Suppose the price of an asset is 110 with probability 0.5 and 90 with probabilit
ID: 2807394 • Letter: S
Question
Suppose the price of an asset is 110 with probability 0.5 and 90 with probability 0.5. There are uninformed noise traders present who buy or sell one unit of the asset with equal probability, and informed traders who buy one unit if they know the price is 110 and sell one unit if they know the price is 90. There are 9 uninformed traders for every informed trader. The market is cleared by a risk neutral competitive market maker quoting prices at which the trading takes place. What are the initial bid and ask quotes?Explanation / Answer
Number of Uninformed Traders = N(1) = 9 , Number of Informed Traders = N(2) = 1
Probability of Price Being 110 = P(1) = 0.5 and Probability of Price Being 90 = P(2) = 0.5
Probability of Uninformed Trader Buying = p(1) = 0.5 and Probaility of Uninformed Trader Selling = p(2) = 0.5
Bid Quote is the average price at which traders buy assets and Ask Quote is the average price at which traders sell assets.
Therefore, Expected Bid Quote (Initial) = Number of Uninformed Traders x probability of buying x probability of price being 90 x Price + Number of Uninformed Traders x probability of buying x probability of price being 110 x Price + Number of Informed traders x probability of price being 110 x probability of buying x Price = 9 x 0.5 x 0.5 x 90 + 9 x 0.5 x 0.5 x 110 + 1 x 0.5 x 1 x 110 = 505
Similarly, Expected Ask Quote (Initial) = Number of Uninformed traders x probability of selling x probability of price being 90 x Price + Number of uninformed traders x probability of selling x probability of price being 110 x price + number of informed traders x probability of price being 90 x probability of selling x price = 9 x 0.5 x 0.5 x 90 + 9 x 0.5 x 0.5 x 110 + 1 x 0.5 x 1 x 90 = 495
Therefore, the Initial Bid Quote = 505 and Initial Ask Quote = 495
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