Question

2 portfolios:A&B.In A she will get 100$ with a probability %50 and 25$ with a probability of 50%. In B she will get 125$ with a probab. of 50%, 25$ with a probab. of 20% and 0 with a probab. of 30%.We know that this individual is INDIFFERENT between A&B.Now,she is presented 2 additional portfolios:C&D.In C she will get 100$ with a probability of 50%, 25$ with a probability of 30%, and 0 with a probability of 20%.In D she will get 125$ with a probability of 50%, 100$ with a probability of 20%, and 0 with a probability of 30%. Will she prefer C to D, or D to C, or be indifferent between C and D?

Answer 1

She will definitely choose D and here is why.
Note the following expected returns:
\[A: 100\times0.5+25\times0.5=62.5\]\[B: 125\times0.5+25\times0.2+0\times0.3=67.5\]\[C: 100\times0.5+25\times0.3+0\times0.2=57.2\]\[D: 125\times0.5+100\times0.2+0\times0.3=82.5\]
Note the similarity in probabilities between B and D.
In case of A and C she can be expected to demand higher return for higher risk. Since expected return on B is higher than on A, and A and B have no difference in terms of preference, return on C should be higher than on A. So, D and B are the same in terms of risk but C has lower expected return than A. This means that C and D are not indifferent for her and she will definitely prefer D.