There are 3 categories of investors: uninformed, informed, and very informed. The very informed know the stock price is either 90 or 110. The informed know that the expected stock price is either 95 or 105. The probabilities of uninformed, informed, and very informed trading depend on the dealer's bid-ask spread as follows:

Probability of trading as a function of the bid-ask spread

Very informed Informed Uninformed

0% 0% 100% bid-ask spread 6

20% 30% 50% 6 < bid-ask spread 10

100% 0% 0% 10 < bid-ask spread 20

No trading No trading No trading 20 < bid-ask spread

The dealer is risk neutral and sets a bid-ask spread centred at 100 to maximize the expected profit of the next trade.

What is the dealer's optimal bid-ask spread and corresponding expected profit? You must clearly justify your answer to receive full credit. In particular, if you are not explicitly testing every possible bid-ask spread, you must explain why.

Answer rating: 100% (QA)

To find the dealers optimal bidask spread and corresponding expected profit we need to evaluate the expected profit for each possible bidask spread an... View the full answer