Question: State Prob. Return Stock A Return Stock B Return Stock C Recession 0.3 -0.04 0.06 0.6 Normal 0.5 0.05 0.07 0 Boom 0.2 0.2 0.06

State	Prob.	Return Stock A	Return Stock B	Return Stock C
Recession	0.3	-0.04	0.06	0.6
Normal	0.5	0.05	0.07	0
Boom	0.2	0.2	0.06	-0.3

1. You want to build an efficient portfolio with an expected return of 10%. What are the weights of this portfolio (xA, xB, xC )? What is the volatility of this portfolio (P )?

2. You want to build an efficient portfolio with an expected return of 8%. What are the weights of this portfolio (xA, xB, xC )? What is the volatility of this portfolio (P )?

3. What are the weights of the minimum variance portfolio (xA, xB, xC )? What is the expected return of this portfolio (rP )? What is the volatility of this portfolio (P )?

4. Assume that we add to this world a risk-free asset. What is the return on this risk-free asset (rf )?

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