The quant pipeline

M0 and M1 were about how markets work. M2 is about trying to make money in one, and it opens with the least glamorous and most important observation in the field:

A quant strategy is a pipeline, not a formula.

Newcomers picture the whole enterprise as finding the signal — the equation that predicts returns. In practice the signal is one of four stages, it is rarely the hardest, and a good signal wired into bad execution is simply a losing business with extra steps.

   ┌──────────┐   ┌──────────┐   ┌───────────┐   ┌──────────┐
   │  SIGNAL  │──▶│  SIZING  │──▶│ EXECUTION │──▶│   RISK   │
   └──────────┘   └──────────┘   └───────────┘   └──────────┘
    what do you    how much do     how do you      what kills
    believe?       you bet?        get filled?     you?

    fails by:      fails by:       fails by:       fails by:
    overfitting    over-betting    impact & fees   correlation
    (M2.7)         a real edge     (M1.5)          you didn’t
                   into ruin                       model

Each stage has its own literature and its own way of destroying you, and they are not interchangeable — an improvement in execution cannot rescue a signal that was never there, and a genuine signal can be entirely consumed by the costs of harvesting it. M2.6 runs one strategy through all four; M2.7 explains why the backtest of it lied.

Alpha and beta

The first question asked of any return stream is where did this come from? The standard decomposition:

   r_p  =  α  +  β·r_m  +  ε

     β·r_m   the part explained by exposure to a known factor
     α       the part that isn’t
     ε       noise

Beta is cheap. Exposure to the market is available in an index fund for a few basis points a year. So if your strategy’s returns are mostly market exposure in a costume, you are charging for something the client can buy at Vanguard.

Alpha is what survives the explanation. And the uncomfortable historical pattern is that alpha keeps turning into beta: value, size, momentum, carry, quality, low-volatility, and now trend — each was someone’s alpha until it was identified, named, and packaged into an ETF. Factor is just the industry’s word for “alpha we have caught and domesticated.”

The practical form of the question is therefore: against what benchmark, and controlling for which known factors, is this return actually unexplained? A strategy that hasn’t been regressed against the obvious factors hasn’t been evaluated.

The Sharpe ratio, and why its estimate lies

The standard scorecard is return per unit of risk:

   S  =  (mean excess return) / (standard deviation of return)

   annualised from daily data:   S_annual  =  S_daily × √252

Rough calibration, so the numbers mean something:

   Sharpe    what it is
   ────────────────────────────────────────────────────────────
   ~0.4      the equity market, long-run. Buy-and-hold.
   ~1        a good systematic strategy. Genuinely hard.
   ~2        excellent. A real business.
   3+        either a high-turnover market-making operation
             (thousands of near-independent bets a day), or —
             far more often — a bug, a lookahead, or a backtest
   ────────────────────────────────────────────────────────────

Now the part that changes how you read every performance claim you will ever see. The Sharpe ratio is an estimate, and it is a noisy one. For roughly independent returns, its standard error is

   SE(Ŝ)  ≈  √( (1 + S²/2) / n )   per period

   ⟹  annualised, for n daily observations:   SE  ≈  √(252 / n)

Put actual numbers on that:

   data          n       SE of the annualised Sharpe estimate
   ────────────────────────────────────────────────────────────
   1 year       252              1.00      ◀ useless
   2 years      504              0.71
   4 years    1,008              0.50
   10 years   2,520              0.32

One year of daily data gives a standard error of about 1.0. A strategy that backtests at Sharpe 1.0 over a year is, statistically, indistinguishable from a strategy with no edge whatsoever. Two years is not much better. You need something like four years before you can separate Sharpe 1 from zero at two standard errors — and that assumes the returns are independent and the world stayed still, neither of which is true.

This single fact does more damage to more strategies than any other in quantitative finance. Hold on to it, because M2.7 makes it worse: those figures are for testing one strategy chosen in advance. Search over hundreds, keep the best, and the best will look wonderful by construction.

The culture, which is the real content

The roadmap is blunt that for a quantitative reader the mathematics here is mostly straightforward and the value is the vocabulary and the culture. That is right, and worth saying plainly:

The hard part of this field is not deriving Black–Scholes. It is the discipline to hold out data you are desperate to look at, to size a position smaller than your conviction, to regress your beautiful signal against boring factors and watch it evaporate, and to subtract costs you would rather assume away. The maths is undergraduate. The temperament is not.

Source: Ernie Chan, Quantitative Trading — start here; it is short, practical, and honest about costs in a way most of the genre isn’t. On the statistics of performance evaluation, Andrew Lo, “The Statistics of Sharpe Ratios” (2002) is the canonical reference for the standard error above and is worth reading properly.