Question

You have $1,000 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 10 percent if the Democrats are elected, an event you believe to have a 40 percent probability; otherwise the shares pay a zero return. Shares of ElephantInc will pay 8 percent if the Republicans are elected (a probability of 60 percent), zero otherwise. Either the Democrats or the Republicans will be elected.

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

a. If your only concern is maximizing your average expected return, with no regard for risk, you should invest your $1,000 in  (Click to select)  DonkeyInc.  ElephantInc.  and your expected return will be  %.

b. What is your expected return if you invest $500 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 two decimal places.

Expected rate of return:    %


c. The strategy of investing $500 in each stock does not give the highest possible average expected return. You would:

multiple choice 2

• 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.

• not choose it because a less risky strategy cannot compensate for a lower expected return.

• choose it anyway because this strategy guarantees the same return regardless of which party wins.

• not choose it because you should always choose the strategy with the highest average expected return.

d.  Devise an investment strategy that is riskless, that is, one in which the return on your $1,000 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.

e. Using the investment strategy devised in part d, you will earn  % regardless of which part wins.

Answer 1

Prob A x ($ amount invested) x (% return) = expected value of A
Prob B x ($ amount invested) x (% return) = expected value of B
Then you sum the expected value of the two in order to get the expected returns.

A) 0.6 x $500 x 0.10 = $30 expected value of A
0.4 x $500 x 0.08 = $16 expected value of B
Expected Value of A + expected value of B = expected return so $30 + $16 = $46

B) In order to solve for the strategy that gives us equal returns we need to set two equations equal to each other, create an additional equation, and solve for the size of the two investments necessary. First we're going to set the expected value formulas equal to each other:

(Prob A 0.6) x 0.1 x (X dollars) = (Prob B 0.4) x .08 x (Y dollars)
By multiplying the decimals on both sides we get:
.06X = 0.032Y

Now remember X+Y has to equal $1000 because that's the amount we can invest. So the equation we will create will be X + Y = 1000

By solving for Y, we can rearrange that equation to be Y = 1000 - X
Now plug that into the other equation:

0.06X = 0.032 (1000 - X)
0.06X = 32 - 0.032 X
0.092X = 32
X = $347.83 ( Donkey inc.)
Y = 1000 - $347.83 = $652.17 (Elephant Inc.)