Given generic asset 1, with expected return 1 and risk 1, and generic asset 2, with expected return 2 and risk 2, let 1,2 be the covariance between the two assets.

1. Derive the formulas for a generic proper portfolio p expected return and risk as a function of asset 1 weight p 1

2. Derive the formulas for a generic long-short portfolio ls expected return and risk as a function of asset 1 weight ls 1

3. What is the condition under which the two portfolios have the same expected return given p 1 = ls 1 ?

4. What is the condition under which the two portfolios have the same risk given p 1 = ls 1 ?

5. Are the two above conditions mutually exclusive? Why? 6. Given 1 = 0.16, 2 = 0.12, 1 = 0.2 and 2 = 0.2

if the proper portfolio has an expected return of 0.15, what is the proportion invested in asset 1?

if the long-short portfolio has an expected return of 0.15, what is the proportion invested in asset 1?