Question

2. The following table shows that the economy next year has three possible states: Good , Average and Poor. It also shows the correponding probability of each states. The column of stock A shows the investment rate of return (%) for stock A; and the column of Stock B shows the invesment rate of return for stock B.

		Return (%)
State	Probability	Stock A	Stock B
Good	0.4	15	8
Average	0.5	9	10
Poor	0.1	6	12

a) Calculate the expected value of stock A and B’s return (1 mark)

b) Calculate the variance of the return of Stock A and Stock B

c) Calculate the covariance and correlation of Stock A and Stock B’s return

d) An investor invests in 40% of his money in stock A and 60% of his money in stock B, what is his portfolio’s expected return? What is his portfolio’s variance and standard deviation?

Answer 1

x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)	xy*f(x,y)
15	8	0.4	6	3.2	90	25.6	48
9	10	0.5	4.5	5	40.5	50	45
6	12	0.1	0.6	1.2	3.6	14.4	7.2
	Total	1	11.1	9.4	134.1	90	100.2
	E(X)=ΣxP(x,y)=					11.1
	E(X2)=Σx2P(x,y)=					134.1
	E(Y)=ΣyP(x,y)=					9.4
	E(Y2)=Σy2P(x,y)=					90
	Var(X)=E(X2)-(E(X))2=					10.89
	Var(Y)=E(Y2)-(E(Y))2=					1.64
	E(XY)=ΣxyP(x,y)=					100.2

a)from above:

  expected value of stock A =11.1

  expected value of stock B =9.4

b)

variance of the return of Stock A =10.89

variance of the return of Stock B =1.64

c)

Cov(X,Y)=E(XY)-E(X)*E(Y)=					-4.14
Correlation =Cov(X,Y)/sqrt(Var(X)*Var(Y))=					-0.9796

d)

here wA =0.4 and wB =0.6

expected value=wx*E(x)+wy*E(Y)=

10.08

Variance = (wxơx)2 + (wyơy)2 + 2*ρwxwyơxơy =					0.3456
standard deviation = √((wxơx)2 + (wyơy)2 + 2*ρwxwyơxơy )=					0.5879