(i) Define "efficient portfolio" and explain "efficient frontier" in the context of

Mean-Variance Portfolio Theory [2]

(ii) Explain how an efficient frontier changes its shape with the introduction of

risk-free lending and borrowing.

An investor can invest in two assets A and B. A B expected return 6% 8% variance 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 expected utility functions of the form Ea(U) = E(r ) - a Var(r ) where a is a positive constant and r, is the rate of return on the assets held by the investor. (i) Determine, as a function of o, the portfolio that maximises the investor's expected utility. [8] (ii) Show that, as o increases, the investor selects an increasing proportion of asset A. [1]A stock price is modelled by a two period recombining binomial model with the following parameters where each period represents a day. Assume that there are 3&5 days in a year. {i} (ii) [iii] {iv} cc {vi} r = 5% pa [risk-free rate, continuously compounded) o = sass pa. = volatility of share price process s= lll=sharepriceat timet} a = exp-[6.365%] = return per unit investment of an up jump probability of an up jump = 611% By considering the risk neutral probability or otherwise, evaluate the state price sits} [at time zero) for each of the three possible states the share price is in after two steps [assume that one step is one day]. [3] Calculate the state price deator (at time ill for each of the three possible states- [2] By considering the cashows arising from a call option on the stock with exercise price I: = 99 at time two, use the above to determine the value of this option at time zero. [2] Estimate the delta of the option in (iii) at time zero. [3] Determine the appropriate minimum value delta hedging investment portfolio at time zero for the option described in {iii}. [1] Explain what is meant by risk neutral valuation, [2}