Let P be the price of a stock. The broker has an initial margin requirement of m0, where 0 < m0 < 1 for shorting the stock. At this requirement, the investor is able to sell short Q units of this stock and does so.

A. What is the investor’s initial equity E as a function of m0, P, and Q?

B. Now, the price of the stock changes to λP, λ > 0. What is the investor’s equity now? Write your answer in terms of λ, m0, P and Q.

C. Find the new margin m0 in terms of λ and m0.

D. Discuss how the sign (positive, negative) of the new margin depends on λ and m0.

E. Given a maintenance margin, c, what is the smallest λ, call it λ ∗ such that, given an initial margin m0, whenever price is greater than or equal to λ ∗P broker will issue a margin call on the short position.