You have 3 assets A, B, C in a world with two future states, High and Low. These assets have the following net return structure:

Low High

A 0.02 0.02

B 0 0.1

C -0.2 0.2

1. Compute the expected returns and the standard deviation of the returns of each asset if the probability that the state High occurs is 0.5.
2. Using the criterions below, can you assess which of these assets is the most and least desirable?
3. State-by-state dominance
4. Expected return
5. Mean-variance dominance
6. Sharpe Ratio
7. For each asset, plot their expected returns and standard deviation of returns as a function of probability of the High state. You can do it for the following values of this probability {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}. You can use Excel.
8. Using your findings from question 3, answer the following questions:
9. For each asset, explain the shape of the expected returns and standard deviation of the returns as a function of the probability of the high state.
10. Assume you are a risk-averse investor - are there any values of the probability of the High State, for which you would always prefer one asset to the other two, without having to specify an exact utility function?