Question

4. Consider the following annual returns on 2 stocks: (10 pts)

Year	HCA	WLMT
2017	35%	3%
2016	20%	5%
2015	3%	9%
2014	-12%	15%

1. Calculate the expected return on each stock. (2 pts)
2. Calculate the standard deviation on each stock. (3 pts)
3. Assume you create a portfolio with equal weight in each stock. Calculate the expected return of the portfolio. (2 pts)
4. Calculate the standard deviation of the equally weighted portfolio. (3 pts)

Answer 1

	(Return in %)
Year	HCL(x)	WLMT(y)	(x-(∑x/n))^2	(y-(∑y/n))^2	(x-(∑x/n))(y-(∑y/n))
2014	-12	15	552.25	49.00	-164.5
2015	3	9	72.25	1.00	-8.5
2016	20	5	72.25	9.00	-25.5
2017	35	3	552.25	25.00	-117.5
Total	46	32	1249.00	84.00	828

Ans a.

			HCL(x)	WLMT(y)
Expected Return = ∑x/n		Total return/total years	11.50	8.00

Ans b

Standard deviation=		Formula	((∑(x-(∑x/n))^2)/n)^(1/2)	((∑(y-(∑y/n))^2)/n)^(1/2)
		S.D	17.67	4.58
		Working	(1249/4)^(1/2)	(84/4)^(1/2)

Ans c

Expected Return of Portfolio=	(Return of stock A* weight of stock A) + (Return of stock B* weight of stock B)
(11.5*0.5)+(8*0.5)
			9.75

Ans d

covariance (x,y)=	(∑(x-(∑x/n))(y-(∑y/n)))/n
	207	(828/4)

Standard Deviation of Portfolio=	[{(weight of A)^2 * (sigma of A)^2} + {(weight of B)^2 + (sigma of B)^2} + {2*(weight of A)*(weight of B)*Covariance of A&B }^(1/2)
=	(((0.5^2)*(17.67^2))+((0.5^2)*(4.58^2))+(2*0.5*0.5*207))^(1/2)
=	13.67