Kindly help answer the following.,,,

1 An investor can invest in two assets, A and B: style A B expected return 6% 8% variance 4%% 25%% The correlation coefficient of the rate of return of the two assets is denoted by p and is assumed to take the value 0.5. The investor is assumed to have an expected utility function of the form: Ea (U) =E()-a Var(p) where a is a positive constant and ro is the rate of return on the assets held by the investor. (1) Determine, as a function of a , the portfolio that maximises the investor's expected utility. [8] (ii) Show that, as a increases, the investor selects an increasing proportion of Asset A. [1] [Total 9] 2 Colin's preferences can be modelled by the utility function such that: U'(w) =3-2w, (w > 0). (i) Determine the range of values over which this utility function can be satisfactorily applied. (ii) Explain how Colin's holdings of risky assets will change as his wealth decreases. (ii) Which of the following investments will he choose to maximise his expected utility? Investment A Investment B Investment C outcome probability outcome probability outcome probability 0.1 0.3 0 0.3 0.2 0.45 0.3 0.4 0.2 0.2 0.3 0.1 0.5 0.3 0.9 0.5 0.4 0.45