Short selling

Short selling is a trading strategy in which an investor sells a security that they do not currently own, typically by borrowing the security, with the expectation that its market price will decline. The investor later seeks to purchase the security at a lower price and return it to the lender.

Short selling is commonly used for speculation, hedging, and portfolio risk management.

Concept

A simplified short-selling transaction consists of:

$Borrow Security \to Sell Security \to Repurchase Security \to Return Security$

For a short position, the simplified trading profit before costs is:

$Profit = P_{0} - P_{T}$

where:

$P_{0}$ = price at which the security is initially sold;
$P_{T}$ = price at which the security is subsequently repurchased.

If the security price declines:

$P_{T} < P_{0} \Rightarrow Positive Short-Selling Profit$

If the security price increases:

$P_{T} > P_{0} \Rightarrow Short-Selling Loss$

Example

Suppose an investor borrows 100 shares of a company and sells them at $50 per share.

The initial sale proceeds are:

$100 \times 50 = $ 5, 000$

If the share price subsequently falls to $35, the investor purchases 100 shares for:

$100 \times 35 = $ 3, 500$

The simplified gross profit is:

$$ 5, 000 - $ 3, 500 = $ 1, 500$

The calculation excludes borrowing costs, commissions, taxes, dividends, financing costs, and other expenses.

If the share price instead rises to $70, the repurchase cost becomes:

$100 \times 70 = $ 7, 000$

The resulting gross loss is:

$$ 5, 000 - $ 7, 000 = - $ 2, 000$

Short position

The investor holding a short position has an economic exposure opposite to that of a conventional long position.

A simplified long-position payoff is:

$Long Payoff = P_{T} - P_{0}$

A simplified short-position payoff is:

$Short Payoff = P_{0} - P_{T}$

Therefore:

$Short Payoff = - Long Payoff$

before financing costs and other adjustments.

Margin requirements

Short selling generally involves margin requirements because the broker or lender must manage the risk that the security price rises and the short seller cannot fulfill the obligation to return the borrowed securities.

The investor may be required to deposit collateral and maintain a minimum level of equity in the account.

A simplified margin relationship is:

$Account Equity = Collateral + Unrealized P/L$

The exact margin requirements depend on the security, broker, market, regulatory framework, and applicable trading rules.

Borrowing securities

In a conventional short sale, the investor generally borrows the securities through a broker or other securities-lending arrangement.

The borrowed securities are then sold in the market.

The short seller remains responsible for returning equivalent securities to the lender.

A simplified sequence is:

Failed to parse (syntax error): {\displaystyle \text{Lender} \rightarrow \text{Securities} \rightarrow \text{Short Seller} \] followed by: <math> \text{Short Seller} \rightarrow \text{Equivalent Securities} \rightarrow \text{Lender} \] ==Borrowing costs== Short sellers may incur costs for borrowing securities. The borrowing cost depends on factors such as: * availability of the security; * demand for short positions; * market conditions; * security characteristics; * lending terms. A simplified net short-selling return can be represented as: <math> \text{Net Profit} = P_0-P_T -\text{Borrowing Costs} -\text{Transaction Costs} -\text{Other Costs} }

Dividends and distributions

When a short seller borrows a dividend-paying security, the lender generally remains economically entitled to the dividend.

The short seller may therefore be required to make a corresponding payment to the lender, commonly referred to as a payment in lieu of dividend.

A simplified net payoff is:

$Net Profit = P_{0} - P_{T} - D - C$

where:

$D$ = applicable dividend or distribution payment;
$C$ = other applicable costs.

The precise treatment depends on the security, lending arrangement, and applicable rules.

Short squeeze

A Short squeeze occurs when a sharp increase in the price of a heavily shorted security forces short sellers to buy the security to close their positions.

Short covering can add further buying pressure.

A simplified feedback relationship is:

$Price Increase \to Short Covering \to Additional Buying \to Further Price Pressure$

A short squeeze can result in rapid losses for short sellers.

Short interest

Short interest represents the number or value of securities that have been sold short and remain open.

A simplified short-interest ratio relative to shares outstanding is:

$Short Interest Percentage = \frac{Shares Sold Short}{Shares Outstanding} \times 100$

A high short-interest percentage can indicate substantial short exposure, although it does not by itself predict future price movements.

Days to cover

Days to cover is a commonly used measure comparing short interest with average daily trading volume.

A simplified calculation is:

$Days to Cover = \frac{Shares Sold Short}{Average Daily Trading Volume}$

A higher value can indicate that closing outstanding short positions may require a greater number of trading days under the assumed volume conditions.

Risks

Short selling can involve several risks, including:

Market risk;
Leverage risk;
Liquidity risk;
Counterparty risk;
Short squeeze risk;
securities-borrowing risk;
margin risk;
dividend or distribution obligations;
regulatory risk.

The potential loss from a conventional short position is theoretically unlimited because the price of a security can continue to rise.

Unlimited loss potential

For a long position, the maximum loss on an unleveraged purchase of a security is generally limited to the amount invested if the security's value falls to zero.

For a short position, there is no theoretical upper limit to the loss because the security price can rise without a fixed maximum.

The short-position loss can be represented as:

$Loss = P_{T} - P_{0}$

As $P_{T}$ increases, the loss increases.

For example, if a security is shorted at $50 and subsequently rises to $150:

$$ 50 - $ 150 = - $ 100$

The loss is $100 per share before other costs.

Short selling for hedging

Short selling can be used to hedge an existing long exposure.

For example, an investor holding a portfolio of technology stocks may establish a short position in a related technology index to reduce some exposure to a decline in the technology sector.

A simplified hedged position is:

$Hedged Portfolio = Long Exposure + Short Exposure$

The effectiveness of the hedge depends on the correlation between the long and short positions.

Short selling and speculation

Short selling is commonly used for speculation.

A trader who expects a security's price to decline may establish a short position in an attempt to profit from the decline.

The strategy can be represented as:

$Expected Price Decline \to Short Position \to Potential Profit$

However, an incorrect price forecast can result in substantial losses.

Short selling and derivatives

Short exposure can also be established through derivatives rather than directly borrowing and selling the underlying security.

Examples include:

The risk and payoff characteristics differ among these instruments.

For example, buying a put option can provide downside exposure while limiting the buyer's maximum loss to the premium paid, subject to the option's terms.

Regulation

Short selling is subject to securities-market rules that vary by jurisdiction.

Regulatory frameworks may address:

disclosure of short positions;
securities borrowing;
settlement requirements;
margin requirements;
restrictions during periods of market stress;
Naked short selling;
market manipulation;
reporting requirements.

The specific rules depend on the applicable jurisdiction, security, market, and regulatory authority.

Naked short selling

Naked short selling generally refers to selling a security short without first borrowing the security or making the arrangements required to ensure timely delivery.

It differs from conventional short selling, where the securities are borrowed or an appropriate borrowing arrangement is established.

Naked short selling is subject to specific restrictions and regulatory requirements in many jurisdictions.

Importance

Short selling plays a role in modern financial markets by allowing market participants to express negative views on securities, hedge existing exposures, provide liquidity, and participate in price discovery.

Short sellers may identify securities that they believe are overvalued or businesses facing deteriorating financial conditions. Their transactions can contribute information to market prices.

However, short selling also involves significant risks, particularly because losses can theoretically be unlimited and short positions can be affected by borrowing costs, margin requirements, liquidity constraints, and short squeezes.