Math of Finance

7. Jeremy Smithson invests his wealth in two assets: a European call option and shares in a stock. Suppose that the expected rate of return for trading the option is 5% with standard deviation 0.035, and the expected rate of return of trading the stock is 7% with the standard deviation ?2-0.04. Suppose that the rates of return have a correlation P1,-0.56. (a) Find the portion of Jeremy's investment in the option so that his portfolio has the minimum risk. (b) After a while, Jeremy decides to add a risk-free asset with a 3.5% rate of return into his market portfolio. Now, his new portfolio consists of one risk-free asset and two risky assets (which can be treated as the single efficient fund). Find the efficient market portfolio. c) Write down the equation of the capital market line for the combined portfolio in (b). 7. Jeremy Smithson invests his wealth in two assets: a European call option and shares in a stock. Suppose that the expected rate of return for trading the option is 5% with standard deviation 0.035, and the expected rate of return of trading the stock is 7% with the standard deviation ?2-0.04. Suppose that the rates of return have a correlation P1,-0.56. (a) Find the portion of Jeremy's investment in the option so that his portfolio has the minimum risk. (b) After a while, Jeremy decides to add a risk-free asset with a 3.5% rate of return into his market portfolio. Now, his new portfolio consists of one risk-free asset and two risky assets (which can be treated as the single efficient fund). Find the efficient market portfolio. c) Write down the equation of the capital market line for the combined portfolio in (b)