1. a. Two investors, A and B, areevaluating the same investment opportunity, which has an expectedvalue of £100. The utility functions of A and B are ln(x) and?????x?², respectively. Which investor has a certaintyequivalent higher than 100? Which investor requires the higher riskpremium?

b. (i) Describe suitable measures of risk for‘loss-aversion’ and ‘risk aversion’.

(ii) Concisely define the term ‘risk neutral’with respect to a utility function u(w), where w isthe realisation of a random variable W.

(c) Suppose you are facing a lottery that has apayoff of 10b pounds with probability 0.01 andthat of 0 with probability 0.99. You are an expected utilitymaximiser with a utility function,u(x) =?exp(?ax) wherex is the payoff in money terms and a> 0 is a parameter. What is the risk premium for thislottery - describe the risk premium as a function of‘a’ and ‘b’.

(d) How does the risk premium in (c) change as‘b’ changes.

2.

???????There are two distinct portfolios, A and B.

Portfolio	Expected Returns	Standard Deviation
A	0.2	0.1
B	0.3	0.2

1. A portfolio D assigns weight w to portfolio Aand weight (1-w) to portfolio B. What shouldw be so as to minimise the variance ofportfolio D, if ?_AB = -0.5? The variance of a portfoliois given by:   
2. If ?_AB = 0.5, and A and B are frontier portfolios,what is the expected return and standard deviation of the minimumvariance portfolio?
3. Given that A and B are frontier portfolios and that anotherfrontier portfolio C, has an expected rate of return of 25% andvariance of 2 %, evaluate the new?_AB.

3.

1. Project A has a payoff of 1 with probability 0.8 and 100 withprobability 0.2. Project B has a payoff of 5 with probability 0.99and 1585 with probability 0.01 Which project is preferred by aninvestor who maximises expected utility and has an utility functionu(x) = ln 2x? Comment on thepreferences.
2. Is it true that if an investor with utility function u(x) = x ^1/2 prefers risky project A to riskyproject B, another investor with utility functionv(x) = 5x^1/2 + 5also prefers A to B? Explain.
3. A risk neutral expected utility maximiser is facing a riskyinvestment opportunity. Her utility is a function of the net payoffof the project in terms of money u(y) where £ y is the net payoff.When she makes an investment of £ x (> 0 ), the project yields agross payoff of £ 30*x ^1/2on the investment withprobability 0.4 and a gross payoff of £ 10* x^1/2withprobability 0.6. The net payoff is the difference between grosspayoff and the cost of the investment. How much should she investto maximize her expected utility?
4. State the conditions needed to ensure that the choices made tomaximise expected utility will coincide with the choices in amean-variance framework.

4.

1. The cash flows of a firm that has just conducted an InitialPublic Offering (IPO) are expected to be either £10 million perannum for 10 years and zero afterwards with probability‘p’ or £5 million forever with probability(1-p). The risk-adjusted discount rate for thisfirm is 10% per annum. I. Express the current fundamental value ofthe firm in terms of ‘p’. II. If the currentstock market value of the firm is £55 million, what is the value of‘p’ implied by the market?

(b) The cash flows of a firm areexpected to be £1 million per year starting next year for the firstten years and are then expected to start declining forever at therate of 5% per year. The risk-adjusted discount rate is 10% perannum. What is the present value of the cash flows?

c) Investment analysts regularlyprepare forecasts and reports for their clients on the valuation ofthe firms they follow as analysts. Briefly discuss the factors thatshould be taken into account in arriving at such valuations.