Is the Efficient Market Hypothesis True? SPY Since 1993

Does yesterday's move tell us anything about today's? We tested it on SPY (the S&P 500 exchange-traded fund, or ETF) from 29 January 1993 to 26 October 2026, with dividends counted. The mean return was 0.0774% on the day after a down day, but 0.0220% after an up day. The weak form holds closely for SPY. A rule that trades on the gap beat chance at the same exposure, but a cost of 0.13 basis points per change erases that lead. A basis point is 0.01%.

The efficient market hypothesis says that prices already reflect the information available. Eugene Fama divided it into three forms in 1970. We test the first on SPY. For the other two, we report the Royal Swedish Academy of Sciences' 2013 scientific background on Fama's work (the Academy's summary).

The Academy's summary describes the hypothesis as prices that incorporate all relevant available information. A price then changes only on new information, which is unpredictable by definition. Fama's 1970 review gave the framework for testing it.

Our post on why Nobel economists disagree about market efficiency covers Fama's disagreement with Robert Shiller.

Each form names the information that prices already reflect.

Source: Royal Swedish Academy of Sciences, 2013 scientific background

We test the weak form on SPY below. The other two forms rest on published studies.

Semi-strong tests use event studies. An event study measures a stock's return around a dated piece of news, after removing the part that the whole market explains. Fama, Fisher, Jensen and Roll introduced the method in 1969, on stock splits. The Academy's summary reports no returns beyond what the market explained after the announcement, once dividend changes are accounted for.

The Academy's summary reports that the vast majority of event studies support the hypothesis, with some exceptions. In 1993, Jegadeesh and Titman found that buying past winners and selling past losers earned significant excess returns. Our post on momentum investing covers it.

Strong-form tests ask whether prices reflect any information, public or private. The Academy's summary calls this hard to test, because it needs the private information of all insiders.

Mutual funds give indirect evidence. Jensen's 1968 study found that the majority of funds did not earn excess returns after adjusting for risk. Our posts on whether hedge funds beat the market and why the S&P 500 is so hard to beat cover the later record.

Correlation measures how closely two series move together, on a scale from -1 to +1. Serial correlation compares one series with itself, a set number of days earlier. A value of 0 means the earlier day tells us nothing about the later one. The weak form predicts a value near 0.

We used SPY's closing prices, adjusted for dividends and splits. That is 8,493 trading days and 8,492 daily returns, over 33.7 years. A daily return is the percentage change from one close to the next.

To define "near", we re-ordered the same 8,492 returns at random 10,000 times, then measured the serial correlation each time. A re-ordering keeps every return and removes only the order. The middle 95% of the 10,000 values is the range that chance produces.

The correlation between a day's return and the previous day's is -0.082. Chance gives values between -0.021 and +0.021 in 95% of the 10,000 re-orderings. The most extreme re-ordering reached 0.049.

Squared, the -0.082 accounts for 0.675% of the variation in daily returns.

Chart 1 shows gaps of one to five days. The blue bars use each day's return. The orange bars use its size, with the sign dropped.

Direction is close to unpredictable, but size is not. The size correlation runs from 0.275 to 0.353, outside the range at all five gaps. Large moves follow large moves, which our post on what volatility is covers.

Chart 2 shows the 10,000 re-ordered values for the one-day gap.

The actual SPY value sits to the left of every re-ordered value.

A down day is a close at or below the day before. Re-ordering puts the gap between the next-day mean returns, 0.0774% against 0.0220%, within 0.05 percentage points of zero in 95% of cases. SPY's gap of 0.0554 points sits just outside the range.

The contrarian rule holds SPY on the day after a down day and holds cash after an up day. Cash earns nothing. We set trading costs to zero. The rule turned $10,000 into $147,683.

Random re-orderings hold SPY on almost exactly the same number of days. They give a median of $49,229, with a middle 95% from $17,410 to $139,758. The rule sits just above the top of that range.

The rule changed position 4,319 times. Each change pays the bid-ask spread, the gap between the price a buyer pays and the price a seller receives. A cost of 0.13 basis points per change cuts the rule to the top of the random range. A cost of 2.5 basis points cuts it to the random median.

Fama and Blume found in 1966 that deviations from random-walk pricing were too small to survive trading costs, the Academy's summary reports.

Staying invested every day turned $10,000 into $318,358. Chart 3 shows the rule, the random median and staying invested.

Staying invested ends highest, but it holds SPY every day. The rule holds SPY on 46% of days, so only the random median shares its exposure.

We repeated the one-day test on each half of the dates, on weekly returns and with the 20 largest-move days removed. The correlation stayed outside its range every time, at -0.068, -0.102, -0.095 and -0.041. It was negative in 23 of the 34 calendar years, counting 1993 and 2026 as part years.

The next-day gap held up less well. It sat inside its range in both halves and with the 20 days removed. The negative correlation survives every check, but the profit from trading it does not.

The test uses one fund over one window, while Fama's early tests used individual stocks. It covers days and weeks. It makes no forecast.

SPY is one of the names covered in our Multi-model Signals. This test is not one of its results. Our post on behavioural finance covers why real investors depart from the textbook model.

In 33.7 years of SPY, yesterday's move left a small but real trace in today's return. A cost of 0.13 basis points per change erases the rule's lead over chance. The weak form holds in practice.

The Academy is free to read, here on the web. The Long Trend, our free weekly letter, comes by email.

This explainer is part of the YX Insights Academy. Each one takes a single idea and checks it against real data.

The same approach runs through everything else we publish:

Good places to start on the website:

The three forms differ by the information that prices already reflect. The weak form covers past prices. The semi-strong form adds public information, such as news releases. The strong form adds private information. Fama set them out in 1970. Each form includes the one before it.

Nearly, in SPY. One day's return correlated with the next day's at -0.082, which is outside what chance produces but explains only 0.675% of daily variation. Fama's 1965 tests on large US companies also explained under 1% of the variation for individual stocks, the Academy's 2013 summary reports.

Not quite. The hypothesis says that using information should not systematically beat the market, after adjusting for risk. Our SPY rule, which traded on yesterday's direction, turned $10,000 into $147,683, against $318,358 for staying invested. A cost of 0.13 basis points (hundredths of 1%) per change erases its lead over chance.

Testing whether prices reflect information also needs a model of the return to expect, so every test checks both at once. A pattern means either that prices miss information or that the model is wrong. Our SPY test does not address it. The Academy's 2013 summary says the problem is negligible for day-to-day moves.

DISCLAIMER: This article is intended for educational purposes only. Any information or analysis in this note does not constitute an offer to sell or a solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice, nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.