Question

You have $1,200 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 8 percent if the Democrats are elected, an event you believe to have a 30 percent probability; otherwise the shares pay a zero return. Shares of ElephantInc will pay 6 percent if the Republicans are elected (a probability of 70 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 $1,200 in ElephantInc.  Correctand your expected return will be 4.2  Numeric Response1. Edit Unavailable.4.2correct.%.

 

b. What is your expected return if you invest $600 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:    3.33  Numeric Response2. Edit Unavailable.3.33correct.%

  

d. Devise an investment strategy that is riskless, that is, one in which the return on your $1,200 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 party wins.
 

FILL IN THE EMPTY BOXES 

1.52% for e. is not correct

Answer 1

a. Let's calculate the expected return if all of $1200 is invested in either donkeylnc or ElephantInc.

Expected return from donkeylnc,

= 0.3 × 8%

= 2.4%

Similarly the expected return from ElephantInc,

= 0.7 × 6

= 4.2%

So the all of 1200 should be invested in ElephantInc that will offer a expected return of 4.2%.

b. The expected return when 600 is invested in each donkeylnc or ElephantInc will be equal to,

= 0.3 × 0.08 × 600 + 0.7 × 0.06 × 600

= 0.024 × 600 + 0.042 × 600

= 14.4 + 25.2

= 39.6

So the expected return if 600 each is invested in donkeylnc and ElephantInc will be equal to 39.6.

And the expected rate of return will be simply equal to,

= 39.6/1200 × 100

= 39.6/12

= 3.33%

C. The correct answer is option 2.

We should choose to invest 600 in each option because the lower return is compensated by the strategy being less risky, as you'll receive a reasonable return no matter which party wins.

d.

Let the amount invest in Donkeylnc be X and amount invested in ElephantInc be 1200 - X. And we need to choose X such that the return remains the same.

Let return be Y from both investment so that irrespective of whoever wins investor will get Y.

So, return from donkeylnc will be equal to

0.3 × 0.08 × X = Y

0.024X = Y -----------------(1)

And similarly return from ElephantInc will be equal to,

0.7 × 0.06 × (1200 - X) = Y

0.042(1200 - X) = Y

50.4 - 0.042X = Y --------------(2)

Now we can solve equation (1) and (2) to calculate X and Y.

50.4 - 0.042X = 0.024X

50.4 = 0.024X + 0.042X

50.4 = 0.066X

X = 50.4/0.066

X = 763.63

So the amount invested in Donkeylnc should be $763.63.

And similarly the amount invested in ElephantInc will be equal to,

= 1200 - 763.63

= $436.37.

e. And the regardless of whoever wins the investor will get,

= 0.024 × 763.63

= $18.32

And in terms of percentage this will be equal to,

= 18.32/1200 × 100

= 18.32/12

= 1.52%

This is the rate of return that the investor will get regardless of who wins the election.

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