Question

Suppose that you want to create a portfolio that consists of a corporate bond​ fund, X, and a common stock​ fund, Y. For a​ $1,000 investment, the expected return for X is $ $77 and the expected return for Y is $ 91. The variance for X is 1,375 and the variance for Y is 13,850. The covariance of X and Y is 4,624. Complete parts​ (a) through​ (d).

a. Compute the portfolio expected return and portfolio risk if you put

$ 300$300

in the corporate bond fund and

$ 700$700

in the common stock fund.

Answer 1

Solution :-

Given data:

Total investment = $1,000

Expected return for X = $77

Expected return for Y = $ 91

Variance for X, $Var_x$ =1,375

Variance for Y, $Var_{y}$ = 13,850

Co-variance of X and Y, $C.V_{xy}$ = 4,624

$\Rightarrow$ Here we have to calculate the portfolio expected return and portfolio risk.

Given as, X = $300 and Y = $700

$\Rightarrow$ Now consider the tabular form,

Security	X	Y
Return	= $77/ $1,000 = 0.077 = 7.7%	= $ 91 / $1,000 = 0.091 = 9.1%
Risk (S.D= $\sqrt{Var}$ )	= $\sqrt{1,375 }$ = 37.0809	=   $\sqrt{13,850}$ = 117.6860
$C.V_{xy}$	4,624

$\Rightarrow$ Now we have to calculate the Coefficient of correlation.

Here we know the formula, i.e

Coefficient of correlation = $\frac{ C.V_{xy }}{ SD of X * SD of Y }$

By substituting values we get,

Coefficient of correlation = $\frac{ 4624 }{ 37.0809 * 117.6860 }$

Coefficient of correlation = 1.0596

$\Rightarrow$ Now consider the tabular form,

Security	Weights (w)	Return (R)	W * R
X	= 300 / 1000 = 0.30	= 0.077	= 0.30 * 0.077 = 0.0231
Y	= 700 / 1000 = 0.70	= 0.091	= 0.70 *  0.091 = 0.0637
Return			= 0.0231 + 0.0637 = 0.0868 = 0.0868 * 100 = 8.68%

$\therefore$ Expected return = 8.68%

Now consider the Variance of the portfolio, to find out the risk.

Variance of the portfolio = $\left (W_{X} \right )^{2}* Var_x + \left (W_{Y} \right )^2* Var_y + 2* SD_x * SD_y * W_x * W_y * \left (Coefficient Of Correlation \right )xy$

By substituting values we get,

Variance of the portfolio =  

Variance of the portfolio = 123.75 +6786.5+1942.07639

Variance of the portfolio = 8852.32

Then, Risk = $\sqrt{Variance }$

$Risk = \sqrt{8852.32}$

Risk = 94.08680

$\therefore$ Risk = 94.08680