Quant Memo
Core

Equity Market Neutral

A long/short book built so that the market's direction does not matter — target beta zero, keep only the relative call. Neutrality raises the Sharpe ratio but shrinks the raw return, which forces leverage, which is where the risk quietly comes back in.

Prerequisites: Beta (β), Long/Short Equity

Equity market neutral is Long/Short Equity with the market bet deliberately removed. A conventional long/short fund keeps a net long tilt and earns some of its return from the index going up. A market-neutral fund gives that up on purpose: it wants a P&L that depends only on whether its longs beat its shorts, so that a 20% bear market and a 20% bull market both leave the strategy roughly where it started. Everything hard about the strategy follows from that one decision.

Three things "neutral" can mean

They are not the same, and funds are sloppy about which they claim.

  • Dollar neutral. Long dollars equal short dollars. Easy to compute, and by itself close to meaningless.
  • Beta neutral. The dollar-weighted beta of the book is zero. This is the one that removes market direction.
  • Factor neutral. Zero exposure to market and to size, value, momentum, industries and anything else in the risk model. This is what serious books target.

Start with why dollar neutrality is not enough. A $100m long book of quality compounders averages βL=1.2\beta_L = 1.2; a $100m short book of tired defensives averages βS=0.8\beta_S = 0.8. The book is perfectly dollar neutral and its market exposure is

βbook=100×1.2100×0.8100=0.40\beta_{\text{book}} = \frac{100 \times 1.2 - 100 \times 0.8}{100} = 0.40

Forty percent net long the market, in a fund that markets itself as neutral. A 15% market fall costs 6% of capital that the pitch deck said was hedged.

There are two fixes. Rebalance the sizes so 1.2×L=0.8×S1.2 \times L = 0.8 \times S — with $100m of longs you would need $150m of shorts, which restores beta neutrality but leaves you $50m net short in dollars and pushes gross to 250%. Or keep the book dollar neutral and sell $40m of index futures against it, which costs almost nothing in capital and is what nearly everyone actually does.

Dollar neutral is an accounting statement. Beta neutral is a risk statement. Get the position-level betas, compute the dollar-weighted book beta, and hedge that number with index futures — do not assume matching notional matches exposure.

What neutrality is for: seeing the residual

The point of hedging is that it separates the part of your return you have a view on from the part you do not. Plot the book's monthly returns against the market's and fit a line: the slope is the beta you are trying to kill, and the vertical distance from each point to the line is the residual — the only thing a market-neutral manager is actually paid for.

Regression explorer
amber = residuals
fitted slope 1.133true slope 1.00 0.642SSres 42.0

Drag the slope towards zero and watch the fitted line flatten. The scatter around it barely changes: that spread is your alpha and your idiosyncratic risk, and it is unaffected by whether you hedged. Hedging does not make you better at picking stocks. It removes a large source of variance you were never being compensated for.

Put numbers on it. Say the book has 4% expected annual alpha and 5% idiosyncratic volatility, and the market runs at 16% volatility.

Unhedged, at beta 0.40. Market contributes 0.40×16=6.40.40 \times 16 = 6.4 percentage points of volatility. Total volatility is

6.42+52=40.96+25=8.12\sqrt{6.4^2 + 5^2} = \sqrt{40.96 + 25} = 8.12

so about 8.1%. Ignoring the market's own expected return, the ratio of alpha to risk is 4/8.12=0.494 / 8.12 = 0.49.

Hedged, at beta 0. Volatility falls to 5%, and the ratio becomes 4/5=0.804 / 5 = 0.80. Same stock picking, 63% better risk-adjusted return, purely from deleting a bet you had no opinion on.

The leverage that neutrality forces

Notice what the hedge did to the level of return: it left it at 4%. Nobody pays hedge fund fees for 4%. So market-neutral books lever up — a fund targeting 8% volatility on a 5% unlevered book runs about 1.6 times, and stat-arb style books running 2–3% unlevered volatility lever four to eight times, reaching 300–600% gross.

That is the trade the whole strategy makes: swap market risk for funding risk. Levered books are marked daily, financed by a prime broker and redeemable by investors, which is precisely the machinery described in Limits to Arbitrage. Neutral to the index does not mean neutral to a margin call.

August 2007 is the demonstration. Quantitative market-neutral books had beta near zero and were holding near-identical value and momentum positions. One large manager delevered, the shared positions moved against everyone, margin requirements rose, and the resulting forced selling drove three days of 20–30% losses — most of which reversed within a week, by which time the funds that had been forced out had crystallised the loss. The market went nowhere. The books lost a third.

"Market neutral" describes exposure to one factor. Books that are beta-zero routinely carry large unintended loadings on momentum, size, or a single industry, and those loadings supply most of the drawdown when it comes. Run the book through a factor risk model, not just a market regression, and neutralise what you find — being uncorrelated with the S&P is not the same as being uncorrelated with everyone else's positions.

In interviews

Distinguish dollar, beta and factor neutrality with the 1.2-versus-0.8 example, and give both fixes (resize the legs, or overlay index futures). Explain the Sharpe arithmetic: hedging does not raise alpha, it removes uncompensated variance, and show the 6.42+52\sqrt{6.4^2 + 5^2} step. Then close the loop honestly — the low absolute return forces leverage, leverage substitutes funding risk for market risk, and August 2007 is what that substitution looks like when it goes wrong.

Related concepts

Practice in interviews

Further reading

  • Grinold & Kahn, Active Portfolio Management (residual return and risk)
  • Khandani & Lo (2007), What Happened to the Quants in August 2007?
  • Chincarini & Kim, Quantitative Equity Portfolio Management
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