Lesson 9.2: The strategy map of hedge funds
Learn the main hedge fund strategy families, from long/short equity to macro, event-driven and managed futures, and the shape of each one's returns.
By the end of this lesson you will be able to describe the main families of hedge fund strategy, say what each one bets on and where its return comes from, read a fund's gross, net and beta-adjusted exposures, price the odds that the market is putting on a merger completing, recognise which strategies have the shape of selling insurance and which have the shape of buying it, and tell a source of genuine skill from compensation for bearing a known risk. You will show that a long-short fund with 100 long and 60 short has a net exposure of 40, a gross exposure of 160 and a beta-adjusted net of 28, that a merger target at 96 with a cash offer of 100 and a break price of 70 implies a 96.4 per cent chance of completion, that the same trade earns 4.2 per cent in six months if the deal closes and loses 27.1 per cent if it breaks, and that the expected return falls below cash if the true chance of completion is below 96.4 per cent. You should have read Lessons 4.2, 5.1, 5.2, 5.3 and 9.1. The mathematics is expectations and percentages. This course is education about how markets and research work, not investment advice.
Lesson 9.1 treated the hedge fund as a business. This lesson looks at what it does with the money. The phrase "hedge fund returns" is almost meaningless: a fund that buys bankrupt companies' debt and a fund that trades currency futures by computer have little in common except their fee structure. They have different sources of return, different risks, different relationships with the market and different ways of failing. A map of the main families lets you ask the right question of any fund: what is it betting on, why should that bet pay, and what does the loss look like when it does not?
Two questions that sort the strategies
Almost every strategy can be placed by answering two questions.
1. Is the bet directional or relative? A directional bet takes a view on where a market, a sector or a rate is going: long equities, short bonds, long oil. A relative bet takes a view on the gap between two things, such as one stock against another, and tries to be neutral to the direction of the whole market.
2. Where does the edge come from? Four sources recur. Information and analysis: knowing more, or understanding better, than the price reflects. Risk premia: being paid for taking a risk others avoid, such as lending against illiquid or risky assets. Structure and constraints: exploiting investors who are forced to buy or sell, such as index funds, indebted borrowers or merger targets. Speed and data: acting faster, or on better data, than others, as in the market making of Lesson 5.4.
The main families, with the lessons where their mechanics appear, are in the table.
Family · What it bets on · Typical return shape · Main risksLong/short equity · Stock selection: long the best, short the worst · Roughly symmetrical, with market exposure left over · Crowded shorts, short squeezes, hidden factor bets
Equity market neutral and statistical arbitrage · Many small relative bets with no market exposure (Lesson 5.3) · Smooth, low volatility, negative skew in crises · Crowding, leverage, factor reversals
Event-driven: merger arbitrage · Announced deals completing · Small gains with rare large losses (negative skew) · Deal breaks, regulatory or financing failure
Event-driven: distressed and special situations · Recovery values of troubled companies, restructurings · Lumpy, illiquid, long holding periods · Legal outcomes, illiquidity, valuation
Global macro · Economic and policy trends in rates, currencies, commodities and indices · Lumpy, large gains and losses · Wrong view, policy surprises, crowded trades
Relative value: fixed income and convertible arbitrage · Convergence of related prices (curves, bases, convertible bonds against stock) · Steady small gains, tail losses, high leverage · Spreads widening, funding withdrawn
Managed futures (CTAs) · Trends in futures markets (Lesson 5.1) · Many small losses, few large gains (positive skew) · Whipsaws, long drawdowns
Credit · Spreads and default risk · Carry with tail risk · Defaults, liquidity
Multi-strategy · Several of the above in one firm (Lesson 9.3) · Smoother, from diversification and risk limits · Costs, crowding, correlation in stress
## Long/short equity
The classic hedge fund buys stocks it thinks will do well and sells short stocks it thinks will do badly. The long book earns the stocks' returns, the short book earns the opposite, and a profit can be made in a falling market if the shorts fall more than the longs. Three numbers describe the exposure.
Gross exposure: long plus short, as a share of the fund's capital. It shows how much risk is taken in total, and how much leverage is used.
Net exposure: long minus short. A net of 40 per cent means the fund moves, to a first approximation, 40 per cent as much as the market.
Beta-adjusted net exposure: the sum of each position's value times its market beta, which accounts for the fact that a short in a volatile stock offsets more market risk than a long in a calm one.
Worked example 1. A fund has capital of 100. It holds longs of 100 with an average beta of 1.0 and shorts of 60 with an average beta of 1.2. Its gross exposure is 100 + 60 = 160 per cent, its net exposure 100 − 60 = 40 per cent, and its beta-adjusted net exposure 100 × 1.0 − 60 × 1.2 = 100 − 72 = 28 per cent. If the market falls 10 per cent, the fund loses roughly 2.8 per cent from market exposure alone, before any stock-selection effect. A fund that markets itself as "market neutral" while its beta-adjusted net is 28 per cent is not.
The sources of return are the stock-selection skill on both sides, the cost saving from shorting (the short rebate on cash from the sale), and any systematic exposure to factors such as value and momentum that are not apparent. The risks of Lesson 5.3 apply: crowded positions, short squeezes (a heavily shorted stock rises sharply and forces shorts to cover), and unintended factor bets. A fund with a large short book also faces the practical limits on shorting in each market.
Event-driven: merger arbitrage
Event-driven funds trade around corporate events: mergers, takeovers, restructurings, bankruptcies and spin-offs. Merger arbitrage is the best known. When a company, the acquirer, announces a deal to buy another, the target, for cash at a fixed price, the target's shares jump towards the offer price, but trade below it, since there is a chance the deal fails. The arbitrageur buys the target's shares at the discount and earns the difference if the deal closes.
Worked example 2. A target is offered ₹100 a share in cash. It trades at ₹96, the deal is expected to close in six months, and if it breaks the shares would fall to ₹70, the price before the offer. The risk-free interest rate is 6 per cent a year.
If the deal closes, the arbitrageur gains 100 ÷ 96 − 1 = 4.17 per cent in six months, about 8.5 per cent a year, compounded.
If the deal breaks, the loss is 70 ÷ 96 − 1 = −27.08 per cent.
What chance of completion does the price of 96 imply? Apply the risk-neutral logic of Lesson 7.3: the share's price is the discounted expectation of its two outcomes, so 96 = e^(−0.03) × [p × 100 + (1 − p) × 70]. Solving, p = (96 × e^(0.03) − 70) ÷ 30 = (98.92 − 70) ÷ 30 = 0.964. The market is pricing a 96.4 per cent chance that the deal closes, and 3.6 per cent that it breaks.
The trade is attractive only if the true probability of completion is higher than that. With a true probability of 98 per cent, the expected return over six months is 0.98 × 4.17 + 0.02 × (−27.08) = 3.54 per cent, better than cash at 3.05 per cent. With a true probability of 95 per cent, it is 0.95 × 4.17 − 0.05 × 27.08 = 2.60 per cent, below cash: a losing proposition on average.
True chance the deal closes · Expected return over six months90% · 1.04%
92.5% · 1.82%
95% · 2.60%
96.4% (the market's implied chance) · 3.05% (equal to cash)
98% · 3.54%
100% · 4.17%
The payoff has a familiar shape: a small, nearly certain gain with a small chance of a large loss. In effect, the arbitrageur is selling insurance against the deal breaking, which is the same shape as selling options in Lesson 6.4 and mean reversion in Lesson 5.2. The Sharpe ratio looks high until a deal breaks, and the strategy has a negative skew. The arbitrageur earns the spread as a premium for bearing deal risk, and the skill lies in judging the odds of regulatory approval, financing and shareholder votes better than the market. Risks include: a regulator blocking the deal, financing falling through, a competing bid (which helps the arbitrageur), and crowding when many funds hold the same deals and a break forces them all to sell.
Distressed and special situations funds buy the debt or shares of companies in or near bankruptcy at a deep discount, betting on the recovery value, through restructuring or a sale. Returns can be large and come in lumps over long periods. The work is more legal and financial analysis than trading, and the assets are illiquid, so these funds usually have long lock-ups. Activist funds buy a stake and press a company to change its strategy.
Global macro
Global macro funds take positions across rates, currencies, commodities and equity indices, based on views about economies, central banks and politics. They are often directional and use leverage through futures and options. Some are discretionary, relying on a manager's judgement of policy and cycles, and some systematic, using models of economic data. They have large capacity, since the markets they trade are the largest and most liquid. Their returns tend to be lumpy: long quiet periods and then large gains or losses when a view is right or wrong, often around a policy event. The risk is a wrong view held with leverage, and crowding when many macro funds share the same trade, as in a popular currency carry position.
Relative value and convergence
Relative value funds buy one asset and sell a related one, betting that a gap between their prices will close. Examples are a government bond against another of a different maturity (a curve trade), a bond against its future (a basis trade), an on-the-run bond against an older one, and a convertible bond against the shares it can turn into. In a convertible arbitrage position, the fund buys the convertible, a bond with an embedded call option, and sells short a number of shares equal to the option's delta (Lesson 6.2), so it earns the bond's income and the option's gamma and loses little to price moves.
The common feature is that each gap is small. To turn a spread of a few basis points into a worthwhile return, the fund uses high leverage, often more than ten times its capital. The trades work when the spread converges and fail when it widens, and spreads tend to widen in stress, exactly when funding is withdrawn. The result is steady small gains and rare large losses: negative skew again. Lesson 9.4 shows how this brought down Long-Term Capital Management in 1998.
Managed futures and quantitative strategies
Managed futures funds, also called commodity trading advisers or CTAs, trade futures on equity indices, bonds, currencies and commodities, mostly with the systematic trend-following rules of Lesson 5.1. Their return shape is the mirror image of the strategies above: many small losses, and a few large gains, with positive skew. They tend to do best in sustained trends and in some crises, and lose during choppy markets. Research by William Fung and David Hsieh found that the returns of trend-following funds resemble those of a portfolio of look-back straddles, options that pay off from large moves, which matches the option-like shape of Lesson 5.1.
Quantitative equity funds run the statistical arbitrage and factor strategies of Lesson 5.3, and market-making and high-frequency funds the strategies of Lesson 5.4. They are distinguished less by the asset than by the method, which Lesson 9.3 takes up.
Multi-strategy and credit
A multi-strategy fund runs many of the above in one firm, allocating capital across teams, with centralised risk and the expectation of smoother returns from diversification, using the principles of Lesson 5.1: independent bets add up faster than risk does. The structure is covered in Lesson 9.3. Credit funds lend to, or trade the debt of, companies, earning the credit spread as compensation for default risk and illiquidity, with carry-like returns and tail risk.
Alpha, beta and risk premia
When you look at a fund's returns, an essential question is how much comes from skill and how much from compensation for a risk anyone could have taken. A fund that earns 8 per cent by being 60 per cent long the stock market has earned a premium for equity risk, a market return, which an index provides for a fraction of the fee. A convertible arbitrage fund earns, in part, a premium for providing liquidity and for bearing the risk that spreads widen. Returns of that kind are sometimes called alternative beta: exposures to risk premia, harvested systematically. They are not worthless, and they diversify, but they should not be paid for at the price of alpha.
Distinguishing them is the job of the tools of Lessons 2.3 and 5.3: regress the fund's returns on market and factor returns, and see how much is left. The intercept, the alpha, is what the manager adds beyond exposures. Be careful, though: a strategy that sells insurance has negative skew that a simple regression on market returns will miss, so the alpha can be positive in good times and vanish in a crisis. A fund that looks as if it has a high alpha and a low beta, over a short record, may simply be short volatility (Lesson 4.2).
Putting the map to use
Ask the two questions of any strategy: directional or relative, and where the edge comes from.
Look at the shape of the returns. Does it win small and lose rarely and big (merger arbitrage, convergence trades, short volatility), or lose small and win big (trend following, long volatility)? Matching shapes across strategies diversifies a portfolio.
Check the exposures: gross, net, beta-adjusted and by factor, as in worked example 1.
Check capacity and crowding: how many others hold the same positions, and what happens if they sell.
Compare with cheap alternatives: could an index, a factor fund or a simple trend-following rule have delivered the same?
The code below computes the exposures, the implied probability and the expected returns of the merger arbitrage trade.
python
from math import exp
1. long/short fund exposures
longexposure, shortexposure = 100.0, 60.0
betalong, betashort = 1.0, 1.2
print("gross", longexposure + shortexposure, "| net", longexposure - shortexposure,
"| beta-adjusted net", longexposure betalong - shortexposure betashort)
marketmove = -10.0
print("return from a market move of -10% alone:",
round((longexposure betalong - shortexposure betashort) / 100 marketmove, 2), "%")
2. merger arbitrage: implied probability and expected returns
price, offer, fail, years, rate = 96.0, 100.0, 70.0, 0.5, 0.06
pimplied = (price exp(rate years) - fail) / (offer - fail)
win, lose = offer / price - 1, fail / price - 1
cash = exp(rate years) - 1
print("implied chance of completion", round(pimplied, 4), "| break chance", round(1 - pimplied, 4))
print("return if the deal closes", round(win 100, 2), "% (annualised", round(((offer / price) (1 / years) - 1) 100, 2), "%)",
"| if it breaks", round(lose 100, 2), "% | cash for the period", round(cash 100, 2), "%")
for p in (0.90, 0.925, 0.95, pimplied, 0.98, 1.0):
expected = p win + (1 - p) lose
print(f" true chance {p:.3f}: expected return {expected 100:5.2f}% | against cash {(expected - cash) 100:+5.2f}%")
Common mistakes
Treating "hedge fund" as one asset class. The families have different risks and returns, and averaging them hides the differences.
Reading net exposure as market exposure. A dollar-neutral book can carry a large beta bet.
Ignoring the shape of the returns. Strategies with negative skew look best until the tail event.
Paying alpha fees for beta. Check how much of the return is explained by market and factor exposures.
Treating a merger spread as risk-free. It is the price of a real chance of loss, and the loss is several times the gain.
Assuming convergence trades converge on your timetable. A spread can widen further before it closes, and leverage means you may not survive to see it close.
Ignoring crowding. The most popular trades are the ones that unwind fastest.
Mistaking a short record of smooth returns for skill. It may be a short-volatility position.
Forgetting capacity. The strategies with the most appealing returns, such as small-cap event-driven, often have the least capacity.
Key takeaways
A map of hedge fund strategies starts with two questions: is the bet directional or relative, and is the edge information, a risk premium, structure or speed?
Long/short equity buys the best and sells the worst. With 100 long and 60 short, gross exposure is 160, net 40 and beta-adjusted net 28, so a 10 per cent market fall costs about 2.8 per cent, whatever the stock selection does.
Merger arbitrage buys targets at a discount to the offer. A target at 96 with an offer of 100 and a break price of 70 implies a 96.4 per cent chance of completion, earns 4.17 per cent if the deal closes and loses 27.08 per cent if it breaks. It beats cash only if the true chance of completion is higher than 96.4 per cent.
Merger arbitrage, convergence trades and short volatility have the shape of selling insurance: small steady gains, rare large losses and negative skew. Managed futures and long volatility have the opposite shape.
Global macro takes directional views on rates, currencies, commodities and indices, with lumpy returns. Relative value earns small spreads with high leverage and funding risk.
Managed futures follow trends, with many small losses and a few large gains, and resemble option-like payoffs.
Separate alpha from alternative beta, with regressions on market and factor returns, and beware that insurance-selling strategies can hide their tail in a short record.
Check yourself
1. A fund has long positions of 130 per cent with a beta of 1.1 and short positions of 30 per cent with a beta of 0.9. What are its gross, net and beta-adjusted net exposures?
Gross = 160. Net = 100. Beta-adjusted net = 130 × 1.1 − 30 × 0.9 = 143 − 27 = 116 per cent.
2. A target trades at 48 with a cash offer of 50 in three months. If the deal breaks the shares fall to 36. Interest is 8 per cent a year. What chance of completion does the price imply?
e^(0.02) = 1.0202. p = (48 × 1.0202 − 36) ÷ (50 − 36) = (48.97 − 36) ÷ 14 = 0.926, so about 92.6 per cent.
3. For that deal, what is the return if it closes and if it breaks?
If it closes: 50 ÷ 48 − 1 = 4.17 per cent. If it breaks: 36 ÷ 48 − 1 = −25.0 per cent.
4. Why is a convergence trade with a leverage of 20 times more fragile than the same trade with no leverage?
A small widening of the spread causes a loss of 20 times as large relative to capital, so a loss that an unlevered holder could sit through wipes out the fund, and a margin call may force the position to be closed at the worst time.
5. A fund reports an alpha of 6 per cent a year and a beta of 0.1 over three years of monthly data, with a skew of −2.5. What would you suspect?
That it may be selling insurance: a strategy with negative skew can show a high alpha and low beta in a calm period and give it back in a crisis, which a regression on market returns alone does not show.
Try this
Set aside forty-five minutes. You need Python and the code in this lesson.
1. Run the code. Check the exposures, the implied chance of completion and the expected returns.
2. Take two announced deals from the news, with the offer price, the target's current price and an estimate of the break price. Compute the implied chance of completion for each.
3. Change the break price from 70 to 80 in the simulator. How does the implied probability change, and why?
4. Use the long/short simulator to design a fund with a gross exposure of 200 per cent and a beta-adjusted net of zero.
5. Pick three hedge fund indices or published fund returns by strategy, if you can find them, and compute their volatility, skewness and worst month. Which strategies have negative skew?
6. Regress one fund's monthly returns on an equity index and note the alpha, the beta and the R-squared. Then add the squared index return and see if it matters.
7. Write a short note: which family of strategies you would add to a portfolio that is already long equities, and why its return shape complements the rest.
A good result is a table of strategies with their return shapes, exposures you can compute for a long/short fund and an implied probability for a deal. The next lesson looks at who works inside these firms: how quantitative and discretionary funds differ, and how teams and capital are organised.
Read more
William Fung and David Hsieh's 1997 paper "Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds" in the Review of Financial Studies and their 2001 paper "The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers" examine hedge fund returns and their option-like features. Mark Mitchell and Todd Pulvino's 2001 paper "Characteristics of Risk and Return in Risk Arbitrage" in the Journal of Finance studies merger arbitrage. Andrew Lo's Hedge Funds: An Analytic Perspective surveys the strategies and their statistics. Sebastian Mallaby's More Money Than God tells the story of the industry, and Lasse Pedersen's Efficiently Inefficient describes how many hedge fund strategies work and why they earn what they do.
Tags: Quant Trader Hedge fund strategies Merger arbitrage Long/short equity Global macro