Adverse Selection and the Spread
Market makers usually explain the spread as compensation for risk and costs. That is true and it is vague. There is a sharper version, and it comes straight out of the previous two lessons.
The setup
An instrument is worth either 110 or 90, equally likely, so its expected value is 100. A fraction of the traders who arrive are informed and already know which. The remaining are uninformed, and buy or sell with equal probability for reasons of their own.
You post a bid and an ask. You cannot tell the two kinds of trader apart, and your quote must be one price for both.
What a buy order tells you
An informed trader buys only when the value is 110. An uninformed one buys half the time regardless. So
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