Quantitative Trading

Chan defines the subject narrowly: trading in which a computer program makes every entry and exit, under rules the trader wrote and tested on past data. That takes in more than chart patterns — a program can read earnings, cash flow or the news — and leaves out any chart reading that cannot be written down as a rule.

The kind he teaches is statistical arbitrage in plain instruments: stocks, futures and sometimes currencies. His claim is that a few school-level courses in maths, statistics or programming are enough to start, and he argues it from his own record. After a physics doctorate at Cornell, research at IBM and posts at banks and hedge funds including Morgan Stanley and Credit Suisse, he says his complex models lost money for his employers. Trading simple strategies on his own account from a spare bedroom, he became profitable for the first time.

He sets out the business case in three parts. A strategy scales by changing one number, its leverage; once running it takes little daily time; and it needs no marketing, since a market counterparty cares only about price. He is as firm about what it is not: in his words, “instant wealth is not the objective of quantitative trading.”

His sketch of the right person is modest: some background in finance or programming, savings enough to ride out losses and months without income, and a temper that sits between fear and greed.

The chapter’s opening surprise is that ideas are cheap. Chan says hundreds of strategies sit in public at any time — in academic papers, blogs, forums and books — often with the full method and backtest attached. He lists sources from SSRN and NBER to Quantpedia, an index of academic strategy papers. The scarce skill is telling which few deserve a full test.

For that he gives a screen to run before any serious backtest. Does the strategy beat a benchmark? Is its Sharpe ratio high enough? Are its drawdown and the time spent in drawdown small enough? Is the backtest free of survivorship bias? Has it weakened in recent years? And does it have a niche that shields it from large institutions?

A strategy also has to fit the person running it. Chan works through working hours (while employed, he traded a strategy that needed orders once a day before the open), programming skill (which decides whether faster strategies are within reach) and capital (a small account needs the most leverage it can get, which points to futures, currencies or intraday positions).

Costs get an early warning. His example is a five-minute mean-reversion rule on the S&P 500 E-mini future with a Sharpe ratio of about 3 before costs; subtract one basis point per trade and it falls to about –3.

The niche question carries the book’s main argument. Chan tells the small trader to seek strategies that “fly under the radar” of institutions: ones that trade too often, trade too few stocks, or hold positions too rarely to absorb much money. Low capacity is a defect for a fund and the opening for an individual.

Look-ahead bias is using a fact the strategy could not have known when it traded. Chan’s example is a rule to buy within 1 percent of the day’s low, which nobody knows until the close. Fitting a regression on the full data set and then trading on it inside that same period is the subtler version. The cure is to compute every signal from data lagged to the previous period.

Data-snooping bias comes from fitting too many choices to the same history. His rule of thumb is blunt — “I would not employ more than five parameters” — and he counts entry and exit thresholds, holding period and lookback window among them. He adds that choices that are not parameters at all, such as trading at the open or the close, get tuned the same way by repeated testing. The defences he gives are enough data per parameter (citing Bailey and co-authors on minimum backtest length), a held-back test period, and checking whether results survive small changes to the settings.

Survivorship bias flatters any strategy that buys cheap stocks, because a database of survivors drops the cheap stocks that went on to fail and keeps the ones that recovered.

Costs decide the rest. Example 3.7 tests a simple rule credited to Khandani and Lo — buy the previous day’s worst performers in the S&P 500, short the best. Chan’s 2006 run of it shows a Sharpe ratio of 0.25 before costs and –3.19 after a five-basis-point cost per trade.

Refining a strategy after testing is allowed, Chan says, but each change should rest on economics or a well-studied market effect rather than trial and error. Otherwise the refinement is data snooping under another name.

The first choice is between a retail account and a proprietary trading firm. Chan’s table sets it out: retail leverage is fixed by SEC Regulation T, generally two times overnight and four times intraday; a prop firm sets its own and may allow 20 times or more on intraday or hedged positions. The price is a Series 7 exam, higher fees, less freedom, and an account no insurer covers.

His summary is one sentence long: retail gives freedom and better protection of capital; prop gives leverage. He reports that choosing a retail broker took him under a month, and setting up at a prop firm took several.

Commissions are only part of cost, and sometimes a small part. Chan asks traders to weigh the broker’s speed of execution and access to dark pools, and the range of products it allows. For a quantitative trader the next test is whether the platform lets a program receive data and send orders; without that, he notes, high-frequency trading is impossible.

An automated trading system generates orders and sends them to the broker without a human in the loop. Chan names three gains: it sticks to the tested strategy, it lets one person run several strategies at once, and — the most important — it sends orders fast enough for high-frequency work.

He describes two levels. In a semi-automated system, a program written in Excel, MATLAB, Python or R produces an order list, often the backtest program itself, and the trader uploads it to the broker’s basket tool by hand. A fully automated system fetches the data, runs the model and sends orders through the broker’s interface on its own.

When live results fall short of the backtest, he gives an order of diagnosis. First the easy causes: bugs, trades that differ from the backtest’s, costs above plan, illiquid names moving on the strategy’s own orders. Only then the two he calls most dreaded: data-snooping bias and a change of regime. His test for the first is to strip out rules and parameters and see whether the backtest survives.

The chapter opens with a puzzle. A stock that moves up or down 1 percent each minute with even odds does not leave a holder flat; it loses about half a basis point a minute, because compound growth equals the average return minus half the variance. Chan’s lesson: “risk always decreases long-term growth rate”.

The Kelly formula follows from that. For one strategy the leverage that maximises compound growth is the mean excess return divided by the variance. In his worked example, SPY with a 7.231 percent excess return and 16.91 percent volatility gives a Kelly leverage of about 2.5. Across several strategies the same idea uses their covariance, and the maximum growth rate depends on the portfolio’s Sharpe ratio. Because estimates are noisy and returns are not normal, he notes that many traders use half the Kelly figure.

On stops he is direct: “It is a common fallacy to believe that imposing stop loss will prevent the portfolio from suffering catastrophic losses.” In a crash prices gap, the stop fills far below its level, and the exit locks in the loss. A stop helps only when prices are trending; in a mean-reverting market it cuts positions that would have recovered.

Box 6.1 argues that loss aversion is not a bias. Chan takes Kahneman’s coin toss — lose $100 on tails, win $110 on heads — and shows that a trader who stakes the same fraction of capital each round compounds at a negative rate despite the positive expected value. Citing Ole Peters and Murray Gell-Mann, he tells traders to “take time average, not ensemble average, when evaluating real-world risks.”

The psychological section names despair and greed. In a long drawdown, traders either shut a sound model or double their bets; after a run of gains, they lever up. Chan’s answer to both is the Kelly rule: cut allocation gradually as a model loses, and keep leverage under the formula when it wins. He adds the habit of rebuilding a strategy to dodge the last big loss, which he ties to the representativeness bias.

Chan’s starting point: a strategy can profit only if prices revert to a mean or trend; under a random walk, trading is futile. Mean reversion in a single stock’s price is rare; mean reversion in a pair or a long-short basket is common. He warns that bad price ticks and survivorship bias both flatter mean-reversion backtests.

He traces momentum to slow spread of news, to large orders worked in slices, and to herding — and notes that the last two run for horizons nobody can predict. Competition hurts the two kinds differently: mean-reversion returns wear down towards zero, while trends get shorter as more traders arrive early.

Pairs trading rests on cointegration, not correlation. His example is Coca-Cola and PepsiCo: their daily returns correlate (0.4849, statistically significant), but the price spread between them does not hold to a mean, so the pair fails the cointegration test.

Factor models such as Fama–French explain returns by market beta, size and value. Chan notes their steep drawdowns when investors switch how they value stocks, as in the preference for growth over value in the late 1990s, in 2007 and from 2017 to 2020.

His test of a seasonal trade in stocks comes out negative, while commodity seasonals persist — he suggests because real demand, not speculation, drives them. His natural-gas example — hold the June contract from late February to mid-April — had been profitable for 13 straight years when he wrote.

High-frequency strategies, which he defines as any that close out by the end of the day, earn high Sharpe ratios because many small bets average out. They live on small inefficiencies or on selling liquidity, and he expects their decline, when it comes, as “a slow death” of shrinking returns rather than a sudden loss. They are hard to backtest: without bid and ask quotes, and sometimes the order book, the results mean little.

Chan’s answer turns on capacity. “It is far, far easier to generate a high Sharpe ratio trading a $100,000 account than a $100 million account.” Many small strategies act as market makers, supplying short-term liquidity; a fund with billions becomes the buyer of liquidity instead, has to hold for longer, and so takes on swings in the wider economy.

He lists the large fund’s other handicaps: crowding that thins returns and pushes managers to borrow more, models that grow more complex yet end up holding the same positions, and rules imposed from above — no long-only books, no futures, sector neutrality. As he puts it, any constraint on an optimisation can only lower its best result.

Growth, for an independent trader, means adding strategies once the existing ones reach capacity: faster ones, slower ones, new markets. He accepts that strategies lose force as others find them, and that a major regime change every decade or so can kill some outright. He closes on liquidity: “As long as financial markets demand instant liquidity, however, there will always be a profitable niche for quantitative trading.”

This site does not trade, and the book is not here as a manual. It is here because Chan’s backtesting chapter is the plainest checklist we know for judging any claim built on past prices — including our own. Look-ahead, too many tuned choices, survivors-only data and missing costs are the four ways a historical result lies, and each applies to a fund’s marketing deck as much as to a home trader’s spreadsheet.

The capacity argument is the other reason. When we read a large fund’s quarterly holdings, Chan’s point that size turns a fund from a seller of liquidity into a buyer of it explains why such books hold for long periods and move together when they unwind. The same theme, seen from inside the large firms, runs through Inside the Black Box, and the statistics of overfitting are worked out in full in Advances in Financial Machine Learning.