a. Consider the following expected returns for two different assets (A and B) in five different market states (Boom, Bullish Normal, Bearish and Crisis), all of which have equal probabilities.

Market state	A	B
Boom	30%	6%
Bullish	18%	4%
Normal	8%	3%
Bearish	-5%	-1%
Crisis	-15%	-2%

1. Calculate the expected return and variance of the two assets.

2. You want to construct a portfolio that consists of the asset A and B with equal weights. Your investment advisor, however, suggests an alternative portfolio that consists of the asset A and a risk-free asset with a return of 1.5%. In order to achieve the same level of risk as your initial portfolio (50% in A and 50% in B), calculate the weight you need to invest into the risk-free asset assuming the risk free asset is not correlated with the asset A. What is the expected return and volatility of the alternative portfolio suggested by the advisor?

1. Suppose that Big Foot plc has an expected return of 15% and Little Palm Corp has an expected return of 17%. The market portfolio has an expected return of 12%.

Assume that CAPM holds, Big Foot plc is fairly priced given its risk as measured by a beta of 1.5. Calculate the risk-free rate.