Short selling, hedge funds and hedging: types and how they work

In depth13 min read · 13 sources

With short selling, you sell shares that you have only borrowed and bet on falling prices. Hedge funds use the short side to take out market risk or to bet against individual companies; with hedging, by contrast, an offsetting position serves as insurance for an existing portfolio. Here you will learn how securities lending works, which disclosure obligations apply, which hedge fund strategies exist and how to calculate a hedge ratio.

Short selling: how a short position works

For a short sale, you borrow shares through securities lending, usually arranged by your broker, and sell them immediately. Later you buy them back and return them to the lender. You make money if the buyback price is below the selling price. The lender receives collateral, usually the sale proceeds plus a margin, and a borrow fee in percent per year. If the stock pays a dividend during the loan, you have to compensate the lender for it. The lender should be in the same economic position as if they had never lent the shares.

On top of this come risks that buyers do not face. Recall risk: the lender can demand its shares back at any time; if you cannot find a new lender, you have to buy back. Rising borrow fees for stocks in demand. A growing position: if the price rises, the short position ties up more collateral. A short squeeze occurs when many short sellers have to buy back at the same time, for example because of demands for additional collateral (margin calls): their purchases push the price up and force the next ones to buy back.

Rules: net short positions and disclosure

In the EU, the Short Selling Regulation (Short Selling Regulation 2012) governs this business. Naked short selling of shares is prohibited: anyone who sells short must have borrowed the shares, have an enforceable claim to delivery, or have confirmation that the shares have been located for them (locate). Naked credit default swaps on government bonds are also prohibited. For transparency, what counts is the net short position: short positions in a stock minus long positions in the same stock, as a percentage of the issued share capital.

• Notification to the supervisor, in Germany to BaFin: when the position reaches or falls below 0.1% of the issued share capital, and then at each step of 0.1 percentage points.
• Public disclosure: from 0.5%, and then likewise in steps of 0.1 percentage points, including when falling below.
• Deadline: what matters is the position at 24:00 (midnight) at the end of the trading day; it must be reported by 15:30 on the following trading day at the latest.

In crises, short selling has at times been banned. Beber and Pagano (2013) analyse the bans of 2007 to 2009 worldwide: they harmed liquidity, especially for small caps without traded options, slowed down price discovery and did not support prices, except possibly for US financial stocks.

Hedge funds: strategies with a short side

A hedge fund may sell short, borrow money and use derivatives; in the EU it counts as an alternative investment fund (AIF). How much market risk a fund carries is shown by two figures (gross exposure):

Hedge funds are not equity funds with a bit of a short side. Using fund data, Fung and Hsieh (1997) showed that their strategies differ strongly from those of traditional mutual funds and are highly dynamic; they found five dominant investment styles. Trend followers are covered in the article managed futures, and long/short in practice in the article pairs trading.

Hedging: the main types of hedge

Hedging is meant to reduce the risk of an existing position. Every hedge trades it for other risks: costs, basis risk and forgone gains.

• Beta hedge with index futures: selling index futures reduces the portfolio's beta to zero or to a target value. What remains is alpha and roughly the money market rate embedded in the futures price (cost of carry).
• Delta hedge with options: an options position is offset with the underlying so that small price movements have no effect (delta hedging). Because the delta changes with the price (gamma), the hedge has to be adjusted continuously.
• Duration hedge: interest rate futures or interest rate swaps reduce the basis point value of a bond portfolio (see duration).
• Currency hedging: foreign currency is sold forward through currency forwards. This costs or earns roughly the interest rate differential: with a 2% euro rate and a 4% dollar rate, it comes to 1.02 / 1.04 − 1 = −1.92% a year (see currency risk).
• Tail hedge with puts: far out-of-the-money puts only pay off in large crashes (tail risk hedging, protective put). In calm years they cost premium on an ongoing basis.
• Cross hedge: the hedge uses a related, more liquid instrument because there is none for the risk itself, e.g. European small caps hedged with a future on large caps (cross hedge).
• Macro hedge: against a macroeconomic risk rather than against a single investment, e.g. government bonds against a recession.
• Static or dynamic: a static hedge stays in place, e.g. a put until expiry; a dynamic one is adjusted continuously, as with a delta hedge or a CPPI.

How to calculate the hedge ratio: beta and minimum variance hedge

How much hedging is needed is described by the hedge ratio h: futures notional per euro of portfolio. Minimising the variance of the hedged position gives the minimum variance hedge ratio, as derived by Hull (2021):

ρ × σ_S / σ_F is the slope of a regression of portfolio returns on futures returns, i.e. the portfolio's beta relative to the future. The beta hedge with index futures is therefore a special case: N = β × V / (F × m). How well the hedge works is shown by ρ²: the share of the variance it eliminates.

For interest rate risk, the same logic applies with durations instead of betas: N ≈ (D_P × V) / (D_F × F × m). €10 million of bonds with a modified duration of 7 need around 67 contracts of an interest rate future with a contract value of €130,000 and a duration of 8.

Basis risk: why no hedge is perfect

For futures, the basis is the spot price minus the futures price; more generally, it is the gap between the hedged value and the hedge. It converges to zero by expiry and fluctuates in between. Basis risk arises wherever the portfolio and the hedge are not the same:

• A different underlying: in the example above, with ρ = 0.9, almost half of the volatility remains, 8.72% out of 20%.
• Estimated hedge ratio: betas and correlations drift; a ratio from calm years can be too small in a crisis.
• Maturity and rolling: if the future expires before the end of the hedging period, it has to be rolled; the basis and the roll yield change in the process.
• Liquidity: futures settle daily. You cover losses on the hedge immediately with cash (margin), while the gain in the portfolio exists only on paper.

For bonds, CDS and futures, the basis is itself a traded object; see basis trades.

For advanced readers: derivation, estimation error, gamma

Derivation: a position that is short h units of the future has the variance σ_S² − 2hρσ_Sσ_F + h²σ_F². Differentiating with respect to h and setting the result to zero gives h* = ρσ_S/σ_F = Cov(S, F) / Var(F), the slope of the least squares regression. The residual variance is σ_S² × (1 − ρ²); that is why ρ² is used as a measure of hedge effectiveness.

Estimation error: h* comes from past returns. The standard error of the slope is roughly σ_resid / (σ_F × √n). With the figures from the example and 60 monthly observations, this is 8.72% / (15% × √60) ≈ 0.075; the 95% interval ranges from about 1.05 to 1.35, i.e. between 42 and 54 contracts. Estimated on a rolling basis or with a Kalman filter, h reacts faster but is noisier.

Delta hedging in discrete time: between two adjustments, a delta-neutral option holder earns roughly ½ × Γ × (ΔS)² + Θ × Δt, where Θ is negative. So what counts is realised versus implied volatility (see option pricing).

Beta of hedge funds: monthly returns of illiquid funds are often smoothed. A beta estimated only from contemporaneous months then underestimates the market risk; it is better to also regress on the market returns of the preceding months and add up the betas.

What the research shows

Short sellers are informed on average. Boehmer et al. (2008) analyse NYSE order data from 2000 to 2004: short sales accounted for more than 12.9% of trading volume, and heavily shorted stocks underperformed lightly shorted ones on a risk-adjusted basis by 1.16% on average over the following 20 trading days, or 15.6% annualised. Using data from 2005, Diether et al. (2009) even find 24% of volume on the NYSE and 31% on Nasdaq; short sellers traded more after price rises and correctly predicted negative abnormal returns.

Short selling is risky in itself. According to Engelberg et al. (2018), the risk of rising borrow fees and recalled loans affects prices: stocks with greater short selling risk have lower returns, are less efficiently priced and are shorted less often. This fits the limits of arbitrage described by Shleifer and Vishny (1997).

Hedge fund returns are hard to measure. Fung and Hsieh (2001) show that hedge fund strategies often generate option-like returns that linear factor models explain poorly; trend followers can be replicated with lookback straddles. Asness et al. (2001) find significantly more market risk in hedge fund indices from 1994 to 2000 once stale or “managed” prices are taken into account. They then find no added value. Getmansky et al. (2004) attribute the strong autocorrelation of many hedge fund returns mainly to illiquidity; smoothed returns flatter volatility and the Sharpe ratio.

Hedging costs money, but does not bring the same benefit everywhere. Campbell et al. (2010) show for 1975 to 2005 that the US dollar, the euro and the Swiss franc moved against global equity markets. For risk-minimising equity investors, these currencies are therefore useful, while for bond investors the best strategy is close to a full hedge. Puts as insurance are expensive on average: according to Coval and Shumway (2001), the expected returns on puts are below the risk-free rate.

Limitations and common mistakes

• Short is not a mirror image of buying: unlimited loss, limited gain.
• Forgetting the borrowing costs: for stocks in demand, the fee eats up the expected profit.
• Confusing net exposure with risk: a market-neutral fund with 400% gross exposure can fluctuate more than an equity fund if the long and short sides diverge.
• Overhedging: a hedge that is larger than the risk becomes a bet in itself.
• Not investment advice: short sales, futures and options are risky and unsuitable for many private investors. This article only explains the mechanics.

How Portfolio Lab calculates it

Long/short: under Long/Short you can test four long/short methods with daily prices. The proceeds of the short sales are held as collateral in cash and earn the cash rate; a borrow fee is charged on the previous day's short notional, 0.5% p.a. by default. The defaults also include 5 basis points of trading costs and gross leverage of 2. With the factor residuals method, each stock is hedged with beta times a factor ETF; with the rank method, you weight dollar-neutral or beta-neutral. The app does not simulate recalls, rising borrow fees or short squeezes, and the module does not calculate taxes. More in the methodology.

Options: the Options calculator shows delta, gamma, vega, theta and rho and combines up to eight legs, including the underlying itself. Templates such as protective put and collar show the delta of a hedge (methodology).

Currencies and hedge fund series: in the Backtest, every price series is converted into the base currency daily, i.e. unhedged. You can model currency hedging with currency-hedged share classes, which are available as separate securities with their own price series. Under Asset classes there are hedge fund strategies approximated with liquid funds in euros, such as equity long/short, equity market neutral, merger arbitrage, global macro and tail-risk hedging.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.