Question

A broker has decided to to build a portfolio of two stocks for a retired individual. The first stock "G" has an expected return of 10.25% with a variance of 73.96. The second stock "K" has an expected return of 7.75% with a variance of 18.49. The correlation between the two stocks is -0.58.

a) With the given information, what is the covariance between the two stocks, to two decimal places?

b) With the given information, what is the variance, to two decimal places, of a portfolio of the two stocks where seven times as much is invested in stock K compared to how much is invested in stock G?

c)  With the given information, what is the standard deviation, to two decimal places, of a portfolio of the two stocks where seven times as much is invested in stock K compared to how much is invested in stock G?

d) With the given information, what is the expected return, to two decimal places, of a portfolio of the two stocks where seven times as much is invested in stock K compared to how much is invested in stock G?

Answer 1

Given:

Let investment in G be x, so, investment in K = 7x

But the total weight of the investment should be 1

Hence, x+7x=1 ==> 8x = 1 ==> x= 1/8 =0.125

So, weight of G= 0.125, and weight of K= 0.875

Correlation (r) = -0.58

SD of G= 73.96 ^1/2 = 8.6%, SD of K= 18.49^1/2 = 4.3%

a. Co variance = r * = -0.58 * 8.6 * 4.3 = -21.45%

b, c , d calculated below:

Variance of the portfolio with the mentioned weights is 10.62 %²

^{SD of the portfolio = 3.26%}

Expected return = 8.06%

Weights	Expected return	Variance	Standard deviation
G	K	G	K	Portfolio return	G	K	G	K	Standard deviation of portfolio	Variance of portfolio
0.125	0.875	10.25%	7.75%	8.06%	73.96	18.49	8.60	4.30	3.26	10.62%2

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