September 2002
Myths and Legends of the P/E Ratio
| "It's simple. It's just things with chalk on a board." |
| --Helmut Vogel, when asked to explain a physics equation |
ACK IN THE BUBBLE DAYS, IT didn't matter what stock you bought -- especially if was a tech stock -- it was probably going to go up. Folks who should have known better speculated that this was the beginning of a "new economy" and that prior valuation measures just didn't work anymore.
But the past two years were a return to reality. Investors who got accustomed to buying high in the hopes of selling higher have had their heads handed to them. If there's any lesson to be learned from the recent past it's that fundamentals really do matter.
Even something as basic as the Price-to-Earnings (P/E) Ratio can provide more information than you might at first think. Not only does it give the relation between price and earnings (duh!) it also sheds light on potential risks, too.
Yet how reliable is the P/E when it comes to estimating equity fundamentals? After all, there's no use in looking a valuation measures if they ultimately fail to add value (no pun intended).
With these questions in mind, we decided to separate the myths from the legends surrounding the simple P/E ratio. We based our investigation on one of the longest running series of market data available, Professor Robert J. Shiller's S&P Composite data.
For those of you not familiar with his work, Professor Shiller is the Stanley B. Resor Professor of Economics at Yale University. His extensive research in economics, behavioral finance, and financial markets is well documented at his Website. There you'll find some of his online papers, information about his books (including Irrational Exuberance and Market Volatility) as well as downloadable market data.
Our P/E studies are based on the Shiller market data extending back to 1871. We needed an extensive database since we wanted to consider trends in as many market conditions as possible and in as many instances as possible.
Third Grade Math
The P/E ratio is a remarkably simple relation. It's nothing more than a basic ratio or fraction like you learned in third grade math.If you were paying attention back then, you learned that when the number on the top (the numerator or in this case the Price) gets larger while the number on the bottom (the denominator or in this case Earnings) remains relatively unchanged, the entire ratio gets larger. If the numerator decreases, the exact opposite occurs.
Similarly, if the denominator gets larger while the numerator remains relatively constant, the entire ratio grows smaller. It becomes larger if the denominator falls relative to the numerator.
OK, enough of these math terms. What this really means for the P/E ratio when earnings rise faster than the stock price (denominator grows relative to the numerator) the P/E declines. When this happens, stocks are perceived to be if not cheap, at least more fairly valued.
On the other hand, when prices rise faster than underlying earnings (numerator grows relative to the denominator), stocks become overpriced as the P/E grows. In essence, you pay more for the same earnings.
The "earnings" you pay for when you buy a stock are future earnings -- you can't buy last years'. While this may seem painfully obvious, many investors confuse a company's future with past performance. Trailing earnings can tell you how a company did in the past, but not necessarily how it will do in the future.
Estimating a company's P/E is really a method of assigning a price to the future earnings stream. If earnings are expected to rise, you'd be willing to pay more and vice-versa.
Easy Money
Which brings us to the first P/E myth: Nominal earnings increase at a greater rate during inflationary times. On the face of it, this seems to make sense. When inflation heats up, companies can increase earnings by simply increasing what they charge for their finished goods. When all prices are rising, it's relatively easy for them to raise their prices too. Firms may not be productive, but both revenues and nominal earnings go up just the same. Investors are willing to pay more for these increased earnings so P/E multiples remain constant or even expand.It makes sense, but the evidence suggests that it really doesn't happen. Chart 1 uses annualized Shiller data to compare earnings growth rates with inflation as measured by the CPI. If the myth were true, earnings would rise with CPI, but they don't.
Chart 1
S&P Composite Annual EPS Percentage Change vs. CPI Percentage Change
Instead, notice how earnings rise when CPI falls during 1921, 1929-1931, and the late 1990s. Conversely, earnings fell during World War I, in the mid-1940s, and mid-1970s when CPI spiked up. This is a negative correlation, not the positive one envisioned by common wisdom.
Statistically, the relation between annual earnings and CPI percent change is -0.33410. Correlation can range from +1 (perfect correlation with both series moving in tandem) to -1 (perfect negative correlation with each moving as an opposite mirror image) with 0 signifying no relation between the two series. Correlation of -0.33410 is a moderate yet statistically significant negative relation between the two series. So much for Myth Number 1.
Inflated Prices
In a similar vein, Myth Number 2 holds that stock perform better in an inflationary environment. The belief here is that share prices tend to rise like all others due to inflation. (Perhaps it's because nominal earnings are thought to be rising, but that's back to Myth Number 1.)Once again, the facts don't bear this out. Again drawing from the Shiller data, Chart 2 shows the historical relation between annual CPI and price percentage change. There's not much positive relation here.
Chart 2
S&P Composite Annual Price Percentage Change vs. CPI Percentage Change
Actually there's almost no relation to speak of. Statistically annual price and CPI percentage change have an almost imperceptible correlation of 0.07429. Yes, it's positive, but not much more than zero.
In fact, you could reasonably argue that the two have no actual relation at all. For every point where stock prices and CPI fell in tandem (e.g. 1929-1931 and the 2000-2001) there are other points where they move in opposite directions (e.g. the mid-1940s and early-1970s). At the very least, there's no support here for the belief that share prices thrive during inflation.
Discounted Earnings
According to Myth Number 3, P/Es can reasonably be expected to rise when inflation is low.Why? Because investors use the P/E as a way to price stocks by discounting the value of future earnings. If inflation is low, a dollar's worth of earnings out in the future will be worth more than when high inflation eats away at its value. As a result, during periods of low inflation, investors can safely pay more for future earnings causing the P/E multiple to expand.
Chart 3
S&P Composite Annual P/E vs. CPI Percentage Change
As you'll notice from Chart 3, this tidy little relation doesn't hold either -- that's why it's Myth Number 3. In fact, if you look closely at the chart, you'll notice there's a slightly negative relation between P/E and CPI. It's especially evident during World War I and the mid to late-1970s when inflation was high as well as the late 1920's, early 1960s and late 1990s when inflation was abnormally low.
As we've noted before (see Inflation Wars I: The Phantom Menace), stocks perform best when prices are stable, neither inflationary nor deflationary. This is validated not only because of the lack of relation between share prices and CPI (Myth 2) but also by the relatively low correlation (-0.11377) between P/E and CPI.
Risky Business
The P/E is often used as a measure of risk. When P/Es are high, investors have paid dearly for each dollar of earnings. Any stumble -- whether from poor management or changing economic conditions -- is magnified when investors pay up for their equity positions.High P/Es could also indicate high demand for stock, driving prices above traditional levels relative to earnings. If momentum turns, stocks can quickly fall back to more reasonable levels, leaving remaining shareholders with sharp losses.
As a result, Myth Number 4 holds that high P/E levels indicate greater risk in the market. Conversely, low P/Es should signify lower risk.
Chart 4
S&P Composite Annual P/E vs. Annual Standard Deviation
As you can see from Chart 4, this one's a myth, too. Again if you look closely, you'll notice periods where the average annual P/E actually rises when standard deviation falls (e.g. mid-1940s and early 1960s). More impressive are the spans where P/Es fall as standard deviations rise (e.g. early 1920s, early 1930s, and early 1980s).
This, of course, suggests a negative correlation between the two rather than the positive relation envisioned by Myth Number 4. Indeed, the statistical correlation is a mild negative, -0.12485.
| S&P Composite P/E Lagged Against Standard Deviation |
|
|---|---|
| Lag Period | Correlation |
| None | -0.12375 |
| 3 Months | -0.11548 |
| 6 Month | -0.09261 |
| 12 Months | -0.02212 |
| 24 Months | 0.10399 |
| 36 Months | 0.18036 |
This, however, may not be giving Myth Number 4 a fair shake. Unlike the prior myths, this one postulates a predictive rather than concurrent relation. It doesn't say P/Es rise when volatility does but rather high P/Es signal a coming increase in volatility.
Take another look at Chart 4. See that spike in P/E in the mid-1920s? Did it warn of the coming volatility in the late 1920s and early 1930s? How about that P/E decline from the late 1960s through the 1970s? Could it have signaled the falling volatility of the late 1980s and early 1990s? If you slid the P/E line a little to the right, would it result in a positive correlation with standard deviation?
We tested this, too. We lagged the P/E anywhere from 3 months to 3 years. The results are reflected in the nearby table.
As the lag time grow, correlations become less negative until going positive with a 2-year lag. The 3-year lag has the highest correlation with a mildly positive 0.180359.
But let's think about this a minute. Does it really make sense? Can you make trading decisions based on three-year-old P/E values? Even if you did, how confident would you be knowing the underlying correlation was less than 0.2?
It still looks like a myth.
P/What?
Despite the previous myths, the final one is perhaps the most unexpected. According to Myth Number 5, the P/E ratio is affected by earnings trends. That's a given, right?Well actually, no, it isn't. While it seems like a reasonable assumption, the statistics don't bear it out.
Chart 5 uses the Shiller data to compare annual earnings percent change to the corresponding P/E. As you'd guess from the chart pattern, there's almost no relation between the two.
Chart 5
S&P Composite Annual P/E vs. Annual EPS Percentage Change
Remembering your third grade math, as earnings rise, you'd expect the P/E to fall. This would imply a negative correlation since the two series would move in opposite directions.
The correlation is negative, but it's barely existent (-0.05804). Evidently price movements -- the other element of the ratio -- are so random as to offset the intuitive relation between earnings trends and P/E.
Perhaps that makes sense given that investors buy stocks for other reasons than changes in earnings trends. Some (technicians) follow price patterns while others look for momentum. Others buy on emotion or a strong sales pitch. In light of these determinants of price, why should you think earnings would have a strong influence over the P/E?
It's All Relative
So what's the P/E good for if it doesn't reflect many of the things as commonly thought? Can it really play a legitimate role in equity valuation?Well yes it can. As we've pointed out before (see Why Value), the P/E like other ratios, is best used as a relative measure. A stock's P/E can be compared to other benchmarks (e.g. the index or other stocks in its sector) or its own historical levels.
Comparisons to other benchmarks can be informative in determining if a stock is fairly priced relative to either the market or industry peers. This can be a helpful tool in individual stock selection.
A look back at a stock's own historical P/E average or range can lend some insight as to where it currently falls in its market cycle. If it's priced above its historical average or towards the upper end of its historical range, it may be overpriced. If it falls below its historical mean or at the low end of its range, you have an idea of how far it can appreciate before it becomes overvalued.
If a stock's P/E is radically above or below its own historical range of that of its peers, that should raise a red flag. What can account for this difference? Has it had a surprise earnings spike or is it experiencing fundamental difficulties unique from its peers? At the very least a divergent P/E suggests you should examine these issues before committing any funds to this stock.
So yes, the P/E ratio can be an important tool in valuing stocks relative to historical measures or other benchmarks. But using P/Es -- even market P/Es -- to gauge current or future economic or market conditions lacks similar justification.
It's nice to see investors considering the P/E again, nevertheless they shouldn't count on this ratio to reveal more than it's capable of. Myths make great stories but they're lousy investment tools.
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