Consider the following two assets:

Asset As expected return is 3.5% and return standard deviation is 45%.

Asset Bs expected return is 1.0% and return standard deviation is 35%. The correlation between assets A and B is 0.4.

The table below indicates the expected return and the return standard deviation for portfolios that put weight w on asset A and weight 1 w on asset B.

weight	Expected Return	Return Standard Deviation
w=1.3	4.25%	55.15%
w=0.7	2.75%	36.97%
w=0.2	1.5%	32.66%

i)Draw a careful sketch of the portfolio frontier associated with assets A and B. Clearly indicate assets A and B as well as the three portfolios from the above table. Also, clearly label the part of the portfolio frontier in which you shortsell asset A as SHORT A and the part (of the portfolio frontier) in which you short-sell asset B as SHORT B.

ii)Now, suppose that the correlation between assets A and B is changed to 0.4. What is the expected return and the return standard deviation for the portfolio associated with the following three portfolio weights:

w = 1.3

w = 0.7

w = 0

If you can make a clear argument for the value of the expected return or the return standard deviation, provide this argument. Otherwise, show the computation(s).

iii) According to your answer to part (ii), how do you evaluate the following statement:

Independent of the portfolio weight, lowering the correlation between assets A and B implies that an investor whose utility strictly increases in expected return and strictly decreases in return standard deviation is always at least as well off as before. In short, lowering the correlation between assets A and B always entails diversification benefits.

Thnak you so much!