Question

here are two stocks in the market, Stock A and Stock B. The price of Stock A today is $78. The price of Stock A next year will be $67 if the economy is in a recession, $90 if the economy is normal, and $100 if the economy is expanding. The probabilities of recession, normal times, and expansion are .23, .57, and .20, respectively. Stock A pays no dividends and has a correlation of .73 with the market portfolio. Stock B has an expected return of 14.3 percent, a standard deviation of 34.3 percent, a correlation with the market portfolio of .27, and a correlation with Stock A of .39. The market portfolio has a standard deviation of 18.3 percent. Assume the CAPM holds.

a-1.	What is the return for each state of the economy for Stock A? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
a-2.	What is the expected return of Stock A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

a-3.	What is the variance of Stock A? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

a-4.	What is the standard deviation of Stock A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

a-5.	What is the beta of Stock A? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

a-6.	What is the beta of Stock B? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

	a-1. Recession % Normal % Expansion % a-2. Expected return % a-3. Variance a-4. Standard deviation % a-5. Beta of Stock A a-6. Beta of Stock B

b-1.	What is the expected return of a portfolio consisting of 70 percent of Stock A and 30 percent of Stock B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b-2.	What is the standard deviation of a portfolio consisting of 70 percent of Stock A and 30 percent of Stock B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c.	What is the beta of the portfolio in part (b)? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
	b-1. Expected return % b-2. Standard deviation % c. Beta of the portfolio

Answer 1

The excel sheet showing the results is as follows: A E F 15 a-1 Economy State Probability Return 16 Initial Price Expected Price Gain 17 -14.10 % 18 Recession 0.23 78 67 -11 19 Normal 0.57 78 90 12 15.38% 28.21 % Expanding 20 0.20 78 100 22 21 22 23 24 a-2 25 Expected Return of Stock A 11.17% 26 27 a-3 Variance of Stock A 28 0.0215 29 30 31 a-4 Standard deviation of Stock A 32 14.67% 33 34 35 а-5 Standard deviation of Stock A 36 14.67% 37 Standard deviation of Market 18.30% Correlation of Stock A with Market 38 0.73 39 Beta of Stock A 0.585 40 41 42 43 a-6 44 Standard deviation of Stock B 45 34.30% Standard deviation of Market 46 18.30% Correlation of Stock B with Market 47 0.27 48 Beta of Stock B 49 0.506

A В C E 52 b-1 53 11.17% Expected Return of Stock A 54 0.7 Weight of Stock A 55 56 14.30% Expected Return of Stock B 57 Weight of Stock B 58 0.3 59 12.11% Expected Return of Portfolio 60 61 62 63 b-2 Standard deviation of Stock A 14.67% 64 0.7 Weight of Stock A 65 66 34.30% Standard deviation of Stock B 67 Weight of Stock B 68 0.3 69 Correlation of Stocks 0.39 70 71 17.14% Standard Deviation of Portfolio 72 73 74 75 c 76 Beta of Stock A 0.585 77 Weight of Stock A 0.7 78 79 Beta of Stock B 0.506 80 Weight of Stock B 81 0.3 82 Beta of Portfolio 0.561 83

The excel sheet showing the formulas used is as follows: A B C E F G 15 a-1 Economy State Probability Expected Price 16 Initial Price Gain Return 17 -E18- D18 =F18/D18 67 Recession 18 0.23 78 0.57 -E19-D19 -E20-D20 -F19 /D19 78 90 19 Normal 20 Expanding -F20/D20 0.2 78 100 21 22 23 24 a-2 (G18 C18 ) + (G19 C19)+(G20*C20) Expected Return of Stock A 25 26 27 a-3 - ( G18- E25 ) 2 +C18+(G19-E25) 2*C19+(G20-E25) 2*C20 Variance of Stock A 28 29 30 31 a-4 Standard deviation of Stock A -E28 0.5 32 33 34 35 a-5 Standard deviation of Stock A Standard deviation of Market -E32 36 0.183 37 0.73 Correlation of Stock A with Market 38 39 - ( E36 Beta of Stock A E38 ) E37 40 A В C D E 43 a-6 44 Standard deviation of Stock B Standard deviation of Market 0.343 0.183 45 46 0.27 Correlation of Stock B with Market 47 48 ( E45 *E47 ) E46 Beta of Stock B 49 50 51 52 b-1 53 Expected Return of Stock A 0.1117 54 Weight of Stock A 0.7 55 56 0.143 Expected Return of Stock B 57 0.3 Weight of Stock B 58 59 Expected Retur of Portfolio (D54*D55) + (D57*D58) 60 61 62 63 b-2 Standard deviation of Stock A14.67% Weight of Stock A 64 0.7 65 66 Standard deviation of Stock B 0.343 Weight of Stock B 67 0.3 68 69 Correlation of Stocks 0.39 70 71 ( (D64*D65 ) 2 +(D67*D68) 2+2*D64 D65 D67*D68*D70) 0.5| Standard Deviation of Portfolio 72

A D B C 75 C 76 Beta of Stock A 77 0.585 Weight of Stock A 0.7 78 79 Beta of Stock B 80 0.506 Weight of Stock B 0.3 81 82 - (D77*D78)+(D80*D8 1) Beta of Portfolio 83