Question

You are given the following information about the stocks in a two-stock portfolio:

Stock	Return	Portfolio Weight	Standard Deviation
The Blue Hotel, Inc.	22%	45%	9%
Joys Food, Inc.	25%	55%	11%

Correlation coefficient between the two stocks is 0.5.

Using the information above, calculate the following:

1. The expected return of the portfolio,
2. The variance of the portfolio,
3. The standard deviation of the portfolio.

（All calculations must be shown for intermediate calculations）

Answer 1

Solution:
a.	Expected return of the portfolio	23.65	%
b.	variance of the portfolio	0.00775
	[If required variance in more or less decimal please comment in comment section , I will be definitely replying in that decimal format)
c.	Standard deviation of the portfolio	8.80	%
Working Notes:
	Here for ease of solving we assume
	Stock The Blue Hotel, Inc = Asset A
	Stock Joys Food, Inc. = Asset B
Notes:	The portfolio consist of two asset A & asset B, and in the portfolio Asset A (Blue Hotel) is 45% then balance of 55% in Asset B (Joys Food, Inc.)
	We computed Expected return of the portfolio using formula where Expected return of portfolio = Weighted average expected return of Individual assets = Weight of asset A x ErA + Weight of asset B x ErB
	And variance & standard deviation is computed using formula of computation of risk of a portfolio consisting of two risky assets. And we know square re of standard deviation is variance, so first we get variance with this formula then standard deviation by square rooting the variance.
	Variance of the portfolio = (S.d of Port folio )^2 =risk of a portfolio consisting of two risky assets using below formula
(S.d of Port folio )^2 = (WA^2 x Sd. Of A^2) + (WB^2 x Sd. Of B^2) + 2 x WA x WB x Sd. Of A x Sd. Of B x rA,B
Data Given
	Standard deviation of the portfolio = S.d of Port folio =??
	Weight of asset A (Blue Hotel)   = WA = 45% =0.45
	Weight of asset B (Joys Food, Inc.)= WB = 55% =0.55
	Standard deviation of the asset A (Blue Hotel) = S.d of A = 9%=0.09
	Expected return of Asset A (Blue Hotel) = ErA = 22%
	Standard deviation of the Asset B (Joys Food, Inc.)= S.d of B = 11%=0.11
	Expected return of Asset B   (Joys Food, Inc.)= ErB = 25%
	correlation coefficient (rA,B) = 0.50
First	Expected Return of the portfolio
Expected return of portfolio = Weighted average expected return of Individual assets
	= Weight of asset A x ErA + Weight of asset B x ErB
	=22% x 0.45 + 25% x 0.55
	=23.65%
Variance of the portfolio = (S.d of Port folio )^2
(S.d of Port folio )^2 = (WA^2 x Sd. Of A^2) + (WB^2 x Sd. Of B^2) + 2 x WA x WB x Sd. Of A x Sd. Of B x rA,B
(S.d of Port folio )^2 = (0.45^2 x 0.09^2) + (0.55^2 x 0.11^2) + 2 x 0.45 x 0.55 x 0.09 x 0.11 x 0.50
(S.d of Port folio )^2 =0.00775075
(S.d of Port folio )^2 =0.00775
Hence	Variance of the portfolio = (S.d of Port folio )^2= 0.00775
Now	Standard deviation of the portfolio
	(S.d of Port folio )^2 = variance = 0.00775075
	(S.d of Port folio )^2 = 0.00775075
	S.d of Port folio = ( 0.00775075)^(1/2)
	S.d of Port folio = 0.088038344
	S.d of Port folio = 8.80383%
	S.d of Port folio = 8.80%