Question

3. Create a portfolio using the four stocks and information below:

	Expected Return	Standard Deviation	Weight in Portfolio
Stock A	26.00%	39.00%	18.00%
Stock B	19.00%	20.00%	23.00%
Stock C	32.00%	31.00%	14.00%
Stock D	29.00%	40.00%	45.00%
----------------------	----------------------	----------------------	----------------------
Correlation (A,B)	0.6100	----------------------	----------------------
Correlation (A,C)	0.2500	----------------------	----------------------
Correlation (A,D)	0.9000	----------------------	----------------------
Correlation (B,C)	0.4500	----------------------	----------------------
Correlation (B,D)	0.7300	----------------------	----------------------
Correlation (C,D)	1.0000	----------------------	----------------------

(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?

Answer 1

Soln -> Variance = square of standard deviation.

So, i) Variance of A = 0.39² = 0.1521 = 15.21%

Variance of B = 0.20² = 0.04 = 4%

Variance of C = 0.31² = 0.0961 = 9.61%

Variance of D = 0.40² = 0.1600= 16%

=> Correlation on same variable =1

So, Correlation(A,A) = Correlation(B,B) = Correlation(C,C) = Correlation(D,D) = 1.

Now, Covariance(1,2)= s₁.s₂ * Correlation(1,2)

Also, Covariance(1,1) = s₁² * 1 = var(1)

So, Cov(A,A) = 0.1521, Cov(B,B) = 0.04, Cov(C,C) = 0.0961 Cov(D,D) = 0.16

Moreover, Cov(1,2) = Cov(2,1). and Correlation(1,2) = Correlation(2,1)

So, Cov(A,B) = Cov(B,A) = 0.39*0.2*0.61 = 0.04758

Cov(A,C) = Cov(C,A) = 0.39*0.31*0.25 = 0.030225

Cov(A,D) = Cov (D,A) = 0.39*0.4*0.9 = 0.1404

Cov(B,C) = Cov(C,B) = 0.2*0.31*0.45 = 0.0279

Cov(B,D) = Cov(D,B) = 0.2*0.4*0.73 = 0.0584

Cov(C,D) = Cov(D,C) = 0.31*0.4*1 = 0.124

Now, expeected return on portfolio = W_A.E(R_A) + W_B.E(R_B) + W_C.E(R_C) + W_D.E(R_D)

So, E(R_P) = 0.18*26% + 0.23*19% + 0.14*32% + 0.45*29% = 26.58%

Variance of portfolio with 4 assets is possible with excel. Please check the same in excel.