Explanation:
The expected transaction cost including liquidity risk is calculated as:
Liquidity Cost = Mid-Price * (1/2) * (Mean Spread + Z * Standard Deviation of Spread)
First, find the mid-price and the mean percentage spread:
Ask = $200, Bid = $199
Mid-Price = (200 + 199) / 2 = $199.5
Mean Spread in percentage = (Ask - Bid) / Mid-Price = 1 / 199.5 ≈ 0.0050125
At a 99% confidence level, the Z-score is 2.326.
Liquidity Cost = 199.5 * 0.5 * (0.0050125 + 2.326 * 0.0004)
Liquidity Cost = 99.75 * (0.0050125 + 0.0009304) = 99.75 * 0.0059429 ≈ 0.5928
This is closest to 0.5927 (Option B).
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Q.19 Suppose Delight Inc. traded at an ask-price of $200 and a bid price of $199. The sample standard deviation of the spread is 0.0004. What is the expected transaction cost at a 99% confidence level?
A
0.4872
B
0.5927
C
0.6982
D
0.804