Question

	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

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%