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

a) What are the portfolio weights (xA, xB, xC )? Are your positions in stocks A, B, and C long (you buy) or short (you short-sell)? Justify.

b) What is the expected return of the portfolio (rP )?

c) What is the volatility of the portfolio (P )?

We now want to draw the efficient frontier and obtain the minimum variance portfolio. Note that you can use a solver (Excel, matlab, R, ...) if you want.

d) You want to build an efficient portfolio with an expected return of 14%. What are the weights of this portfolio (xA, xB, xC )? Are your positions in stocks A, B, and C long (you buy) or short (you short-sell)? Justify. What is the volatility of this portfolio (P )?

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