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State the assumptions, additional to those used in modern portfolio theory, that allow the capital asset pricing model (CAPM) to be consistent with an equilibrium model of prices in the whole market. [5] (ii) Explain why in the CAPM all investors should hold all risky assets in proportion to the market capitalisation of those assets. [2] In an investment market there are three risky assets available. The table below shows the returns each of the assets will earn in the three possible states of the world and the current market capitalisation of the assets. Assume a risk free rate of return of 4% is available. States Probability Asset ] Asset 2 Asset 3 04 5% 70% 0.1 8% 1% W N - 05 3% 50% 4 Market Capitalisation 30,000 50,000 30.000 (iii) Calculate the market price of risk under the CAPM. 141 [Total 11]A stock is currently priced at 68.20. A writer of 100,000 units of a one year European call option on this stock with an exercise price of 68 has hedged the option with a portfolio of 75,000 shares and a loan. The annual risk-free interest rate (continuously compounded) is 7% and no dividends are payable during the life of the option. Assume the Black-Scholes pricing formula applies. (a) Derive an expression for the Delta of the option (b) State the value of the Delia in this case. [4] (ii) Calculate the implied volatility of the stock to within 0.1% p.a., assuming that it is below 100%. [5] (iii) Calculate: (a) the value of the loan (b) the price of the option [4] (iv) (@) Calculate the current price of a one year European put option with the same exercise price. (b) State any assumptions you make in your calculation in (iv)(a) [3] [Total 16]