Consider the following probability distribution for stocks A and B:

scenario	probability	return on stock A	return on stock B
1	.25	5%	-10%
2	.5	15%	12%
3	.25	-15%	20%

Assume that the risk-free rate is 3%. Assume the correlation between A and B is -0.5.

1 Suppose the tangency portfolio on the efficient frontier has an expected return of 7%. Please solve for the optimal weights of the tangency portfolio. For the answer to this question, write only the weight the tangency portfolio has on stock A.

2.1 (From Q3) What is the risk to volatility ratio (Sharpe Ratio) of stock A?

2.2 (From Q3) What is the risk to volatility ratio (Sharpe Ratio) of the tangency portfolio?

3 Suppose two investors are making the optimal capital allocation decisions. Investor 1 is more risk-averse than Investor 2. Which of the following allocation is consistent with Markowitz portfolio selection analysis?

• Investor 1 decides to invest 80% of his wealth in the tangency portfolio, while Investor 2 decides to invest 50% of his wealth in the tangency portfolio.

• Investor 2 decides to invest 100% of his wealth in the tangency portfolio, while Investor 1 decides to invest 65% of his wealth in the tangency portfolio and 35% in the risk-free asset.

• Two investors choose to invest 25% of their entire wealth in the risk-free asset.

• Investor 2 decides to go with 100% of his wealth in Stock B