Core Path · L1.5.07

Short selling and securities lending

10 minEquitiesMarkets

By the end you will be able to

  1. 1Explain how a short sale works: borrow, sell, buy back, return.
  2. 2Describe securities lending: who lends, collateral, fees, recalls and dividends.
  3. 3Calculate the profit or loss on a short position, including the borrow fee and dividends.
  4. 4Explain the risks of short selling, and how regulators oversee it.

Why it matters

Buy a share and the most you can lose is what you paid. Sell one you do not own and there is no limit at all. Short sellers profit when prices fall, and when they are wrong, they can be wrong without end.

Core explanation

Selling what you do not own

Imagine a friend lends you a concert ticket that is selling for £100. You sell it straight away for £100, promising to give your friend an identical ticket before the concert. If the price drops to £60, you buy one, hand it back and keep £40. If the price jumps to £300, you still have to find a ticket, and you are £200 out of pocket.

That is a short sale. An investor who thinks a share is overpriced borrows it, sells it at today's price, and later buys it back to return to the lender. The profit is the fall in price, less the costs of borrowing. Buying a share in the usual way is called going long.

Where do the shares come from? From securities lending. Large long-term owners, such as pension funds, insurers and index funds, lend shares they plan to hold anyway, usually through their custodian bank. A hedge fund borrows them through its prime broker. Step through the life of one loan:

The life of a short position

1 / 5

Day 0

Borrow and sell

The fund borrows 10,000 shares and sells them at $50.00. It gives the lender collateral worth a little more than the shares, often 102% to 105% of their value, in cash or bonds.

Why short? Some short sellers bet against companies they think are overvalued or fraudulent, and their research has exposed real accounting frauds. Many more short to hedge: a fund that owns one bank's shares may short another's to remove the risk of the whole sector falling. Market makers short to fill buyers' orders. Shorting adds sellers to the market, which helps prices reflect bad news as well as good.

The risks. Which of these is the short seller's problem? Pick one for each.

Spot the short seller's risk

0 of 3
  1. A rival company bids to buy the target at a 60% premium.

  2. The pension fund that lent the shares wants them back to vote at a contested AGM.

  3. Many funds are short the same stock. Good news lifts the price, and they all rush to buy back.

The formal version

The profit or loss of a short position, shown in full. With NN shares sold at P0P_0, bought back at P1P_1, a borrow fee ff a year for dd days (actual/360) and dividends DD per share paid while short:

P&L=(P0−P1) N⏟price  −  f×P0N×d360⏟borrow fee  −  D N⏟dividends\text{P\&L} = \underbrace{(P_0 - P_1)\,N}_{\text{price}} \; - \; \underbrace{f \times P_0 N \times \frac{d}{360}}_{\text{borrow fee}} \; - \; \underbrace{D \, N}_{\text{dividends}}

The price term can be at most P0NP_0 N, if the price falls to zero. As P1P_1 rises, it falls without limit. That asymmetry is the opposite of the limited liability of L1.5.01. In practice the fee accrues daily on the current value of the shares; using the starting value keeps the example simple.

Try it

Start at the worked example below. Slide the buy-back price above $50 and keep going: the short line keeps falling. Then raise the borrow fee to 30%, as happens to crowded shorts, and watch the break-even price drop.

Try itShort position P&L

Net profit or loss
+$74,750
Price gain or loss+$80,000
Borrow fee−$1,250
Dividend paid−$4,000
Break-even price$49.48
Profit or loss against the buy-back price short, after costs long, for comparison
−$1.0m−$0.5m$0.0m$0.5m$1.0m$0$50$100$150

10,000 shares sold short at $50. The most the short can make is $500,000 less costs, if the price falls to zero. The loss has no limit: the line keeps falling as the price rises. Fee accrued actual/360 on the starting value.

Worked example

Shorting Ridgeway Retail

A hedge fund thinks Ridgeway Retail, a US chain, is overvalued. It shorts 10,000 shares at $50.00. The borrow fee is 1% a year, accrued actual/360 on the starting value; collateral is 102% of the shares' value. All amounts in US dollars.

When the short works

Step 1 of 5
  1. 1

    Sell the borrowed shares

    10,000×50.00=500,00010{,}000 \times 50.00 = 500{,}000 in sale proceeds. The fund posts $510,000 of collateral with the lender.

Now the same trade when it goes wrong.

When the short is squeezed

Step 1 of 4
  1. 1

    Good news, and the price runs

    Ridgeway reports strong sales. Other short sellers rush to buy back and the price climbs to $80.00. The shares are now hard to borrow and the fee jumps to 30% a year.

Regulatory lens

In the EU, the Short Selling Regulation requires anyone with a net short position of 0.1% or more of a company's shares to report it to the regulator, and to disclose it publicly from 0.5%. It bans naked short selling of shares: the seller must have borrowed the shares or have a firm arrangement to borrow them. In the US, Regulation SHO requires a broker to locate shares that can be borrowed before a short sale, and Rule 201 restricts short sales in a stock whose price has fallen 10% in a day. In the 2008 crisis, regulators in the US, the UK and elsewhere temporarily banned short selling of financial shares.

Looking ahead

Securities lending is one form of securities financing, alongside repo (L1.6.04). For banks, the collateral and the borrowed securities create counterparty exposures that capital rules cover (L4.2).

Sparks

SparkFor one day, the world's most valuable company
In October 2008 Porsche revealed that, through shares and options, it controlled around three-quarters of Volkswagen. With the state of Lower Saxony holding about a fifth, very few shares were left for the many funds that were short. They scrambled to buy, and Volkswagen's share price multiplied in two days, briefly making it the most valuable company in the world.
SparkGameStop, 2021
In January 2021, short interest in the US video game retailer GameStop exceeded its free float: some shares had been lent, sold, and lent again. Retail investors coordinating online piled in, and the price rose from about $20 to above $400 within weeks. Several hedge funds closed their shorts at heavy losses.

Key takeaways

  • A short seller borrows shares, sells them, buys them back later and returns them, profiting if the price falls.
  • Shares are borrowed through securities lending, from long-term holders who earn a fee and are protected by collateral.
  • Net P&L = (sale price − buy-back price) × shares − borrow fee − dividends paid to the lender.
  • The most a short can make is the sale value; the loss has no limit. Recalls, margin calls and squeezes can force a close at the worst time.
  • Regulators require disclosure of large short positions and ban naked short selling in the EU; the US requires a locate.

Reaction

Check what stuck

Question 1 · objective 1

What is the right order of steps in a short sale?

Question 2 · objective 3

You short 2,000 shares at $30 and buy them back at $24. Before costs, what is your profit, in dollars?

$

Question 3 · objective 3

Same trade. You were short for 180 days at a borrow fee of 2% a year (actual/360, on the starting value), and the company paid a $0.50 dividend. What is your net profit, in dollars?

$

Question 4 · objective 4

You short 1,000 shares at $20. A takeover bid sends the price to $50 and you buy back. Ignoring costs, how much have you lost, in dollars?

$

Question 5 · objective 2

Why do pension funds and index funds lend their shares?

Glossary

Short sale
Selling shares you do not own, having borrowed them, in the hope of buying them back later at a lower price.
Securities lending
Lending shares or bonds to another firm for a fee, against collateral, with the right to have them returned.
Lender
The owner who lends its shares, typically a pension fund, insurer or index fund, often through its custodian bank.
Prime broker
A bank that provides hedge funds with services such as borrowing shares, financing and settlement.
Collateral
Cash or securities the borrower hands over to protect the lender if the shares are not returned.
Borrow fee
The annual rate the borrower pays the lender, charged on the value of the shares borrowed.
Recall
The lender's right to ask for its shares back, which can force the borrower to close the short.
Manufactured dividend
A payment the borrower makes to the lender equal to any dividend paid while the shares are on loan.
Short squeeze
A sharp price rise that forces short sellers to buy back, which pushes the price up further.
Short interest
The number of shares sold short and not yet bought back, often shown as a percentage of the free float.
Naked short selling
Selling shares short without having borrowed them or arranged to borrow them.

Deep Dives & Origins

Deep Dives

  • Bodie, Kane and Marcus, Investments, McGraw Hill, the section on short sales in the chapter on how securities are traded. Beginner.
  • Financial Stability Board, Strengthening Oversight and Regulation of Shadow Banking: Policy Framework for Addressing Shadow Banking Risks in Securities Lending and Repos, August 2013. Intermediate.

Origins

  • Bodie, Kane and Marcus, Investments, McGraw Hill.
  • Regulation (EU) No 236/2012 on short selling and certain aspects of credit default swaps.
  • US SEC, Regulation SHO (17 CFR 242.200 to 242.204) and Rule 201.
  • US SEC, Staff Report on Equity and Options Market Structure Conditions in Early 2021, October 2021.

Module complete

You have finished Module 1.5 Equities. Try the Lab Test: applied problems that combine the module's seven lessons.

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