(i) Explain what is meant by an excessively volatile market. [2]

(ii) Describe how you would test if a market is excessively volatile.

(iii) Explain the practical and conceptual difficulties in using a test of an

excessively volatile market to establish whether or not a market is efficient.

Total returns for the market are assumed to be lognormally distributed with parameters , o-. (i) Calculate the parameters u, o' given an expected rate of return for the market of 8% per annum and a standard deviation of 16% per annum. [3] (ii) (a) Show that the probability of a rate of return exceeding 50% in a year is 0.161% [3] (b) In any given year there are 200 trading days. Calculate the probability of the rate of return on the market exceeding 0.25% in any day. [3] (c) Find the rate of return required on the market in a day such that this event has a probability of 0. 161%. [2] (iii) Comment on the results in (ii). [3] [Total 14] 4 Explain in broad terms how a model that assumes a flat yield curve will give rise to arbitrage opportunities and hence why a flat yield curve would exist for only short periods of time. [5]