Adam Smith Business School Subject of Economics FMM Economics 5074 In-course exam/2021 

Instructions to students: There are two questions. Each question is worth 100 points Complete only ONE question Time allotted: 1 hour CONTINUED OVERLEAF 1 Glosten-Milgrom. Suppose V = .25, V = 5.5, 0 = .32 and = .22. 1.1 Suppose the first order is a buy order: what is 1? 1.2 Suppose the second order is a sell order: what is 2? 1.3 What are the bid and ask prices associated with 2? (25 points) (25 points) (50 points) 2 Practicalities of trading. Hedge funds have practical models that they use in trading. Marylebone Ltd, a UK hedge fund, have the following model that they use to forecast prices from their trades on GSAT, a satellite communication company: pt =pt1 +Xt +ut where pt1 is the price of the stock for the last publicly posted trade, Xt is the size of the order that Marylebone submits to the market in shares, ut is a random term that is not under the control of Marylebone, and is the estimated impact of the Marylebone trade on the price of GSAT: 2.1 (40 points) Suppose that Marylebone wants to estimate . How would they do it, using the recent history of orders they submitted? In your answer give a formula for the estimate. (You can use the population approach.) 2.2 (60 points) Suppose the estimate of is .00008 per share. Maryle- bone want to execute a market order for 10,000 shares efficiently. What should they do? The initial price of GSAT is $1.20 and the minimum trade size is 10 shares. CONTINUED OVERLEAF/ Glosten-Milgrom Formula Sheet k1 (1) 1+(12k1 ) k1 (1+) 1(12k1 ) k = k(1)V +(1k)(1+)V k(1+)V +(1k)(1)V 1+(12k) 1(12k) Bayes rule: P [dataevent]P [event] = P [eventdata]P [data] Covariance algebra (incomplete): E[a + bx] = a + bE[x] cov(a + bx, y) = bcov(x, y) where a and b are constants. / END OF QUESTION PAPER