Question

Probability of the state of economy Rate of return if state occurs Stock T Recession 0.3...

Probability of the state of economy

Rate of return if state occurs

Stock T

Recession

0.3

2 %

Boom

0.7

12 %

If you want an expected return of 6%, when holding a portfolio invested in stock T and risk free asset. (The expected return on risk free asset is 2%.) What percentage of stock T should you hold? Express you answer as percent.

could you answer this in 40 minutes? thanks very much! I leave a like

Homework Answers

Answer #1

Step 1 - Expected return from stock T

Probability (A) Return (B) Expected Return (A*B)
Recession 0.3 2% 0.60%
Boom 0.7 12% 8.40%
Expected Retun 9.00%

Expected return from Stock T = 9%

Step 2 - Expected return of portfolio

Let the precentage of Stock T in out portfolio be X

Then the precentage of risk free asset in portfolio = (1-X)

Now as per question return of the portfolio should be equal to 6%

(X*9) + (1-X)*2 = 6

9X + 2 -2X = 6

7X = 4

X = 0.5714 or 57.14%

Therefore percentage of stock T in the portfolio = 57.14%

Precentage of risk free asset = (1-0.5714) = 0.4285 or 42.86%

Step 3 - Proof

Precentage (A) Expected Retrun on Assets (B) A*B
Stock T 57.14% 9% 5.14%
Risk Free Asset 42.86% 2% 0.86%
Expected return on portfolio 6.00%
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