Consider a portfolio consisting of a short position in 10,000 shares of Facebook and the necessary collateral. At the time the short position was created, Facebook’s share price was $40. The proceeds from shorting these shares, along with the 50% margin requirement, were invested in a US treasury note maturing in 10 years.
(a) What is the liquidation value of the portfolio on the day it was formed?
(b) What are the portfolio weights for Facebook stock and US treasury bonds?
(c) Suppose that one month after this portfolio was formed, Facebook’s stock price had risen by 15% and the treasury note’s price had fallen by 1%. Neither asset payed any dividends or coupons. What is the portfolio’s return for this month?
(d) In the scenario described in part (c), what is the new (at the end of the month) liquidation value of the portfolio?
(e) For standard US equity short sales, in addition to the initial margin requirement of 50%, there is a maintenance margin requirement of 25%. This means that at any point, the value of the collateral must be at least the value of the short position plus an additional 25%. For example, if the short position is currently worth $50,000, the collateral must be worth $62,500 or more. Given the initial short occurred at $40 per share, ignoring the scenario described in parts (c) and (d), and assuming that the value of the treasury note position remains constant, what is the highest per-share price of Facebook such that the initial portfolio does not violate the maintenance margin requirement?