Share Turnover, Beta, And Stock Returns

by: Yuval Taylor

Explains share turnover: what it is, how it works.

Links share turnover to beta.

Explores the interaction of volume and price changes.

Discusses the low-beta anomaly.

Recommends avoiding stocks with high share turnover.

Share turnover is the volume of a stock traded divided by its shares outstanding (or by its float). In this article I want to show what this metric is good for.

(This article is based loosely on a recent working paper by Maria Kasch, a professor at Humboldt University of Berlin, entitled "Systematic Risk and Share Turnover." As it’s not a very well-known article, and as it’s not that easy to get through, I thought it would be worthwhile sharing its conclusions in simpler language, and bolstering them with my own observations. I won’t pretend to understand everything in it, though. For someone without a degree in finance, it's tough going.)

For those who have never before looked at share turnover, there’s only a very weak correlation between the size and the share turnover of a company. In the S&P 500, as of Memorial Day, the ten companies with the highest share turnover (I use the median volume over the last three months divided by the current shares outstanding) are Advanced Micro Devices (AMD), Micron Technology (MU), Discovery (DISCA), Macy’s (M), Range Resources (RRC), Under Armour (UAA), Chipotle Mexican Grill (CMG), Foot Locker (FL), Netflix (NFLX), and Kohl’s (KSS); the ten with the lowest are Johnson & Johnson (JNJ), Coca-Cola (KO), Brown-Forman (BF.B), Berkshire-Hathaway (BRK.B), Marsh & McLennan (MMC), Stryker (SYK), Accenture (ACN), Cincinnati Financial (CINF), Danaher (DHR), and Walmart (WMT). To generalize, older, established, and somewhat boring companies (widows and orphans), often with high-priced shares and low short interest, have low share turnover; and cutting-edge, exciting, controversial, highly hyped, turnaround, high-momentum, and/or heavily shorted companies have high share turnover.

Now let’s look at what happens during a shock to the market, and let’s take Black Monday, October 19, 1987, as an example. (The chart below is from Dr. Kasch’s paper.) If you were to sort the stocks in the NYSE and AMEX into deciles according to their share turnover that day and then look at the decrease of each decile that day, you’d get a chart that looks like this (look at the line marked “contemporaneous turnover”):

Interestingly, if you had classified the same set of stocks according to their share turnover over August and September 1987 you would have seen exactly the same effect (look at the line marked “lagged turnover”).

This is a nice illustration of the fact that stocks with lower share turnover are less subject to market shocks, and the higher their turnover, the more they’ll be moved by the market. In other words, low-turnover stocks have lower beta and high-turnover stocks have higher beta. And both their turnover and their beta remain relatively constant over time. Dr. Kasch studied six decades of data, and found a remarkably high and persistent correlation between share turnover and beta. Dr. Kasch excluded NASDAQ stocks from her study, but I have looked at the data of all Russell 3000 stocks over the last two decades and found the same high and persistent correlation.

Now beta is a rough measurement of how closely a stock’s movements resemble those of the market as a whole. And alpha is a measurement of excess returns after beta is taken into account. Beta is the slope of the linear regression between the stock’s weekly or monthly price movements and those of the market, and alpha is the y-intercept. If a stock’s beta is 1, then one should expect that when the market goes up or down 2%, the stock will go up or down 2% plus its alpha. If its beta is 2, when the market goes up or down 2%, the stock will go up or down 4% plus its alpha. If its beta is close to 0, the stock will act completely independently of the market. And if the stock’s beta is –1, when the market goes up 2%, the stock will, on average, go down 2% plus its alpha.

One has to keep in mind that beta, when it comes to individual stocks, does not really work like this because of the relatively low correlation between most individual stocks' price performance and the market as a whole. Beta essentially measures the relationship if the correlation were perfect. If you look at the price chart of most stocks, you won’t see its beta very well. So let’s look at some stocks whose correlation to the market is relatively high: Berkshire Hathaway (NYSE:BRK.B) has a beta of 1, Cypress Semiconductor (NASDAQ:CY) has a beta of 1.8, and Waste Management (NYSE:WM) has a beta of 0.56. If you look closely at the chart below, you’ll see that the week-to-week price movements of CY tend to exaggerate those of SPY while those of WM tend to be more moderate.

Now why do share turnover and beta go hand-in-hand?

It’s common knowledge that, in general, the larger the price change, the larger the simultaneous increase in volume, and vice versa. This holds true for all asset classes, and is true both of individual assets and the market in general. It’s a function of the axiom that prices and quantities traded are driven by the same forces. And it almost goes without saying that without a large increase in volume, you simply can’t have a large increase or decrease in price. That’s because prices change largely incrementally in a kind of auction. You need a lot of increments for a big price move.

The formula for share turnover is, as I said, the volume traded divided by the number of shares available. Let’s multiply both the top and bottom of that equation by the price per share. Now in the numerator we get dollar volume--the amount of money actually exchanging hands--while in the denominator we get market cap.

If we put everything together, we can see how the price movements in the cap-weighted market as a whole are going to be much more heavily reflected in stocks that experience a high dollar volume compared to their market cap than in stocks that experience a low dollar volume, simply because volume amplifies market-related price movements. Share turnover—average dollar volume divided by market cap--is essentially a measure of investor participation in a company. As Dr. Kasch puts it, “Other things equal, higher investor participation will be associated with a larger amount of capital responding to common shocks. And, other things equal, a larger amount of capital responding to a common shock will result in a stronger price movement.”

As a result, you might guess that stocks with low share turnover would do well in periods with low market returns, and stocks with high share turnover would do well in periods with high market returns. But what actually happens is the precise opposite.

It has long been recognized that low-beta stocks tend to outperform high-beta stocks on a risk-adjusted basis (a phenomenon labeled the low-beta anomaly or the low-volatility anomaly). This is true across international equities and even across asset classes, and it’s been persistent at least since the 1920s. And stocks with low share turnover tend to outperform stocks with high share turnover by an even higher degree than low-beta stocks outperform high-beta ones. If you divided stocks in the Russell 3000 into deciles by their three-month share turnover and rebalanced quarterly, this is what their performance would have looked like since 1999. As you can see, the stocks with really high share turnover drastically underperform, and those with low share turnover outperform.

Why does this happen? There are a number of explanations of the low-beta anomaly, but none of them are terribly convincing. Dr. Kasch’s theory is that because high market returns are more prevalent than low market returns, high-turnover stocks tend to become overpriced rather quickly, and this then offsets their tendency to rise in price. In this case, beta can double as a measure of mispricing. Stocks with low beta or low share turnover are relatively impervious to market-driven price changes, and thus their prices better reflect their worth.

This theory doesn’t convince me at all. I have come up with a simple and elegant mathematical proof that in a market in which returns are mostly positive, low alpha will be correlated with high beta and vice versa. This will be the subject of my next article. The behavior of investors, the intrinsic value of a stock, and the kinds of stocks that exhibit high and low share turnover make no difference at all to the relationship between alpha and beta, which is purely mathematical. The “anomaly” is actually not an anomaly at all, but is built into the relationship between alpha and beta when returns are more often positive than negative. As a bonus, alpha is, mathematically, highly correlated with returns.

Too often when we think about beta as a measure of susceptibility to market increases or decreases we forget to take alpha into account, and the relationship of beta to a stock's returns is meaningless without alpha. If, for example, a stock with a beta of 2 has an alpha of -2%, when the market goes up 2%, the stock will also go up 2%, but when the market goes down 2%, the stock will go down 6%. If during bull markets the relationship of beta and alpha is an inverse one, low-beta stocks will in general outperform high-beta stocks.

To conclude, the behavior of stocks with high and low share turnover is derived from what Dr. Kasch calls “a simple and intuitive fact: A greater investor participation in a stock translates to a greater participation of the stock in market movements.” If you want returns that aren’t very susceptible to larger market movements, that have low beta (or low volatility) and high alpha, by all means avoid high-turnover stocks.

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.