Question

State of the Economy	Probability	HPR (Fund A)	HPR (Fund B)
Boom	.50	7%	25%
Normal growth	.3	-5%	10%
Recession	.2	20%	-25%

1.   What are the expected holding period returns for Fund A and Fund B?

2. What are the expected standard deviations for Fund A and Fund B?

3. What are the covariance and correlation coefficient between the returns of Fund A and Fund B?

4. Now using Fund A and Fund B to construct our optimal risk portfolio P, what are the weights for Fund A and Fund B if risk free rate is 4.25% ?     

5. What are the expected return and Standard Deviation of the optimal risky portfolio P?

6. What is the Sharpe Ratio (Reward-to-Variability) of the CAL line that joins the risk-free asset and optimal risky asset P?

7. If your risk aversion index A = 4, what is your optimal allocation between risky asset P (y) and risk-free asset (1-y)?

8. What are expected rate of return and standard deviation of your complete portfolio that is constructed with risky asset P and risk-free asset?

Answer 1

	Expected Return =SUM of (Probability*Return)
	Variance =SUM of (Probability * (Deviation Squared)
	Deviation =Return -Expected Return
	FUND A	P	R1	A=P*R1	B1=R1-6	C1=B1^2	D1=C1*P
	State of Economy	Probability	Return(%)	Probability*return	Deviation from mean	Deviation squared	Deviation Squared*Probability
	Boom	0.5	7	3.5	1	1.00	0.50
	Normal Growth	0.3	-5	-1.5	-11	121.00	36.30
	Recession	0.2	20	4	14	196.00	39.20
			Total	6.00		Total	76.00
	Expected (Mean) Return	6.00%
	Variance of return	76.00	%%
	Standard Deviation	8.72	Percent	(Square Root of Variance)
	FUND B	P	R2	A=P*R2	B2=R2-10.5	C2=B2^2	D2=C2*P
	State of Economy	Probability	Return(%)	Probability*return	Deviation from mean	Deviation squared	Deviation Squared*Probability
	Boom	0.5	25	12.5	14.5	210.25	105.13
	Normal Growth	0.3	10	3	-0.5	0.25	0.08
	Recession	0.2	-25	-5	-35.5	1260.25	252.05
			Total	10.50		Total	357.25
	Expected (Mean) Return	10.50%
	Variance of return	357.25	%%
	Standard Deviation	18.90	Percent	(Square Root of Variance)
		Fund A	Fund B
1	Expected Holding Period Return	6.00%	10.50%
2	Expected Standard Deviation	8.72%	18.90%
	COVARIANCE BETWEEN A &B= SUM of (Deviation A*Deviation B*Probability)