Question

You have $1,500 to invest and are considering buying some combination of the shares of two companies, DonkeyInc and ElephantInc. Shares of DonkeyInc will pay a return of 12 percent if the Democrats are elected, an event you believe to have a 25 percent probability; otherwise the shares pay a zero return. Shares of ElephantInc will pay 10 percent if the Republicans are elected (a probability of 75 percent), zero otherwise. Either the Democrats or the Republicans will be elected.

a. If your only concern is maximizing your average expected return, with no regard for risk, you should invest your $1,500 in:

	ElephantInc.
	neither DonkeyInc nor ElephantInc.
	DonkeyInc.
	either DonkeyInc or ElephantInc.

b. What is your expected return if you invest $750 in each stock? (Hint: Consider what your return will be if the Democrats win and if the Republicans win, then weight each outcome by the probability that event occurs.)

Instructions: Enter your response as percentage rounded to one decimal place.

Expected rate of return: %.


c. The strategy of investing $750 in each stock does not give the highest possible average expected return. You would:

	choose it anyway because this strategy guarantees the same return regardless of which party wins.
	not choose it because a less risky strategy cannot compensate for a lower expected return.
	not choose it because you should always choose the strategy with the highest average expected return.
	choose it anyway because the lower return is compensated by this strategy being less risky, as you receive a reasonable return no matter which party wins.

d. Devise an investment strategy that guarantees at least a return of 5.3 percent, no matter which party wins.

Instructions: Enter your responses rounded to two decimal places.

You should invest at least $ in ElephantInc and at least $ in DonkeyInc.


e.  Devise an investment strategy that is riskless, that is, one in which the return on your $1,500 does not depend at all on which party wins.

Instructions: Enter your responses rounded to two decimal places.

You should invest $ in ElephantInc and $ in DonkeyInc.

Answer 1

(a) (a)

Expected return, DonkeyInc = 12% x 25% + 0 x 75% = 3%

Expected return, ElephantInc = 10% x 75% + 0 x 25% = 7.5%

So you should invest in ElephantInc since it offers higher expected return.

(b) Investment: $750 in Donkey, $750 in Elephant.

Expected return if Democrats win = $750 x 12% x 25% + $750 x 0 = $22.5

Expected return if Republicans win = $750 x 10% x 75% + $750 x 0 = $56.25

So, average expected return = $(22.5 + 56.25) = $78.75

(c) Last option is correct.

Even though expected return is not highest, the risk is lower since there is probability of some return no matter which party wins.

(d)

Total investment = $1500

Let me invest $Z in Donkey & $(1500 - Z) is Elephant.

Expected return from Donkey + Expected return from Elephant = Overall required return.

$Z x 12% x 25% + $(1500 - Z ) x 10% x 75% = $1500 x 5.3%

0.03Z + 0.075(1500 - Z) = 79.5

0.03Z + 112.5 - 0.075Z = 79.5

0.045Z = 33

Z = 33 / 0.045 = 733.33

So I'll invest $733.33 in DonkeyInc & $(1500 - 733.33) = $766.67 in ElephantInc.

NOTE: Out of 5 questions, the first 4 are answered.