Question

In: Finance

Create a portfolio using the four stocks and information below: Expected Return Standard Deviation Weight in...

Create a portfolio using the four stocks and information below:

Expected Return Standard Deviation Weight in Portfolio
Stock A 21.00% 21.00% 15.00%
Stock B 5.00% 17.00% 28.00%
Stock C 7.00% 12.00% 11.00%
Stock D 22.00% 22.00% 46.00%
---------------------- ---------------------- ---------------------- ----------------------
Correlation (A,B) 0.7000 ---------------------- ----------------------
Correlation (A,C) 0.4900 ---------------------- ----------------------
Correlation (A,D) 0.2500 ---------------------- ----------------------
Correlation (B,C) 0.4400 ---------------------- ----------------------
Correlation (B,D) 0.9600 ---------------------- ----------------------
Correlation (C,D) 0.2000 ---------------------- ----------------------

(Do not round intermediate calculations. Record your answers in decimal form and round your answers to 4 decimal places. Ex. x.xxxx)

What is the variance of A?

What is the variance of B?

What is the variance of C?

What is the variance of D?

What is the Correlation (A,A)?

What is the Correlation (B,B)?

What is the Correlation (C,C)?

What is the Correlation (D,D)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (A,C)?

What is the Covariance (A,D)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the Covariance (B,C)?

What is the Covariance (B,D)?

What is the Covariance (C,A)?

What is the Covariance (C,B)?

What is the Covariance (C,C)?

What is the Covariance (C,D)?

What is the Covariance (D,A)?

What is the Covariance (D,B)?

What is the Covariance (D,C)?

What is the Covariance (D,D)?

What is the expected return on the portfolio above?

What is the variance on the portfolio above?

What is the standard deviation on the portfolio above?

make sure they are all answered and they are correct please

Solutions

Expert Solution

1) Variance of A = Standard Deviation 2 = 212 = 441

2) Variance of B = Standard Deviation 2 = 172 = 289

3) Variance of C = Standard Deviation 2 = 122 = 144

4) Variance of D = Standard Deviation 2 = 222 = 484

5) Correlation (A,A) = Co-variance (A,A) / (SD(A) * SD(A)) = Variance of A / (SD(A) * SD(A)) = 441/(21*21) = 1

6) Correlation (B,B) = Co-variance (B,B) / (SD(B) * SD(B)) = Variance of B / (SD(B) * SD(B)) = 289/(17*17) = 1

7) Correlation (C,C) = Co-variance (C,C) / (SD(C) * SD(C)) = Variance of C / (SD(C) * SD(C)) = 144/(12*12) = 1

8) Correlation (D,D) = Co-variance (D,D) / (SD(D) * SD(D)) = Variance of D / (SD(D) * SD(D)) = 484/(22*22) = 1

9) Co-variance(A,A) = Variance of A = 441

10) Co-variance (A,B) = Correlation(A,B) * SD(A) * SD(B) = 0.7000 * 21 * 17 = 249.90

11) Co-variance (A,C) = Correlation(A,C) * SD(A) * SD(C) = 0.4900 * 21 * 12 = 123.48

12) Co-variance (A,D) = Correlation(A,D) * SD(A) * SD(D) = 0.2500 * 21 * 22 = 115.50

13) Co-variance (B,A) = Co-variance (A,B) = 249.90

14) Co-variance (B,B) = Variance (B) = 289

15) Co-variance (B,C) = Correlation(B,C) * SD(B) * SD(C) = 0.4400 * 17 * 12 = 89.76

16) Co-variance (B,D) = Correlation(B,D) * SD(B) * SD(D) = 0.9600 * 17 * 22 = 359.04

17) Co-variance (C,A) = Co-variance (A,C) =123.48

18) Co-variance (C,B) = Co-variance (B,C) = 89.76

19) Co-variance (C,C) = Variance (C) = 144

20) Co-variance (C,D) = Correlation(C,D) * SD(C) * SD(D) = 0.2000 * 12 * 22 = 52.80

21) Co-variance (D,A) = Co-variance (A,D) =115.50

22) Co-variance (D,B) = Co-variance (B,D) =359.04

23) Co-variance (D,C) = Co-variance (C,D) =52.80

24) Co-variance (D,D) = Variance (D) = 484

25) Expected Return of portfolio = sum (Expected return (Stock) * Weight(Stock))

= (21 * 0.15) + (5 * 0.28) + (7 * 0.11) + (22 * 0.46) = 15.44%

26) Variance of Portfolio = [SD(A) * W(A)]2 + [SD(B) * W(B)]2 + [SD(C) * W(C)]2 + [SD(D) * W(D)]2 + [2* W(A) * W(B) * SD(A) * SD(B) * Cor (A,B)] + [2* W(B) * W(C) * SD(B) * SD(C) * Cor (B,C)] + [2* W(C) * W(D) * SD(C) * SD(D) * Cor (C,D)] + [2* W(A) * W(D) * SD(A) * SD(D) * Cor (A,D)] + [2* W(A) * W(C) * SD(A) * SD(C) * Cor (A,C)] + [2* W(B) * W(D) * SD(B) * SD(D) * Cor (B,D)]

= (21% * 0.15)2 + (17% * 0.28)2 + (12% * 0.11)2 + (22% * 0.46)2 + [2* 0.15 * 0.28 * 21% * 17% * 0.7] + [2* 0.28 * 0.11 * 17% * 12% * 0.44] + [2* 0.11 * 0.46 * 12% * 22% * 0.2] + [2* 0.15* 0.46 * 21% * 22% * 0.25] + [ 2* 0.15 * 0.11* 21% * 12% * 0.49] + [2* 0.28 * 0.46 * 17% * 22% * 0.96]

= 9.92 + 22.66 + 1.74 + 102.41 + 20.99 + 5.53 + 5.34 + 15.94 + 4.07 + 92.49

= 281.09

27) Standard Deviation on portfolio = root of 281.09 = 16.77%


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