Question

onsider two assets X and Y , each of which costs $100 to purchase. After one year, X pays out $130 with probability p and 75 with probability 1 − p. Asset Y pays out $60 with probability p and $200 with probability 1 − p

1-A) Find the value of p such that the two assets have identical expected returns

1-B)Given this value of p, calculate the standard deviation of the return of these two assets.

Answer 1

1(A) We know that ,

E(X) = 130 p + 75(1-p)

Also ,

E(Y) = 60p + 200(1-p)

Given

E(X) =E(Y)

1(B) Let us find Standard deviation of X and Y

We know that

V(X)= E(X²) -(E(X))²

E(X) = = 130*0.6410 +75*(1-0.6410) = 110.26

E(X²) = = 130² p+ 75²(1-p)

= 130² *0.6410+ 75²(1-0.6410)

= 12852.5641

V(X) =12852.5641 - ( 110.2564)² = 696.0881

Therefore , standard deviation of X =

Thus standard deviation of return of asset X = 26.38

Now ,

V(Y)= E(Y²) -(E(Y))²

E(Y) = = 60*0.6410+200*(1-0.6410) = 110.26

E(Y²) = = 60² *0.6410+ 200²*(1-0.6410)=16666.67

V(Y) = 4510.19

Therefore , standard deviation of Y =

Thus standard deviation of return of asset Y = 67.15