Long, short and margin positions

What is the difference between a long and a short position?

A long position gains when the price rises. A short position gains when it falls. That one difference changes the risk completely.

A long position means you own the asset or hold a right to receive it. Your loss is at most 100% (the price goes to zero) if no liabilities are attached, and your gain has no ceiling. In a contract, the long side is the one that benefits when the quoted price rises. In currencies the sides are symmetrical: being long one currency against another means being short the other.

A short position means you have sold something you do not own. For shares, the short seller borrows them from a lender, sells them, and later buys them back (“covers”) to return them. For a contract, the short seller simply creates it by selling it. A short position gains at most 100% (the price cannot go below zero), but the loss is unlimited, because the price can keep rising.

Positions in an asset

• Long Memorize own it, or hold the right to receive it
  • Gains when the price rises gain unlimited
  • Maximum loss 100% with no liabilities attached
• Short Memorize sold what was borrowed, or sold a contract
  • Gains when the price falls maximum gain 100%
  • Loss unlimited price can rise without limit
  • Pays dividends to the lender payments in lieu
  • Proceeds held as collateral earn the short rebate rate

Short sellers of shares have three obligations to know. First, any dividend or interest paid while the shares are borrowed must be passed to the lender as payments in lieu of dividends . Second, the lender holds the sale proceeds as collateral. Third, the lender invests that cash and pays most of the interest back to the short seller at the short rebate rate . When a share is hard to borrow, the rebate rate shrinks and can turn negative. The share is then said to be “on special”.

A seller of a put option is short the put, but gains when the underlying share rises. The label long or short refers to the position in the contract itself, so think about which direction helps you.

Go deeper Hard-to-borrow shares and negative rebate rates

Lenders lend because the interest they earn on the cash collateral exceeds the rebate they pay back. The difference acts as a loan fee. When many traders want to short the same share and few holders will lend it, the fee rises and the rebate falls, even below zero. The short seller then pays to hold the position on top of paying dividends.

What is the leverage ratio?

The leverage ratio is the value of the position divided by the equity in it. It tells you how many times larger your position is than the money you put up.

$$L = \frac{\text{position value}}{\text{equity}}$$

In a margin purchase you borrow part of the price from your broker. The borrowed money is the margin loan , and the interest rate on it is the call money rate . The initial margin requirement is the minimum fraction of the purchase price that must be your own equity. It caps the leverage you can take.

$$L_{\max} = \frac{1}{\text{initial margin}}$$

How do you calculate the return on a margin purchase?

Compare the equity you end with against the equity you started with, after every cash flow. Interest is charged whether the share goes up or down.

Follow three steps.

1. Starting equity = the equity you pay plus the purchase commission.
2. Ending equity = sale proceeds − loan repayment − margin interest + dividends − sale commission.
3. Return = (ending equity − starting equity) ÷ starting equity.

Return on equity(ending equity − starting equity) ÷ starting equity

• Starting equity E₀ Use it equity paid plus purchase commission
• Ending equity E₁ Use it
  • Sale proceeds plus
  • Loan repayment minus
  • Margin interest minus, loan × call money rate
  • Dividends received plus
  • Sale commission minus

$$R = \frac{E_1 - E_0}{E_0}$$

Now run the same trade with a fall to EUR 44.00. Ending equity = 17,600 − 10,000 − 600 + 400 − 20 = 7,380. The return is (7,380 − 10,020) ÷ 10,020 = −26.35%, against a price fall of only 12%. Leverage magnifies the loss and the interest adds to it.

Exam tip If every option is a clean multiple of the price return, a cost is missing. Check for interest first.

At what price does a margin call arrive?

A margin call arrives when your equity falls below the maintenance margin requirement. The maintenance margin requirement is the minimum equity as a fraction of the current position value, often about 25 to 30%. Below it, the broker asks for more equity, or closes the position.

Equity per share is the price minus the loan per share, and the loan is fixed at P₀ × (1 − initial margin). Set equity ÷ price equal to the maintenance margin and solve for the price.

$$P_{\text{call}} = P_0 \times \frac{1 - \text{IM}}{1 - \text{MM}}$$

The formula ignores interest and commissions, as the curriculum does. P₀ × (1 − MM) is the classic trap: it ignores the loan, which is set by the initial margin.

Go deeper The margin call price for a short sale

A short seller’s equity falls as the price rises. With the proceeds held as collateral, equity is P₀ × (1 + IM) − P, and a call comes when that equals MM × P. So P_call = P₀ × (1 + IM) ÷ (1 + MM). For a EUR 50 share, 50% initial and 30% maintenance: 50 × 1.5 ÷ 1.3 = EUR 57.69. The learning outcome only requires the long case, but the short case shows why shorts feel the risk as prices climb.

Go deeper Why brokers ask for more than the minimum

Regulators or exchanges set minimums, but brokers often demand more equity because they bear the loss if a position falls faster than they can close it. Where a broker uses a risk model to look at the whole portfolio rather than each position, the arrangement is called portfolio margining and it can allow more borrowing.