Question

Create a portfolio using the four stocks and information below:

Expected Return Standard Deviation Weight in Portfolio

Stock A 18.00% 19.00% 29.00%

Stock B 8.00% 16.00% 28.00%

Stock C 6.00% 31.00% 26.00%

Stock D 8.00% 16.00% 17.00%

Correlation (A,B) 0.5000

Correlation (A,C) 0.5200

Correlation (A,D) 0.8700

Correlation (B,C) 0.4700

Correlation (B,D) 0.2900

Correlation (C,D) 0.1200

(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 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?

Answer 1

1) Variance of A = Standard Deviation ² = 19² = 361

Variance of B = Standard Deviation ² = 16² = 256

  Variance of C = Standard Deviation ² = 31² = 961

Variance of D = Standard Deviation ² = 16² = 256

Correlation (A,A) = Co-variance (A,A) / (SD(A) * SD(A)) = Variance of A / (SD(A) * SD(A)) = 361/(19*19) = 1

2) Correlation (B,B) = Co-variance (B,B) / (SD(B) * SD(B)) = Variance of B / (SD(B) * SD(B)) = 256/(16*16) = 1

3) Correlation (C,C) = Co-variance (C,C) / (SD(C) * SD(C)) = Variance of C / (SD(C) * SD(C)) = 961/(31*31) = 1

4) Correlation (D,D) = Co-variance (D,D) / (SD(D) * SD(D)) = Variance of D / (SD(D) * SD(D)) = 256/(16*16) = 1

5) Co-variance(A,A) = Variance of A = 361.0000

6) Co-variance (A,B) = Correlation(A,B) * SD(A) * SD(B) = 0.5000 * 19 * 16 = 152.0000

7) Co-variance (A,C) = Correlation(A,C) * SD(A) * SD(C) = 0.5200 * 19 * 31 = 306.2800

8) Co-variance (A,D) = Correlation(A,D) * SD(A) * SD(D) = 0.8700 * 19 * 16 = 264.4800

9) Co-variance (B,A) = Co-variance (A,B) = 152.0000

10) Co-variance (B,B) = Variance (B) = 256.0000

11) Co-variance (B,C) = Correlation(B,C) * SD(B) * SD(C) = 0.4700 * 16 * 31 = 233.1200

12) Co-variance (B,D) = Correlation(B,D) * SD(B) * SD(D) = 0.2900 * 16 * 16 = 74.2400

13) Co-variance (C,A) = Co-variance (A,C) =306.2800

14) Co-variance (C,B) = Co-variance (B,C) = 233.1200

15) Co-variance (C,C) = Variance (C) = 961.0000

16) Co-variance (C,D) = Correlation(C,D) * SD(C) * SD(D) = 0.1200 * 31 * 16 = 59.5200

17) Co-variance (D,A) = Co-variance (A,D) =264.4800

18) Co-variance (D,B) = Co-variance (B,D) =74.2400

19) Co-variance (D,C) = Co-variance (C,D) =59.5200

20) Co-variance (D,D) = Variance (D) = 256.0000

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

= (18 * 0.29) + (8 * 0.28) + (6 * 0.26) + (8 * 0.17) = 10.38%

22) 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) * Correlation (A,B)] + [2* W(B) * W(C) * SD(B) * SD(C) * Correlation (B,C)] + [2* W(C) * W(D) * SD(C) * SD(D) * Correlation (C,D)] + [2* W(A) * W(D) * SD(A) * SD(D) * Correlation (A,D)] + [2* W(A) * W(C) * SD(A) * SD(C) * Correlation (A,C)] + [2* W(B) * W(D) * SD(B) * SD(D) * Correlation (B,D)]

= (19 * 0.29)² + (16 * 0.28)² + (31 * 0.26)² + (16 * 0.17)² + [2* 0.29 * 0.28 * 19 * 16 * 0.5000] + [2* 0.28 * 0.26 * 16 * 31 * 0.4700] + [2* 0.26 * 0.17 * 31 * 16 * 0.1200] + [2* 0.29 * 0.17 * 19 * 16 * 0.8700] + [ 2* 0.29 * 0.26 * 19 * 31 * 0.5200] + [2* 0.28 * 0.17 * 16 * 16 * 0.2900]

= 30.3601 + 20.0704 + 64.9636 + 7.3984 + 24.6848 + 33.942272 + 5.261568 + 26.077728 + 46.187024 + 7.067648

= 266.0135

where 'W' = weight and 'SD' = standard deviation

23) Standard Deviation on portfolio = root of 266.0135 = 16.3099%