HAVE SOLVED FIRST HALF/ I REQUIRE HELP QUESTIONS 7-12

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. (SHOW WORK)

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

Q1) For the GM stock here, we see here that for the highest probability scenario, that is normal growth the return is 6%, which is highest for that scenario and thatn it is highest for boom as well at 9 which is the second most probable scenario but then it has the lowest value for recession scenario, therefore just by looking at the data here, we can see that the range here is the highest for GM stock and therefore it seems to be riskier than the Gap stock here.

Q2) The expected return for GM stock here is computed as: = 0.3*9 + 0.2*3 + 0.5*6 = 6.3 is the required value here.

Q3) the expected return for dollar tree stock here is computed as: = 0.3*4 + 0.2*10 + 0.5*6 = 6.2 is the required value here.

Q4) For Gap Stock, we have here: E(R) = 0.3*7.5 + 0.2*4 + 0.5*5.5 = 5.8 E(R²) = 0.3*7.5² + 0.2*4² + 0.5*5.5² = 35.2

Therefore, the standard deviation is computed here as: SD = sqrt(E(R²) - [E(R)]² ) = sqrt(35.2 - 5.8²) = 1.2490 is the required value here.

Q5) For Dollar Tree stock, we already know from previous questions: E(R) = 6.2 E(R²) = 0.3*4² + 0.2*10² + 0.5*6² = 42.8

The standard deviation here is computed as: SD = sqrt(E(R²) - [E(R)]² ) = sqrt(42.8 - 6.2²) = 2.0881 is the required value here.

Q6) For GM stock, we have here: E(R) = 6.3 E(R²) = 0.3*9² + 0.2*3² + 0.5*6²

SD = sqrt(E(R²) - [E(R)]² ) = sqrt(44.1 - 6.3²) = 2.1

As the standard deviation for GM stock here is higher as compared to that for GAP stock here, therefore GM is riskier here.

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.