weight 240/1314 = 18.26%
C: $8 x 3m = $24m and weight 24/1314 = 1.83%
D: $50 x 1m = $50m and weight 50/1314 = 3.81%
E: $45 x 20m = $900m and weight 900/1314 = 68.49%
The total market value of the market portfolio is 100+240+24+50+900=$1314m
Using the data in Problem 4, suppose you are holding a market portfolio, and have invested $12,000 in Stock C.
a. How much have you invested in Stock A? 12,000 x 100/24= $50,000
b. How many shares of Stock C do you hold? 12,000 x 240/24)/20 = 6,000 shares c. If the price of Stock C suddenly drops to $4 per share, what trades would you need to make to maintain a market portfolio? There is no trade necessary, because the portfolio’s
FIN :534 Financial management
Final Exam.
13December2010
Solve the following problem showing all the necessary steps and computations.
1. Using the data in the following table, estimate (a) the average return and volatility for each stock, (b) the covariance between the stocks, and (c) the correlation between these two stocks.
A.
Stock A
-10+20+5-5+9/6 = 3.5%
Stock B
21+30+7-3-8+25/6 = 12%
B.
Covariance = 1/5 (-0.1-0.035)(0.21-0.04) + (0.2-0.035)(0.3-0.12) + (0.05-0.035)(0.07-0.12) + (-0.05-0.035)(-0.03-0.12) + (0.02-0.035)(-0.08-.012) + (0.09-0.035)(0.25-.012) = 0.00794
Variance of A = 1/5 (-0.1-0.035)2 + (0.2-0.08)2 + (0105 – 0.035)2 + (-0.05-0.035)2 + (0.02-0.035)2 + (0.09-0.035)2 = 0.01123
Variance of B = 1/5 (0.21-0.12)2 + (0.3-0.12)2 + (0.07-0.12)2 + (-0.03-0.12)2 (-0.08-0.12)2 + (0.25-0.12)2 = 0.02448
C. Correlation = 0.00794/(0.01123) (0.02448) = 0.479
12-4. Suppose all possible investment opportunities in the world are limited to the five stocks listed in the table below.
What does the market portfolio consist of (what are the portfolio weights)?
The market portfolio consists of the market values (share price x number of shares) of ALL assets:
A: $10 x 10m = $100m and weight 100/1314 = 7.61%
B: $20 x 12m = $240m and weight 240/1314 = 18.26%
C: $8 x 3m = $24m and weight 24/1314 = 1.83%
D: $50 x 1m = $50m and weight 50/1314 = 3.81%
E: $45 x 20m = $900m and weight 900/1314 = 68.49%
The total market value of the market portfolio is 100+240+24+50+900=$1314m
Using the data in Problem 4, suppose you are holding a market portfolio, and have invested $12,000 in Stock C.
a. How much have you invested in Stock A? 12,000 x 100/24= $50,000
b. How many shares of Stock C do you hold? 12,000 x 240/24)/20 = 6,000 shares c. If the price of Stock C suddenly drops to $4 per share, what trades would you need to make to maintain a market portfolio? There is no trade necessary, because the portfolio’s