Chapter 3 of 5 · 9 min

The cost of carrying a short

Short proceeds earn interest, but the borrow fee and the dividend come out of it. The net is the hurdle a short must clear.

By the end of this chapter you can

Calculate the rebate, the net carry rate and the carry over a holding period
Work out how far a stock must fall to pay for a negative carry
Find the highest borrow fee before the carry turns negative
Show what a hard-to-borrow name costs

The intuition

To short a stock you borrow the shares, sell them, and later buy them back to return. Like renting a car, borrowing has a fee for as long as you keep it. But you also sold the shares, so you are sitting on the cash, and that earns interest. And if the company pays a dividend while you are short, the owner still expects it, so you pay it.

Put those together and you get the carry of the short: what it earns or costs to hold before the share price moves at all. The interest on the cash, net of the fee, is called the rebate.

The key idea

Rebate = risk-free rate − borrow fee. Net carry rate = rebate − dividend yield. Carry over the hold = position × net carry rate × days ÷ 365. A negative carry is a fall the stock must deliver before the short makes money.

Why it works

The conventions here: short proceeds earn the risk-free rate; the prime broker charges a borrow fee on the stock's value; the short pays any dividend. Simple rates on the starting position, over days ÷ 365.
Most stocks are cheap to borrow, with a fee well under 1% a year, so when rates are high the short earns a positive carry.
Some are 'specials'. When many funds want to short the same name, the fee can reach 10% or 20% a year or more, and the carry turns sharply negative.
The dividend is a real cost to the short, because the lender no longer holds the shares and must be made whole.
Breakeven fall = −carry ÷ position. Over a long hold a negative carry adds up, which is why slow-burning shorts in expensive borrows bleed.
The fee is not fixed. Borrow usually resets daily and the lender can recall the shares, so a cheap borrow can turn expensive while you hold it.

Short $20M for 180 days; risk-free 4%; borrow fee 1%; dividend yield 2%

Rebate: 4% − 1%	3%
Net carry rate: 3% − 2%	1% a year
Carry: 20 × 1% × 180 ÷ 365	+$0.099M
Highest fee for zero carry: 4% − 2%	2%
If it goes hard to borrow at 15%: 4% − 15% − 2%	−13% a year
Carry then: 20 × −13% × 180 ÷ 365	−$1.282M

At that cost the stock must fall 1.282 ÷ 20 = 6.41% over the 180 days just to break even.

The formulas

Rebate = risk-free rate − borrow fee

Interest on the proceeds, less the rent on the shares.

Net carry rate = risk-free − borrow fee − dividend yield

What holding the short earns in a year.

Carry over the hold = position × net carry rate × days ÷ 365

Scaled to the holding period.

Breakeven fall = −carry ÷ position

How far the stock must fall to pay for a negative carry.

Highest borrow fee for zero carry = risk-free − dividend yield

Set the carry to zero and solve for the fee.

Worked example

The rebate first, then take off the dividend, then scale the yearly rate to the holding period.

Drawing the numbers…

See it move

Same short. Change its size, the risk-free rate, the borrow fee, the dividend yield and how long it is held.

Drawing the numbers…

Try this

Raise the borrow fee. The carry falls, and the gap to the hard-to-borrow case narrows.
Raise the dividend yield. The carry falls, and so does the highest fee the short can bear.
Raise the risk-free rate. The carry and the highest fee both rise; the extra cost of a hard borrow does not change.
Lengthen the holding period. The carry grows in whichever direction it already points.

Run it backwards

Same company, reversed: how high can the borrow fee go before the short stops paying for itself?

Drawing the numbers…

Set the net carry rate to zero: risk-free − fee − dividend yield = 0. The fee that does it is the risk-free rate minus the dividend yield.

A quoted fee above that line tells you the name is a special: the fee is the market's price for a crowd already in the trade.

Traps

Treating a short as free to hold.

Add up the rebate, the fee and the dividend. A short in an expensive borrow has a hurdle before it makes a cent.

Forgetting the dividend.

The short pays it to the lender, so it comes straight off the carry.

Using the yearly rate for a shorter hold.

Multiply by days ÷ 365.

Assuming today's fee will last.

Borrow resets daily and can be recalled. Plan for the fee rising.

Reading a high fee as a reason to short.

The fee is high because the trade is crowded, and a squeeze hurts the crowd first.

Say it in the interview

The interviewer asks

“What does it cost to hold a short position?”

Say yours out loud first, then compare.

Check yourself

4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.

Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.

0 of 4

Drawing your questions…

Remember

Net carry rate = risk-free − borrow fee − dividend yield.
Carry over the hold = position × rate × days ÷ 365.
Breakeven fall = −carry ÷ position.
Highest fee for zero carry = risk-free − dividend yield.