For questions 14 to 16, use the following information.

There are three stocks a, b, and c to invest. Their expected returns, volatilities, and correlation coefficients are as follows. ( ) = 0.07, ( ) = 0.13, ( ) = 0.11, ( ) = 0.18, ( ) = 0.20, ( ) = 0.24, (, ) = 0.1, (, ) = 0.1, (, ) = 0.7, = 0.02 Suppose stock b is 6% undervalued and that is why its expected return is 6% higher than stock a. Likewise, suppose stock c is 4% undervalued and that is why its expected return is 4% higher than stock a.

14. Compute the optimal weight on these three stocks a, b, and c so that your portfolio can have the highest possible Sharpe ratio. Here, short sale is allowed. Hint: You need to modify the input part of 2) Tangency portfolio with multiple assets in LN5_part3_R.r.

1) (, , ) = (0.04, 0.64, -0.12)

2) (, , ) = (0.12, 0.64, 0.24)

3) (, , ) = (0.33, 0.71, -0.04)

4) (, , ) = (0.71, 0.33, 0.04) 5) (, , ) = (0.33, 0.12, -0.19)

15. Repeat the previous question but now assume short sale is NOT allowed. Then, which stock(s) should you NOT include in your optimal portfolio? Hint: You will not include the stock(s) with zero weight in your optimal portfolio.

1) Stock a

2) Stock b

3) Stock c

4) Stock a and c

5) Stock a and b

16. Do you include stock c in your portfolio for the question 15? Why? Choose one among the followings that answers the question 15.

1) Yes, because stocks with high Sharpe ratio are better to invest than other stocks with low Sharpe ratio.

2) Yes, because stocks with low correlations with other stocks can be less beneficial for maximizing Sharpe ratio than stocks with high Sharpe ratio.

3) No, because stocks with low Sharpe ratio are better to invest than other stocks with high Sharpe ratio.

4) No, because stocks with low correlations with other stocks can be more beneficial for maximizing Sharpe ratio than stocks with high Sharpe ratio.