1. Suppose that the economy is described by three growth states: strong, moderate, and weak. The probabilities of strong, moderate, and weak growth states are 0.3, 0.5 and 0.2, respectively. Assume that the risk-free rate is 2%.

(a) Assume that you can buy or short three stocks: A, B, and C, with the following return distribution:

Strong Growth Moderate Growth Weak Growth A 30% 10% 10% B 11.8% 4.8% 2.2% C 5% 0% 5%

Is there an arbitrage opportunity? If yes, describe in detail how you would take advantage of it.

(b) Consider a dierent distribution of returns:

Strong Growth Moderate Growth Weak Growth A 30% 10% 10% B 16.3% 3.9% 5.3% C 5.5% 2.7% 18.5%

Is there an arbitrage opportunity? If yes, describe in detail how you would take advantage of it.