You have $102,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

ID: 2716721 • Letter: Y

Question

You have $102,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 11 percent and that has only 80 percent of the risk of the overall market. If X has an expected return of 25 percent and a beta of 2.1, Y has an expected return of 16 percent and a beta of 1.4, and the risk-free rate is 5 percent, how much money will you invest in Stock Y? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.)

Explanation / Answer

let wX,wY and wR be proportion of portfolio invested in Stock X, Stock Y, and a risk-free asset respectively.

expected return of portfolio =wX*expected return X+wY*expected return Y+wR*expected return R

put values,expected return X=25%,expected return Y=16%,expected return R=5%

11% =wX*25%+wY*16%+wR*5%

=>25wX+16wY+5wR=11 ...1)

also proportions should sum to 1=>wX+wY+wR=1 ...2)

beta of portfolio=.80= wX*beta X+wY*beta Y+wR*beta R

put values,beta X=2.1,beta Y=1.4 and beta R=0

=>.80= wX*2.1+wY*1.4+wR*0

=>21wX+14wY=8....3)

solve equations 1,2,3

=>eliminate wR from 1) and 2) =>25wX+16wY+5(1-wX-wY)=11

=>20wX+11wY=11-5=6 ...4)

from 3 and 4 equations,

3-4=>wX+3wY=2 =>wX=2-3wY put this in 4

=>20(2-3wY)+11wY=6

=>34=49wY =>wY=34/49 , wX=2-3(34/49)=(98-102)/49=-4/49

and wR=1-(34/49-4/49)=1-30/49=19/49

Thus u should invest 34/49 proportion of portfolio of sum $102,000 in Y=$(34/49)*102,000=$ 70775.51.

Thus u should invest $ 70776 in Y.

Navigate

You have $102,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

You have $102,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

Explanation / Answer

Related Questions

Navigate