1. An investor wishes to choose between investing£10,000 for one year at a guaranteed interest rate of 12% and investing the same amount over that period in a portfolio of common stocks. If the fixed-interest choice is made, the investor will be assured of a payoff of£1,200. If the portfolio of stocks is chosen, the return will depend on the performance of the market over the year. If the market is buoyant, a profit of £2,500 is expected; if the market is steady, the expected profit is£500; and for a depressed market, a loss of£1,000 is expected. The investor is very optimistic about the future course of the stock market, believing that the probability of a buoyant market is 0.6, while the probability is equal for the other two states.

(a) Draw the decision tree for this problem.

(b) Which investment should the risk-neutral investor choose according to the expected monetary value criterion?

(c) Without calculating anything, explain the term ‘certainty equivalent' of a risky projectin the context of this investment problem.

(d) If the certainty equivalent is less than the expected monetary value, what sort of investor is it? Briefly explain your answer.

2. The established and successful shopping centre. Alternatively, at lower cost, he can locate in a new centre, whose development has recently been completed. If the new centre turns out to be very successful, it is expected that annual store profits from location in it would be£130,000. If the centre is only moderately successful, annual profits would be£60,000. If the new centre is unsuccessful, an annual loss of£10,000 would be expected. The profits to be expected from location in the established centre will also depend to some extent on the degree of success of the new centre, as potential customers may be drawn to it. If the new centre was unsuccessful, annual profits for the shoe store located in the established centre would be expected to be£90,000. However, if the new centre was moderately successful, the expected profits would be£70,000, while they would be only£30,000 if the new centre turned out to be very successful. All profits are inclusive of location cost. The probability that the new shopping centre will be very successful is 0.4 and the probability it will be moderately successful is also 0.4.

(a) Draw the decision tree for this problem.

(b) According to the expected monetary value criterion, where should the shoe store be located? Assume a risk-neutral decision-maker.

(c) Without calculating anything, explain briefly how a perfect forecast of shopping centre success changes the order of the decision tree in (a).