Question

State of Economy	Probability	Stock X	Stock Y
Recession	20%	$400	?
Normal	60%	$550	?
Expansion	20%	$600	?
	Expected Return (ER)	?	9%
	Standard Deviation	?	21%
	Correlation of the Stock to the market	0.8	0.2
	Correlation of X and Y	0.6

The price of Stock X today is $500, market variance is 100% and T-Bill return is 2%

a) Find the expected return of stock X

b) Find the standard deviation of stock X

c) Given the choice between the two stocks which would you prefer?

d) Calculate the covariance of stock X and Y

e) Calculate the covariance of stock X to the market

f) Calculate the covariance of the market to itself

Answer 1

(a) E(X)=sum(x*p(x))=500

(b) standard deviation(X)=sqrt(variance(x))=sqrt(4000)=63.25

variance(X)=E(X2)-E(X)*E(X)=254000-500*500=4000

(c) since expected return of stock X is more as compared to Y , so X would prefer

(d) covaiance (X,Y)=r(x,Y)*sd(X)*sd(Y)=0.6*63.25*9=341.55

(e) covaiance (X,market)=r(x,market)*sd(X)*sd(market)=0.8*63.25*10=506

sd(market)=sqrt(market)=sqrt(100)=10

(f) covaiance (market,market)=r(market,market)*sd(market)*sd(market)=1*10*10=100

correlation between a variable to itself is 1 and covariance of a variable to itself is variance of the variable

following information has been generated using ms-excel

x	p(x)	x*p(x)	x2*p(x)
400	0.2	80	32000
500	0.6	300	150000
600	0.2	120	72000
sum=	1	500	254000
	variance=	E(x2)-E(x)*E(x)=	4000
	sd=	sqrt(variance)=	63.25