Suppose Dean has $500 and there are two companies he could invest X dollars in: Dog Gone Salon,which has a payoff of 2X with 50% probability and $0 with 50% probability and Pretty Kitty Grooming,which has a payoff of 4X with 25% probability and $0 with 75% probability.Which of the following is true?
A) It doesn't matter how distributes his $500 between the two investments, the expected payoff and the standard deviation will always be the same.
B) Even though the expected payoff is the same for both investments, investing in Dog Gone Salon involves less risk.
C) Even though the expected payoff is the same for both investments, investing in Pretty Kitty Grooming involves less risk.
D) Investing in Pretty Kitty Grooming offers a higher expected payoff.

Question

Quizplus · Accepted Answer

We can use the formulas for expected value and standard deviation to compare the two investments:
For Dog Gone Salon: 
Expected value: E(X) = (2X)(0.5) + (0)(0.5) = X
Standard deviation: sqrt(V(X)) = sqrt(((2X-X)^2)(0.5) + ((0-X)^2)(0.5)) = sqrt(X^2) = X

For Pretty Kitty Grooming: 
Expected value: E(X) = (4X)(0.25) + (0)(0.75) = X
Standard deviation: sqrt(V(X)) = sqrt(((4X-X)^2)(0.25) + ((0-X)^2)(0.75)) = sqrt(3X^2) = Xsqrt(3)

So we can see that the expected payoff is the same for both investments, but the standard deviation is smaller for Dog Gone Salon. This means that investing in Dog Gone Salon involves less risk. Therefore, the best choice is B.

Suppose Dean Has $500 and There Are Two Companies He