Question

1 GenLabs has been a hot stock the last few years, but is risky. The expected returns for GenLabs are highly dependent on the state of the economy as follows:

State of Economy	Probability	GenLabs Returns
Depression	.05	-50%
Recession	.10	-15
Mild Slowdown	.20	5
Normal	.30	15%
Broad Expansion	.20	25
Strong Expansion	.15	40

Please calculate the expected return and standard deviation of the stock.

2. A year ago, an investor invested $4,000 in the stock of IBM, $4,000 in the stock of GE, and $2,000 in the stock of Microsoft. The rate of return is 10% for IBM, 12% for GE, and 15% for Microsoft. How much is the overall rate of return for the portfolio?

3. Consider a portfolio that is composed of the following two securities:                                        Security A    Security B

       Expected return   5%         10%

       Standard deviation     6%         12%

If you allocate 40% into A and 60% into B, how much is the expected return on the portfolio?

If you allocate 30% into A and 70% into B, how much is the expected return on the portfolio?

Answer 1

1)

State of Economy	Probability(j)	r	[r]^2	[r bar]^2	{[r]^2-[r bar]^2}*Probability(j)
Depression	0.05	-50%	0.250000	0.015625	0.234375
Recession	0.10	-15%	0.022500	0.015625	0.006875
Mild Slowdown	0.20	5%	0.002500	0.015625	-0.013125
Normal	0.3	15%	0.022500	0.015625	0.006875
Broad Expansion	0.2	25%	0.062500	0.015625	0.046875
Strong Expansion	0.15	40%	0.160000	0.015625	0.144375
Expexcted value[r bar]		12.50%		Variance	0.426
				S.D	0.65288

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2)

Name of Stock	Amount Invested	Proportion	Return
IBM	4000	0.4	10%
GE	4000	0.4	12%
Microsoft	2000	0.2	15%
Total	10000
Expected Return			11.80%

Expectd return = portfolio x rate of return

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Name of Stock	Portfolio 1	Portfolio 2	Return
Security A	0.4	0.3	5%
Security B	0.6	0.7	10%
Expected Return	8.00%	8.50%