Question

In: Finance

Stocks A and B have the following​ returns: Stock A Stock B 1 0.08 0.06 2...

Stocks A and B have the following​ returns:

Stock A

Stock B

1

0.08

0.06

2

0.05

0.01

3

0.12

0.06

4

−0.04   

0.03

5

0.08

−0.02   

a. What are the expected returns of the two​ stocks?

b. What are the standard deviations of the returns of the two​ stocks?

c. If their correlation is0.45​, what is the expected return and standard deviation of a portfolio of 62​%stock A and 38​%stock​ B?

Solutions

Expert Solution

Answer (a)

Expected reutrn of Stock A (mean of stock A) = Sum of all returns / Number of observations

= (0.08 + 0.05 + 0.12 - 0.04 + 0.08) / 5

= 0.058 or 5.80%

Expected reutrn of Stock B (mean of stock B) = Sum of all returns / Number of observations

= (0.06 + 0.01 + 0.06 + 0.03 - 0.02) / 5

= 0.028 or 2.80%

Answer (b)

Standard deviation of stock A:

Return (r) Mean (x) r-x (r-x)2
0.08 0.058 0.022 0.000484
0.05 0.058 -0.008 0.00064
0.12 0.058 0.062 0.003844
-0.04 0.058 -0.098 0.009604
0.08 0.058 0.022 0.000484
Total 0.01448

Standdard deviation of stock A = [(Sum of all (r-x)2) / (Number of observations - 1)]0.50

= [0.01448 / (5 - 1)]0.50

= 0.0602 or 6.02%

Standard deviation of stock B:

Return (r) Mean (x) r-x (r-x)2
0.06 0.028 0.032 0.001024
0.01 0.028 -0.018 0.000324
0.06 0.028 0.032 0.001024
0.03 0.028 0.002 0.000004
-0.02 0.028 -0.048 0.002304
Total 0.00468

Standdard deviation of stock B = [(Sum of all (r-x)2) / (Number of observations - 1)]0.50

= [0.00468 / (5 - 1)]0.50

= 0.0342 or 3.42%

Answer (c)

Weight of stock A (WA) = 62%

Weight of stock B (WB) = 38%

Expected return of portfolio = (Mean of stock A * WA) + (Mean of stock B * WB)

= (5.80% * 62%) + (2.80% * 38%)

= 4.66%

Standard deviation of portfolio = [(WA2 * Standard deviation of A2)] + (WB2 * Standard deviation of B2) + (2 * WA * WB * Standard deviation of A * Standard deviation of B * Correlation)]0.50

= [(0.622 * 0.06022) + (0.382 * 0.03422) + (2 * 0.62 * 0.38 * 0.0602 * 0.0342 * 0.45)]0.50

= 4.47%


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