RSI and Oscillators: The Claim Versus the Evidence

This course is an audit. Over the next three modules we will take the most popular technical indicators — the ones that decorate nearly every retail chart on earth — and put their claims on trial with the statistical machinery you built in the last two courses. We will be fair: each indicator gets a precise definition, a steel-manned version of its claim, and an honest test. But you should know the verdict in advance, because the evidence is not close. These objects are not statistical evidence. They are transformations of the past dressed up as forecasts of the future, and the purpose of this course is to make sure you can never again mistake one for the other — and to show you, in each case, the statistical tool that does the same job honestly.

We begin with the most beloved of them all.

What RSI actually computes

The Relative Strength Index takes the last $n$ price changes (fourteen, by convention), splits them into gains and losses, averages each side, and maps the ratio into a bounded scale:

$\text{RSI} = 100 - \frac{100}{1 + RS}, \qquad RS = \frac{\text{average gain over } n \text{ periods}}{\text{average loss over } n \text{ periods}}$

Strip away the packaging and notice what this is: a rescaled summary of recent returns. Every input is a past price change. The formula adds nothing — no new data, no economic content, no information that the raw return series did not already contain. It is a lossy compression of the recent past, squeezed into a zero-to-one-hundred dial.

That is not, by itself, a crime. The mean and the variance are also summaries of past returns. The difference is what comes next: the claim.

The claim, stated honestly

The folklore says that when RSI rises above seventy the asset is "overbought" and due to fall, and below thirty it is "oversold" and due to rise. Translate that into the language of Course 201 and it becomes a testable statement about conditional probability:

$P(\text{return} > 0 \mid \text{RSI} < 30) \;\stackrel{?}{>}\; P(\text{return} > 0)$

The indicator earns the word evidence only if the conditional probability on the left reliably and materially beats the unconditional base rate on the right — out of sample, after costs, across assets and regimes. That is the entire question. Everything else is decoration.

The evidence

It fails. When researchers run this test honestly, the conditional hit rates hover at the base rate — the same place a random signal would sit. And the deeper problem, documented in one of the most important papers in empirical finance, is data snooping. Sullivan, Timmermann and White tested nearly eight thousand technical trading rules — oscillator thresholds among them — on a century of data, using White's Reality Check to account for the fact that if you test thousands of rules, dozens will look brilliant by pure chance. Once that multiple-testing correction is applied, the apparent performance of the rules evaporates. The "best" rule in a snooped universe is not a discovery; it is the lottery winner you went looking for after the draw.

Recall the base-rate trap from the foundations course: a signal that merely matches what was going to happen anyway is noise that learned to dress well. RSI's thresholds compound the offense — why seventy and thirty? No distributional argument produces those numbers. They are conventions, inherited from a 1978 book, applied identically to assets whose return distributions differ wildly in volatility, skew, and tail weight. A fixed threshold on a statistic whose distribution varies by asset and by regime cannot carry constant meaning. You proved in Course 201 that even a principled percentile needs a reference distribution; RSI's cutoffs do not even attempt one.

The five-gate verdict — and the honest alternative

Walk RSI through the honest-reading checklist from the foundations capstone. Scale: it discards the magnitude structure of returns. Shape: it controls for nothing — fat tails and skew pass straight through. Spread: it ignores volatility clustering, so the same reading means different things in calm and storm. Base rate: its conditional hit rate does not beat the unconditional one once tested honestly. Uncertainty: it ships with no standard error, no confidence interval, no sense of its own noise. Zero gates of five. A number that fails every gate is not evidence. It is a feeling with a decimal point — exactly what this institute exists to replace.

The statistical approach that does this job honestly already sits in your toolkit. If you believe recent returns predict future ones, that is a momentum hypothesis — so state it, pre-register it, and test it: estimate the conditional probability, attach a standard error, correct for the number of variants you tried, and report the result whether you like it or not. That procedure, from Course 201, is everything RSI pretends to be.