Question

1. UNCERTAINTY AND CONSUMER CHOICE 1. Ali is a house flipper: he buys old houses that appear to be bargains, renovates them, and then puts them back on the market for resale. Ali recently discovered a lovely Victorian house that he is considering for a rehab. There is a 2 probability that Ali will lose 10% on the deal, a 7 probability that he will gain 8% on the deal, and a . 1 probability that he will gain 20%. (a) Calculate Ali's expected return from the project. (Note that this is in percentage return.) (b) Suppose that, in a different neighborhood, there is a bungalow selling for the same price. Ali estimates that there is a 3 probability that he will gain 3%, a .5 probability that he will gain 5.8%, and a 2 probability that he will gain 9%. Calculate Ali's expected return from this project. (Again in percentage return.) (c) Assume that Ali has only enough money to flip one house. If he bases his decision solely on expected return, is it clear which house Ali will prefer to flip? If not, is there an additional factor that might tip the balance?

Answer 1

a)

Probability of state 1=p1=0.2

Return in state 1=r1=-10%

Probability of state 2=p2=0.7

Return in state 2=r2=8%

Probability of state 3=p3=0.1

Return in state 3=r3=20%

Expected Return=p1*r1+p2*r2+p3*r3=0.2*(-10%)+0.7*8%+0.1*20%=5.60%

b)

Probability of state 1=p1=0.3

Return in state 1=r1=3%

Probability of state 2=p2=0.5

Return in state 2=r2=5.8%

Probability of state 3=p3=0.2

Return in state 3=r3=9%

Expected Return=p1*r1+p2*r2+p3*r3=0.3*3%+0.5*5.8%+0.2*9%=5.60%

c)

Expected return is same i.e. 5.6% in both cases. So, decision cannot be made solely on the basis of expected return.

As, expected return is same in both cases, Ali should calculate the measure of risk i.e. standard deviation of both proposals and should select the proposal with lower risk i.e. lower standard deviation.