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 $8$ 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 $6$ 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

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 $2$

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

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

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.

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 party wins.