BFF2701 Equity Markets
Tutorial 5 Questions
Question 1
Consider a Kyle (1985) model set-up in which the true value of the stock is $75.00, the unconditional variance of the true value is 8, the variance of uninformed trading is 15,000 and the expected value of the stock is $80.00 without private information. That is:
F(̃) = $75.00
σF(2) = 8.00
σZ(2) = 15,000
F(̅) = $80.00
(a) Calculate the informed trader’s equilibrium trading demand (x). Report your response to four decimal places. Interpret the result.
(b) Calculate the dealers’ price sensitivity in equilibrium (λ). Report your response to four decimal places. Interpret the result.
(c) Calculate the informed trader’s expected profit in equilibrium (̃(π)). Report your response to four decimal places.
(d) Now, let us assume that the realised uninformed trading demand is 500. That is, Z = 500. Let us also assume that the informed trader submits the trading demand derived in Part (a).
(i) Calculate the dealers’ price if they follow their equilibrium strategy (p(w)). Report your response to four decimal places.
(ii) Calculate the informed trader’s realised profit (π). Report your response to four decimal places.
(iii) Calculate the dealers’ realised profit (πMM ). Report your response to four decimal places.
(e) Now, let us assume that the realised uninformed trading demand is -200. That is, z = −200. Let us also assume that the informed trader submits the trading demand derived in Part (a).
(i) Calculate the dealers’ price if they follow their equilibrium strategy (p(w)). Report your response to four decimal places.
(ii) Calculate the informed trader’s realised profit (π). Report your response to four decimal places.
(iii) Explain the difference in the informed trader’s profit from Part (d)(ii) to Part (e)(ii).
Question 2 (Teall (2022) Q6.3)
The model of demand in the Kyle (1985) assumes that perfectly informed trader demand x increases linearly in his expected value of the traded stock. This assumption is important to Kyle's results. Demonstrate that perfectly informed trader demand x in the Kyle model increases linearly in the difference between his expected value of the traded stock and the price p set by the dealer. (This difference, v-po, is the profit per share to the informed trader.)
Question 3 (Teall (2022) Q6.4)
An informed trader has private information that the value of a stock is $100 per share. Without this information, the variance of payoffs on the stock would be $60; this is the level of payoff uncertainty faced by uninformed investors. The variance associated with uninformed investor trades is 10,000 shares.
a. If the value of the stock were to be $100 without the private information, what would be the level of informed trader demand for the stock?
b. If the value of the stock were to be $90 without the private information, what would be the level of informed trader demand for the stock?
c. What will be the informed trader's expected profits from purchasing the number of shares computed in part b?
d. Suppose that actual uninformed demand for the stock were zero. Based on your computations from part b, at what level would the dealer set the stock price?