There are three possibilities for the economy next year: a macroeconomic boom, in which case GDP growth is faster than normal; a recession, in which GDP does not grow; and normal economic growth.

The table shows the probability of each of these events.

The table also shows the return on each of three stocks: GM, Gap, and Dollar Tree. Notice that the return on each stock depends on what happens in the macroeconomy next year.

economy next year	probability	return on General Motors stock	return on Gap, Inc. stock	return on Dollar Tree stock
boom (fast growth)	0.3	9	7.5	4
recession (zero growth)	0.2	3	4	10
normal growth	0.5	6	5.5	6

The expected return on Gap stock is 5.8. The standard deviation of the return on GM stock is 2.10.

1. Without doing any calculations, tell me which stock seems risker based on the returns data in the table, GM or Gap? Explain your answer.

2. Calculate the expected return on GM stock. Show your work.

3. Calculate the expected return on Dollar Tree stock. Show your work.

4. Calculate the standard deviation of the return on Gap stock. Show your work.

5. Calculate the standard deviation of the return on Dollar Tree stock. Show your work.

6. Based on your calculations, which stock is riskier, GM or Gap?

You have $100,000 to invest. Instead of putting all your money into one of the stocks, you will buy two of the stocks, putting $50,000 of your money into each one. Once you do this, you will have an equal-weighted portfolio.

First, lets suppose you buy $50,000 worth of GM stock and $50,000 worth of Gap stock. Lets call this Portfolio 1.

7. Calculate the expected return on Portfolio 1. Show your work.

8. Calculate the standard deviation of the return on Portfolio 1. Show your work.

Another possibility would be to buy an equal-weighted portfolio that includes $50,000 worth of Gap stock and $50,000 worth of Dollar Tree stock. Lets call this Portfolio 2.

9. Calculate the expected return on Portfolio 1. Show your work.

10. Calculate the standard deviation of the return on Portfolio 1. Show your work.

11. If youre trying to decide between Portfolios 1 and 2, what are the arguments for choosing Portfolio 1? What are the arguments for choosing Portfolio 2?

12. One of the portfolios is much less risky than the other one. Try to explain why, with reference to the returns in the table on the previous page.