How Long Until You Know

Fifty trades cannot tell a method making 0.35R a trade apart from a method with no edge whatever: the interval around that measurement runs from below zero to more than twice the number inside it. An edge that has genuinely halved needs 571 trades before your own record can establish it, which is close to three years of live trading. Almost everything a trader concludes from an equity curve is concluded from a sample far too small to carry it.

Prerequisites: Lesson 17, which gave you E and told you it was an estimate, and lesson 18, whose losing runs are what make anyone ask this question in the first place.

How long until you could tell

Excluding zero and detecting a change are different demands, and they give different numbers. Both are correct, and the difference between them is the difference between a confidence interval and a power calculation.

If you observed exactly 0.35R, the interval would stop containing zero at seventy trades. But you will not observe exactly 0.35R, because your observation scatters like everything else here — and at seventy trades the threshold for significance sits almost exactly on your true expectancy, so your odds of clearing it are as near even as makes no difference. Seventy trades is a coin flip on whether a real edge shows up as one.

The sample that gives you a fair chance of finding the edge you actually have is larger:

n = 7.85 × σ² ÷ Δ²

where Δ is the difference you want to catch. The 7.85 is the price of conventional confidence together with a four-in-five chance of detection, and the shape of the formula is the finding: halve the difference you are hunting and the sample you need goes up four times.

What you want to establish	Difference, Δ	Trades	At four trades a week
There is an edge at all	0.35R	143	8 months
The edge has halved	0.175R	571	2.7 years
The edge has slipped a quarter	0.0875R	2,284	11 years

Read the middle row. An edge that has genuinely halved takes close to three years of live trading before your own results can establish it. Which means that for almost every record that exists, “my edge has been degrading lately” is not a finding. It is a feeling with a number attached to make it sound like one.

Now put lesson 10’s charges back, because they do more damage here than they do to the edge itself. At s = 0.17 the same system nets 0.18R a trade rather than 0.35R. The noise is untouched: subtracting the same amount from every trade moves the average and leaves the spread exactly where it was. So the ratio of noise to signal goes from four to eight, and the first row of that table goes from 143 trades to 540 — two and a half years, at four trades a week, to establish that you have any edge at all. The charges did not simply halve your edge. They nearly quadrupled the evidence you need to prove you have one.

What this does not settle

That your results are worthless. They are slow, which is a different complaint with a different remedy: stop asking the equity curve questions it answers in years, and ask the ones it answers in an evening instead. Whether the market behaviour your method feeds on is still happening is one of those, and lesson 68 is the whole treatment of it.

There is a second such question, and it is faster still. Did you take the trade in the conditions you had written down beforehand — yes or no? That is a fact about a single trade. It needs no win rate, no payoff and no sample, so five trades give you a real reading of it where five trades tell you nothing whatever about your expectancy. It is not a substitute for E and it does not tell you whether the method works. It is simply the one measurement of your own trading that is available immediately, and while you are waiting out the five hundred trades for the other one, it is the only feedback you actually have. Lesson 23 is the record that makes it countable, and lesson 36 puts it to work.

Nor does any of this license sitting through whatever arrives. The sample you need to prove an edge has died is not the sample you need to be ruined by one, and the account can be gone long before the arithmetic is ready — which is lesson 22, and the reason lesson 20 sizes against the bad case rather than the average one.

Nor is the table above exempt from its own argument. Every row is computed from a σ² and an E that came out of the same finite record, so the sample sizes carry error bars of their own, and they are wide. Take the two-hundred-trade interval from earlier, which put the edge somewhere between 0.14R and 0.56R, and run the first row at each end: the sample needed to establish an edge at all comes out at 892 trades at one end and 56 at the other, and that is holding the noise fixed, which flatters it. The 143 is an estimate of a sample size rather than a target to count down to, and the honest use of it is as an order of magnitude. Hundreds, not dozens.

The formula also assumes your trades are independent and drawn from one unchanging process, and real records are neither. Several positions taken on the same idea are one position wearing several tickets; a change of regime turns the trades before it and the trades after it into samples from two different processes. Both violations push the same way. They make your effective sample smaller than your trade count, so every figure above is the optimistic version.

And none of it can be computed without a record that contains the losers. p, b and σ all come out of the same file, and a file that quietly omits the trades you would rather forget will report an edge you do not have, with an interval around it that makes the fiction look measured.

Your equity curve is a low-bandwidth instrument. It will tell you the truth eventually, and eventually is measured in years rather than in weeks.

Problems

1. Compute your own noise. From your own p and b rather than the 45 per cent and b = 2 worked above, work out σ² = p·b² + (1 − p) − E², take the square root, and divide by E. That ratio is how much noise sits on top of one trade’s worth of signal in your method rather than in the example, and it is the number that governs everything else here.
2. Find out what your record can settle. Multiply 7.85 by your σ² and divide by your E². Compare the answer with how many trades you have actually logged. Most readers find their record is a fraction of what establishing their own edge would take, which is the ordinary result and is not a verdict on the method.
3. Put your costs in. Subtract the s you computed in lesson 10 from your E, leave σ² exactly as it was, and run problem 2 again. The difference between the two answers is the sample size your costs charge you, and for most instruments it is a larger penalty than the money.

Sources. Jacob Cohen, Statistical Power Analysis for the Behavioral Sciences (2nd edition, 1988), which is where the 7.85 comes from: it is the square of 1.960 + 0.842, the two critical values that a two-sided test at ninety-five per cent confidence and a four-in-five chance of detecting a real effect cost between them. Andrew W. Lo, “The Statistics of Sharpe Ratios” (Financial Analysts Journal 58, 2002), which derives the sampling distribution of a performance statistic and shows how wide its standard errors are at the track-record lengths people actually have. David H. Bailey and Marcos López de Prado, “The Sharpe Ratio Efficient Frontier” (Journal of Risk 15, 2012), which puts this lesson’s question to the Sharpe ratio and calls the answer the minimum track record length.

You now know what your record can and cannot settle, and how long the settling takes. The next lesson stops asking whether the edge is there and asks how much of the account to put behind it — which is what decides whether you are still trading when the sample finally arrives.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.