Create a portfolio using the three stocks and information below: (Do not round i

Question

Create a portfolio using the three stocks and information below:

(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 Correlation (A,A)?

What is the Correlation (B,B)?

What is the Correlation (C,C)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (A,C)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the Covariance (B,C)?

What is the Covariance (C,A)?

What is the Covariance (C,B)?

What is the Covariance (C,C)?

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?

Expected Return Standard Deviation Weight in Portfolio Stock A 34.00% 31.00% 28.00% Stock B 13.00% 30.00% 33.00% Stock C 23.00% 33.00% 39.00% ---------------------- ---------------------- ---------------------- ---------------------- Correlation (A,B) 0.3800 ---------------------- ---------------------- Correlation (A,C) 0.5900 ---------------------- ---------------------- Correlation (B,C) 0.8300 ---------------------- ----------------------

Explanation / Answer

Answer :-:variance formula :- (standard deviation)2

Data given = standard deviation (S.D.) of A = 31%,

S.D. Of B = 30%, S.D. OF C = 33%

1)Variance of Stock A = (31%)2 = 0.0961

2) Variance of stock B = (30%)2 = 0.09

3) Variance of stock C = (33%)2 = 0.1089

4) Expected return of portfolio (RP) :-

Formula used :- expected return *weights

Data given :- expected return of A = 34%, B = 13%, C = 23%

Weight of A = 28%, B = 33%, C = 39%

Rp = 34% * 28% + 13% * 33% + 23% * 39%

Rp = 9.52 + 4.29 + 8.97

Expected return of portfolio (Rp)  = 22.78 %

5) Formula used : Standard deviation of one stock * standard deviation of other stock

Covariance (A, A) = 31% * 31% = 0.0961

In other words covariance (A, A) shall be variance of A

6) Formula used :- correlation (A, B) = Covariance (A, B) / ( Standard deviation of A * Standard deviation of B)

= 0.3800 = Covariance (A, B) /(31% * 30%)

= 0.3800 = Covariance (A, B) /0.093

= Covariance (A, B) = 0.0353

7) Covariance (A, C) :-

= 0.5900 = Covariance (A, C) /(31% * 33%)

= Covariance (A, C) = 0.5900 * 0.1023

= Covariance (A, C) = 0.0603

8) Covariance (B, A) shall be same as Covariance(A, B)

9) Covariance (C, A) shall be same as Covariance (A, C)

10) Covariance (B, B) shall be variance of B

Covariance of (B,B) = 0.09

11) Covariance (C, C) shall be variance of C

Covariance (C, C) = 0.1089

12) Covariance (B, C)

= 0.8300 = Covariance (B, C) /(30% * 33%)

= 0.8300 = Covariance (B, C) /0.099

= Covariance (B, C) = 0.8300 * 0.099

= Covariance (B, C) = 0.0822

13) Covariance (C, B) shall be same as Covariance( B, C)

Covariance (C, B) = 0.0822

14)Correlation (A, A), Correlation (B, B), Correlation (C, C) shall be 1

Formula used :

rA, A = Covariance (A, A) /S. D of A * S.D. of B

rA, A = variance of A / Variance of A

rA, A = 1

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