Question

You have the opportunity to invest $20 , with an uncertain return. To simulate uncertainty, we will use a deck of four playing cards consisting of two aces and two kings. The deck has been shuffled and placed face down on the table in front of you. You will now draw two cards, one after the other:

If you draw two aces, you will receive $60

If you draw an ace and a king, you will receive $30

if you draw two kings, you will have to pay an additional $18 and receive nothing

a) Let's assume that you are risk neutral for these dollar amounts. What is the expected value of the investment?

b) A special risk mitigation opportunity is available, for $5. If you buy the opportunity, you will receive $6 (andnot have to pay $18) if the outcome is two kings. Should you buy it? Explain. c) An expert card dealer can tell you what the first card is. He will charge $6 for the information. Should you pay for the information?

Answer 1

P(2 aces) = 2/4*1/3 = 1/6

P(1 ace, 1 king) = 2*1/2*2/3 = 2/3

P(2 king) = 1/6

a) Expected value = 1/6*60 + 2/3*30 - 18*1/6 = $27

Expected return = 27-20 = $7

b) Now investment = 20+5 = $25

Now, Expected value = 1/6*60 + 2/3*30 + 6*1/6 = $31

Expected return = 31-25 = $6

Now return is lower so we should not buy it.

c) If expert card dealer can tell you what the first card is, then probabilities changes:

P(2 aces) = 1/2*2/3 = 1/3

P(1 ace, 1 king) = 2*1/2*2/3 = 2/3

P(2 king) = 1/3

Now, Expected value = 1/3*60 + 2/3*30 - 18*1/3 = $34

Expected return = 34-20 -6(expert charge) = $8

This is higher return hence we should pay for this information.