A small risky company’s stock is worth either $80 (vL) or $120 (vH) with probability 1/2 each. Market makers expect one in five of trades to be initiated by informed traders (who know whether the stock’s true value is vL or vH and trade to make a profit), while the other four out of five come from uninformed traders who buy or sell with equal probability. Assume that all transactions are for 100‐share lots.
a. What are the bid and ask prices set by risk neutral competitive market makers?
b. Compute the average trading cost to an uninformed trader and the average profit of an informed one.
c. It costs time and energy to collect the insights needed to become an informed trader. Suppose that, as per this example, such research yields actionable information (whether the stock’s true value is vL or vH) only 1/5 of the time, while 4/5 of the time no useful insights about the stock’s value emerges. How much money would a potential informed trader be willing to devote to this activity if (s)he can only trade on the information once?
d. Do you agree with the following statement? “Insider trading does not harm most market participants: it harms only those who are unlucky enough to trade with an insider.” Why? Refer to the example in this exercise to illustrate your argument.
e. Suppose now that one quarter of the uninformed order flow is siphoned off for internal execution by a broker‐dealer, who offers his/her customers execution at a 50% price improvement (i.e. a price that is midway between the mid‐quote and the relevant quote on the main market), so that this part of the order flow never reaches the main market. How will bid and ask prices quoted on the main market be affected? Who gains and who loses (relative to a situation without internalization), and by how much? What price improvement percentage would leave the uninformed traders, including both those whose orders are internalized and those whose orders stay on the main market, equally well off in total?
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