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NoWork's stock at the end of the day is expected to be worth $95 (20% probability) or $105 (80% probability), pending a news announcement. A dealer believes that 80% of the traders are noise traders and 20% are informed traders. The dealer is setting her bid price. At what value of the bid price does she just break even?

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Final answer:

To break even on NoWork's stock, the dealer should set her bid price equal to the stock's expected value, which, using the probabilities provided, would be $103. This is a simplified scenario not accounting for transaction costs or required margins.

Step-by-step explanation:

To determine the dealer's break-even bid price for NoWork's stock, we must calculate the expected value of the stock based on the probabilities given for its potential future prices and the proportion of noise to informed traders. To break even, the bid price should be equal to the weighted average of the stock's possible future values.

Calculation of Expected Value

The expected value (EV) of the stock is calculated as follows:

  1. EV for $95 price = $95 × 20% = $19
  2. EV for $105 price = $105 × 80% = $84
  3. Total EV = $19 + $84 = $103

Considering that 80% of the traders are noise traders, who trade without knowledge of the pending news, and 20% are informed traders, the dealer would want the bid price to average out to $103 to break even, as it reflects the stock's expected value.

Note that the actual set up of the bid price would be complex and requires further assumptions, but for the sake of this simplified example, the dealer would set the bid price at $103 to match the EV and break even.

Additional factors that could affect the bid price, such as transaction costs and the dealer's required margin, are not considered in this simplified scenario.

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