Do Price Trends Exist?

by: Yuval Taylor

Summary

Gives hard evidence for the hypothesis that price trends in individual stocks are optical illusions.

Argues that price momentum when applied to individual stocks is dead.

Advises investors to buy low and sell high without waiting for "trends" to begin or end.

In technical analysis, a trend is defined as the general direction of a security's price over a period of time.

In order for a trend to be useful, it has to have a greater chance of continuing than of reversing. If it has a greater chance of reversing than of continuing, it's no longer a trend.

The stock market as a whole follows an upward trend. It's important to remember that individual stocks don't. A stock's price is more likely to fall than to rise (I'm talking about ex-dividend prices, and I'm including penny stocks and companies that go bankrupt). The upward trend in the stock market as a whole is due in part to the fact that the stocks that have gained in value outweigh, in terms of the size of their increase, the stocks that have lost value. So to determine whether trends exist in individual stocks, we have to compare their performance to the market as a whole.

I recently performed some experiments using the S&P 1500 (the 1,500 largest stocks on the major exchanges), and ran them over the past 18 years (because the data I'm using, on Portfolio123, only goes back to early 1999). I wanted to see whether a stock that was outperforming or underperforming the S&P 1500 as a whole had a better chance to continue or to reverse direction.

I tested all stocks that were beating the benchmark for one, two, three, four, and five weeks in a row - the five-week ones seemed to be exhibiting a very strong trend. In every single case, a stock that was beating the benchmark had a greater chance of not beating the benchmark the following week than of continuing to beat the benchmark, and an underperforming stock had a greater chance of outperforming than of continuing to underperform. In every single case, stocks were more likely to "mean-revert" - to reverse direction - than to continue along their "trend."

Now if all price movements were random, the chance of continuing and failing to continue would be equal; if price trends existed, the chance of continuing would be higher than failing to continue. But those were not the case.

My conclusion is that so-called price trends in stocks - at least those that are measured in days or weeks - are simply an optical illusion.

How is this illusion created? Let's create a benchmark that is the median stock return, and let's assume stock prices are purely random. At any one time, half the stocks will outperform the benchmark for the past week. One-quarter will outperform the benchmark for two weeks running. One-eighth will outperform it for three weeks running and one-sixteenth for four weeks.

Look at the price charts of the stocks in that one-sixteenth (or of the one-sixteenth that have underperformed the benchmark for four weeks running). You'll definitely see what looks like a trend. But it's not really a trend, is it? It's just a happenstance driven by random numbers.

Now let's look at the real-world stocks that have been outperforming for four weeks in a row. Statistically, how many stocks out of the S&P 1500 should be doing this? One-sixteenth, or 6.25%, if stock prices were random. If trends exist, though, it should be greater than one-sixteenth. In fact, however, if you look at the last 18 years, only 6.04% of the S&P 1500 stocks have outperformed the benchmark for four weeks in a row, and only 5.95% have underperformed it for four weeks in a row.

Now let's look at long-term trends. Take, for example, the 30% of stocks with the highest and the lowest Sharpe ratio over the last 10 months (defined as the average monthly return divided by its standard deviation). One would think if trends were real, that the stocks with high Sharpe ratios would outperform the benchmark the following month while those with low Sharpe ratios would underperform it. Well, the proportion of high-Sharpe-ratio stocks that outperform the benchmark the following month is lower than the proportion of low-Sharpe-ratio stocks that outperform it. And the proportion of medium-Sharpe-ratio stocks - those in the middle four deciles - that outperform the benchmark is the same as that of the low-Sharpe-ratio stocks. A stock that has been trending downward or exhibiting no trend at all is more likely to outperform the benchmark the following month than a stock that has been trending upward. In other words, if you want to outperform next month, you should choose stocks that have not outperformed over the past 10 months. What if we look at the top 20%? The really trending stocks? Well, the numbers are the same: the lowest 20% outperform the top 20%.

A lot of people use simple moving averages to gauge trends. One of the most popular is the ratio of the 20-bar SMA to the 200-bar SMA. So let's do the same test. We'll rank all stocks in the S&P 1500 by how far above the 20-bar SMA is from the 200-bar SMA, and see how the top and bottom 30% perform over the next month. The result is the same as for the Sharpe ratio: more of the bottom-trending stocks outperform the benchmark over the next month than the top-trending stocks. Once again, you're more likely to outperform if you're trending downward than if you're trending upward.

I've been racking my brains for months now, trying to prove the persistence of a trend in stocks - some sort of trend, somewhere, somehow. But everything I try - the up-down ratio, the RSI, the rate of change - only proves the opposite. No matter how you look at things, a "trend" is more likely to reverse than to continue (I have not examined very short-term trends - price movements within a day's trading - so I can't reach any conclusion about those).

To me, that implies that trends in individual stocks for the most part don't exist. Obviously, it depends on how you define a trend. And the technical analysts and trend-followers out there will probably argue that it's somehow possible to separate persistent trends from non-persistent ones, to identify the former, and to follow them. I'd be glad to perform further tests if someone suggests a plausible one.

Now some people may think there's a flaw in my method because the tests I've performed have all been on the S&P 1500, which is a momentum index by definition. All the stocks in the S&P 1500 are there because they have "trended upward." The S&P 1500 excludes stocks whose market cap has fallen out of the top 1500. But I got exactly the same results whether I was testing upward or downward trends. In every case, a stock that exhibited any kind of trend was more likely to reverse than to continue that trend.

Does this mean that the so-called "momentum effect" is non-existent? Or, perhaps, dead?

First, it's important to distinguish between momentum studies that look at time-series momentum, which applies to markets as a whole, and those that look at individual stocks. I have no beef with the former: trends do exist in markets as a whole. The classic example of the latter is Jegadeesh and Titman's 1993 study, "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency." It's worthwhile reading this paper because of the authors' profound skepticism of the momentum effect that they document.

Jegadeesh and Titman's conclusion was based on buying and selling stocks in the top decile of past performance vs. the bottom decile, using the stocks in the NYSE and AMEX (notice they excluded NASDAQ stocks). They then measured the total gains of each portfolio. What they did not do was measure the percentage of stocks bought that gained or lost money relative to the benchmark. If, say, only 49% of the stocks in the top decile outperformed the median but their performance was particularly strong, and 51% of stocks in the bottom decile outperformed but their performance was somewhat weak, their results would be consistent with mine. In other words, the "momentum anomaly" might be explained by the outperformance of a few particularly strong-performing stocks that keep beating the market month after month and year after year.

Jegadeesh and Titman's best strategy was to invest in the top decile and short the bottom decile of stocks based on their 12-month performance and hold for three months. That strategy would not have worked since 1999 on the S&P 1500. Here is the performance of investing in each decile for three months since then:

The top decile (in green) underperforms every other decile besides the bottom decile and outperforms that one just by a hair. If we break it down into quintiles instead of deciles, it's even worse: the top quintile (in light blue) underperforms all the other quintiles.

I won't speculate on why Jegadeesh and Titman's strategy seems to have worked prior to 1993 and hasn't worked for the last 18 years. Maybe momentum has been arbitraged away. Maybe NASDAQ stocks make a difference. Maybe it has to do with high-speed and computerized trading. There could be any number of reasons. But it's a fact.

Now let's get to an important question: Why don't trends exist? Why is mean reversion more common than relative price momentum?

It's because the prices of stocks are more variable than the underlying performance of companies. Investors often overreact to some sort of news about a company. That overreaction creates increases and decreases in prices that are not sustainable and are smoothed out by subsequent, more rational behavior on the part of investors (I should add that this view is not original: it has been around for decades).

My conclusion that trends don't exist makes trading a lot easier. I like to buy stocks when they're cheap and sell them when they're not. Since trends don't exist, I don't have to watch for them. I don't have to wait until a stock is "finished trending downward" before I buy it, and I don't have to wait until it's "finished trending upward" before I sell it. I don't have to use trailing stops or look at daily price fluctuations. I know that any direction a stock moves in is more likely to reverse than to persist. So I buy low, wait, and sell high.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.