Short Selling and Margin Requirements for Exam FM

Short Selling Mechanics

Short selling involves borrowing shares and selling them, with the obligation to return the shares later. The short seller profits if the price falls and loses if it rises. The profit on a short sale is S_0 - S_T - dividends paid - borrowing costs, where S_0 is the sale price and S_T is the repurchase price.

The short seller must deposit collateral (the initial margin) and pay any dividends declared during the short period to the share lender. The proceeds from the short sale are held by the broker and earn interest.

Margin Requirements

The initial margin is the deposit required when opening the short position, typically 50% of the short sale proceeds. The margin account value is: proceeds from sale + initial margin - current value of shares owed. The maintenance margin (typically 30% of current share value) triggers a margin call if the account equity falls below this level.

The margin call price can be found by solving: (S_0 + margin - S_call) / S_call = maintenance margin ratio. For example, if S_0 = $100, margin = $50, and maintenance = 30%, then (100 + 50 - S_call) / S_call = 0.30, giving S_call = $115.38.

Exam FM Context

Exam FM tests short selling primarily in the context of arbitrage and derivatives. When spot-forward parity is violated, an arbitrage strategy involves either buying the asset and shorting the forward, or short-selling the asset and going long the forward. Understanding the cash flows from short selling (initial proceeds, margin, dividend obligations, repurchase) is essential for constructing these strategies correctly.