Taming Fat Tails for Fatter Profits

“[The] Fat-tailed gecko . . . is adapted to a far different life-style. . . . It is a relatively docile animal, more shy and with different behavior patterns toward humans. . . . A new owner may cause the animal some distress, but upon becoming used to its owner, the Fat-tailed gecko is usually content to rest on a hand or arm.” (Source: www.familyzoo.us)


As in the picture of the fat-tailed gecko above, “fat tails” in finance tend to occur in pairs. In its most popular rendition, distributions of stock returns, the upper tail represents the persistence of abnormally high profits, occurring with a frequency significantly higher than can be attributed to random chance alone. At the other end of the distribution, the lower tail embodies what we all wish to avoid, persistently below-market returns.

Fat-Tailed Stock Returns

Taking the ShareBuilder Top Stocks cited in my prior post as an example, I plot the return distribution (price data from Yahoo Finance) of the 50 stocks on the list over the 16-year period from 1989 to 2005. Observe how the actual distribution is characteristically leptokurtotic (having a slender body and fat tails) compared to the random or “normal” distribution. (To facilitate comparison between fat-tailed and normal distributions, I calculate annual returns, assign percentile rankings each year across all stocks, and tally up the number of years that a particular stock exceeds that year's median annual return. I scale the number of years to the 13-year average of the 50-stock universe to bring long (e.g., Exxon with 16 years of data) and short (e.g., Yahoo with six years of data) stock price histories onto the same footing for analysis.)

The behavior behind the fat tails is the tendency for a few of the stocks in the universe to exhibit persistent price movement. For example, for the eight-year period, 1989-1997, UnitedHealth (UNH) sported 46% annualized returns, followed by almost-as-impressive 33% returns for the next eight years, 1997-2005, placing the stock solidly in the high-return tail of the distribution. On the other hand, General Motors (GM) and Verizon (VZ) have shown persistently poor returns, banishing these stocks to the low-return tail.

Even Fatter-Tailed EPS Growth

As investors, our interest in fat tails is in figuring out how to identify beforehand which stocks will occupy prominent positions on the proverbial upper fat-tail podium at the winning-stocks award ceremony a few years down the road. We all know that strong earnings drive stock prices higher, as shown in the scatter plot to the right. This is one of the few relationships in investing that has high reliability, with the correlation between EPS growth (data from Value Line) and concurrent stock returns approaching 0.8. Over the past 10 or 15 years, stocks with high EPS growth (exceeding 20% per annum), like Yahoo (YHOO), Starbucks (SBUX), UnitedHealth (UNH), Dell (DELL), Microsoft (MSFT) and Home Depot (HD), have produced high investment returns. Similarly, stocks at the low end of EPS growth (in the lower range of just 3% to 13% per annum), like Verizon (VZ), 3M (MMM), Anheuser-Busch (BUD), McDonald’s (MCD) and Procter & Gamble (PG), have generated low returns.

Knowing that EPS growth and stock returns are tightly correlated, we should take a look at the distribution of EPS growth, to see if fat tails appear here as well. Using the same methodology as for stock returns, I plot in the bar chart to the right the distribution of EPS growth for the 50 stocks on the ShareBuilder Top Stock list. The result is even more striking than for stock returns—the fat tails of the EPS growth distribution are noticeably fatter than the tails of the stock return distribution, showing that EPS growth is more persistent than stock returns. (Note: Part of the upper fat tail is comprised of stocks like eBay and Yahoo which have shorter stock trading histories, making it easier to obtain a perfect or near-perfect record of above-median performance during the full 13-year scaled term of the analysis. However, other stocks in the upper fat tail, like UnitedHealth, Home Depot and Intel, have trading histories spanning all 16 years of our analysis. I have performed the same analysis using the 30 components of the Dow Jones Industrial Average and other stock portfolios, and have found fat-tail EPS growth to persist here as well.)

As with stock returns, a quick peek behind the curtain reveals what drives the fat tails of the EPS growth distribution. Stocks with high EPS growth (like Dell (DELL), Starbucks (SBUX), Cisco (CSCO), Microsoft (MSFT), UnitedHealth (UNH) and Home Depot (HD)) in the period 1989-1997 tend to continue to exhibit high EPS growth in the next eight-year period, 1997-2005. Similarly, stocks with low EPS growth (like Verizon (VZ) and others) in the first eight years continue to show low EPS growth in the next eight years. In many ways, this persistence of EPS growth (correlation of about 0.5 between front and back eight-year periods) in corporate financial performance is as we might expect based on parallels with, for example, how students receiving high grades in school one year tend to continue to achieve high grades in subsequent years, or how athletic ability and other talents tend to persist throughout an individual’s lifetime.

Persistent EPS Growth and Stock Returns

Now, if a) strong EPS growth in one period tends to be followed by strong EPS growth in subsequent periods, and b) EPS growth drives concurrent stock returns, might we use strong EPS growth in one period to help us predict which stocks will exhibit high returns in the next period? To check on the validity of this cause-and-effect relationship, I plot EPS growth during 1989-1997 against stock returns during the next eight years, 1997-2005. Note that the correlation is about 0.2, somewhat lower than for EPS growth vs. concurrent returns (correlation 0.8) and for back-to-back EPS growth (correlation 0.5), though still notably positive.

Just how significant is this correlation of 0.2? In other words, what is the implication for investment returns? Take a look at the chart to the right. Working our way across the ShareBuilder Top Stocks portfolio ranked left to right in the chart from highest to lowest historical EPS growth for the period 1989-1997, we can calculate cumulative averages of individual stock returns for the period 1997-2005. Notice how the cumulative-average line falls from left to right, indicating how stocks with histories of higher EPS growth tend to generate higher future investment returns. For example, if at the end of 1997 we had bought the top-10 high-EPS-growth stocks from 1989-1997, we would have realized stock returns averaging 11.7% per annum, versus the lower 8.3% for the entire portfolio.

Harnessing Low PEG to Do Even Better

One pitfall of the buy-high-EPS-growth strategy is that stocks of rapidly growing companies often are very expensive, i.e., they trade at very high price-to-earnings (P/E) ratios, since everyone is trying to buy into their growth. We can improve our stock selection by taking into account both EPS growth rates and P/E through use of the ratio of P/E to EPS growth, or PEG. Then, instead of high EPS growth, we are interested in low PEG. The scatter plot to the right shows that PEG based on 1989-1997 earnings data and stock prices at the end of 1997 has a correlation of –0.25 to investment returns over the subsequent eight years, 1997-2005. Note that by taking into account the current price of the stock (the “P” in PEG), we are able to increase the magnitude (absolute value) of the correlation slightly.

Proceeding with the same analysis used in the high-EPS-growth case, we can observe that stocks with lower PEG tend to produce higher future investment returns. A purchase at the end of 1997 of the top-10 low-PEG stocks from among the same ShareBuilder Top Stocks list used above would have generated an average return of 13.2% per annum for the period 1997-2005. The additional 150 basis point per annum pick-up over the 11.7% return from the top-10 high-EPS-growth stock portfolio comes from the slightly higher correlation between PEG and subsequent returns (in absolute value terms, 0.25, versus 0.2 for EPS growth and subsequent returns).

Aiming for Fatter Returns

We are finally in a position to apply our results to enhance our chances of realizing better investment returns over the years ahead. The chart to the right shows members of the ShareBuilder Top Stocks list, classified across the two relevant parameters: EPS growth and PEG. For EPS growth, I use historical data from Value Line for the eight-year period, 1997-2005. For PEG, I use current numbers from Yahoo Finance, which are based on analyst consensus earnings estimates for the next five years and current P/E ratios.

At this time, the stocks on the list with the highest historical EPS growth and lowest PEG are: big-box home improvement retailer, Home Depot (HD); its competitor, Lowe’s (LOW); PC-maker, Dell (DELL); health care services giant, UnitedHealth (UNH); and heavyweight motorcycle-maker, Harley-Davidson (HDI). All of these stocks have historical EPS growth above 20% annually and PEG ratios near 1.0. Also of interest may be Google (GOOG) and eBay (EBAY), with triple-digit historical EPS growth rates and relatively attractive PEG ratios around 1.5, corresponding to current 23% (Google at 365 vs. high of 475 in January) and 32% (eBay at 40 vs. high of 59 in December 2004) price discounts from their all-time highs. Yahoo (YHOO), Starbucks (SBUX) and Whole Foods (WFMI) look appealing from the perspective of high EPS growth; however, their relatively high PEG ratios (all above 2.0) lead me to believe that better value resides in the other stocks cited.

To the extent that fat EPS growth tails continue to produce fatter-than-normal future stock returns, as they apparently have over the past 10 to 15 years, we can expect to realize above-average returns by buying stocks of companies with high historical EPS growth at relatively attractive, low-PEG prices.

Back to our lizard analogy . . . In the spirit of the proud owner of a once-timid, now-tamed fat-tailed gecko resting contentedly in the palm of its owner’s hand, may you too one day bask under rich, warm skies with fat-tailed profits lining your pocketbook!