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 (σP )?

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 (σP )?

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