Question

10. What is the expected return and standard deviation of a portfolio comprised of $7,500 in stock M and $5000 in stock N and covariance of M and N is 20%? (20 Points) State of Probability of Returns if State Occurs Economy State of Economy Stock M Stock N Boom 10% 18% 10% Normal 75% 7% 8% Recession 15% -20% 6%

Answer 1

Solution:
	Expected Return of the Portfolio	5.59	%
	Standard deviation of the portfolio	6.75	%
Working Notes:
	This problem can be solved two method one using given covariance and 2nd without using Covariance and under both method you will get same answer . And I m solving below using 2nd method without using given Covariance.
Note	If you want to solve using 1st method please let me know in comment section I will upload that too below this method.
	First of we will calculate weight of each stock in the portfolio.
	Amount of investment in Stock M	7500
	Amount of investment in Stock N	5000
	Total investment in portfolio	12500
	Weight of stock M in portfolio WM
	=(amount in M/total investment) = 7500/12500= 0.60
	Weight of stock N in portfolio WN
	=(amount in N/total investment) = 5000/12500= 0.40
Then	We calculate return of the portfolio at each state of economy the return of portfolio then variance and at last standard deviation.
Return at Boom (rb)	Return of portfolio at Boom (rb)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 18% x 0.60 + 10% x 0.40
	=14.80%
Return at Normal   (r Normal)	Return at Normal    (r Normal)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 7% x 0.60 + 8% x 0.40
	=7.40%
Return at Recession                 (r Recession)	Return at Recession   (r Recession)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= -20% x 0.60 + 6% x 0.40
	= -9.60%
Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=10% x (14.80%) + 75% x (7.40%) + 15% x ( -9.60%)
	=5.59%
The variance of this portfolio = Sum of [(Prob. Of each state) x ( (Return of the portfolio at each state - Expected return of the portfolio))^2 ]
'=10% x (14.80% - 5.59%)^2 + 75% x ( 7.40% - 5.59%)^2 + 15% x (-9.60% - 5.59%)^2
=0.0045549900
=0.00455499
	The standard deviation of Portfolio = Square root of the variance of portfolio
	The standard deviation of Portfolio = (0.00455499)^(1/2)
	The standard deviation of Portfolio =0.06749066
	The standard deviation of Portfolio	6.75%
Please feel free to ask if anything about above solution in comment section of the question.