Consider a portfolio of stocks X, Y, Z whose returns in various economic conditions are set forth below.

State Probability X Y Z
Boom 0.25 22% 10% 4%
Normal 0.60 15% 9% 5%
Recession 0.15 5% 8% 7%

What is the expected return (__.% to two decimals) for a portfolio with an investment of $3000 in asset X and $7000 in asset Y?

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hyderali230 hyderali230 · Answer 1 · 2020-12-09T01:58:36+01:00

Answer:

The expected return is 10.95%

Explanation:

CALCULATE THE EXPECTED RETURN OF X

State _____Probability __X_____Expected return

Boom ____ 0.25 ______22% ___5.50%

Normal ___ 0.60 ______15% ___ 9.00%

Recession _0.15 _______5% ___ 0.75%

Total ______________________15.25%

CALCULATE THE EXPECTED RETURN OF Y

State _____Probability __Y_____Expected return

Boom ____ 0.25 ______10% ___ 2.50%

Normal ___ 0.60 ______9% ____5.40%

Recession _0.15 _______8% ___ 1.20%

Total ______________________9.10%

Now calculate the weighted average return based on investment in each portfolio

Expected return = ( Expected return of Assets X x Weight of Asset X ) + ( Expected return of Assets Y x Weight of Asset Y )

Expected return = ( 15.25% x $3000/$10000 ) + ( 9.10% x $7000/$10000 )

Expected return = 4.575% + 6.370%

Expected return = 10.945%

Expected return = 10.95%