Suppose that a dealer with $20,000 in capital and zero stock inventory has a logarithmic utility of
Question:
Suppose that a dealer with $20,000 in capital and zero stock inventory has a logarithmic utility of wealth function: U5ln(W).
a. Assuming a small risk (the Arrow-Pratt model, as used by Stoll, 1978), what would be his Coefficient of Absolute Risk Aversion (ARA)?
b. Uncertainty, as measured by the price variance on a given stock is 10,000. The consensus price of this stock is 100. What are the bid price and bid discount for this stock? What are the ask price and ask premium for this stock? What is the spread for this stock?
c. Now, suppose that the dealer maintains an inventory of shares of this stock so that the covariance between profits on the stock and this optimal initial inventory is E[rPΧ rpWp] = σi,P = 1000. Calculate the bid discount and price for the stock under this revised circumstance.
d. What is the dealer spread for part c?
Step by Step Answer:
a Based on the standard ArrowPratt risk aversion model used in the Stoll inventory model we ...View the full answer
