# Is there a relationship between P/E ratio and stock price? [2021]

If you search for how the P/E ratio of a stock affects stock price online, you will find hundreds of thousands of results. Nearly every major financial site has an article about P/E ratio, and many of those articles refer to the common wisdom that companies with low P/E ratios (at least within their own sector) should have outsized future earnings. But is this true? Is there really any relationship between P/E and future stock price? In this article, we analyze historical returns versus P/E ratios to find out.

## Introduction

Every basic investing book talks about P/E ratios. They are one of the most basic tools people use to screen stocks and develop a portfolio. And unlike technical indicators, people still believe that P/E ratios are a good way of finding “value” stocks that will increase significantly in price.

The question is: is that true anymore? There have been recent studies that in certain countries (in certain relatively small markets), there is a relationship between P/E ratio and future stock returns.

However, does the same hold true for highly liquid U.S. equities? In this article we attempt to answer to this question.

## Earlier work

There are a few papers worth reading before reading this one:

- The Articulation of Priceâ€“Earnings Ratios and Market-to-Book Ratios and the Evaluation of Growth
- Value Investing with Price-Earnings Ratio in India
- Investment Performance of Common Stock in Relation to their P/E Ratios: Basu Extended Analysis

## The data

To do this analysis, we needed two datasets. First: historical returns. Initially, we chose to limit our analysis to the highly-liquid members of the S&P 500. However, given the small sample size of the S&P (only 500 stocks), we later decided to look at the Russell 2000 as well.

For the analysis, we needed adjusted daily data. This data is available from a wide range of sources, but we chose Quandl for the most up to date and best priced dataset.

We explain how to load this data using Python and Pandas, as well as how to begin doing regressions here.

## Running the Tests

### Choosing Timeframes

Since there are different numbers of days between each quarterly report, we can’t compare the total returns after each report. So instead, we calculate the average daily return (as a percentage) after the report.

We looked at two different timespans: first, the time between the current report and the next report. This would tell us if the current PE ratio has any correlation with the stock’s returns from this report to the next.

Second, we looked at all time after the current report. So we compared the average daily return between the date of the report and today to see if the PE ratio had any bearing on future returns.

### Is there a correlation between P/E ratio and stock price?

We started with the most basic test: is there any correlation between PE ratio and stock returns across all stocks, with no segmentation.

In all of the tests from here on, we removed outliers in order to get a more accurate result.

In this test we compared PE in the first quarter of 2012 to long term average returns after that.

```
OLS Regression Results
===============================================================================
Dep. Variable: lt_avg_daily_change R-squared: 0.000
Model: OLS Adj. R-squared: -0.002
Method: Least Squares F-statistic: 0.1474
Date: Mon, 28 Dec 2020 Prob (F-statistic): 0.701
Time: 10:49:21 Log-Likelihood: 2152.5
No. Observations: 397 AIC: -4301.
Df Residuals: 395 BIC: -4293.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0011 0.000 10.072 0.000 0.001 0.001
start_pe -2.436e-06 6.35e-06 -0.384 0.701 -1.49e-05 1e-05
==============================================================================
Omnibus: 142.124 Durbin-Watson: 2.073
Prob(Omnibus): 0.000 Jarque-Bera (JB): 415.558
Skew: 1.698 Prob(JB): 5.79e-91
Kurtosis: 6.687 Cond. No. 33.8
==============================================================================
```

We ran this test with several different time periods and got similar results. From this, we can see that there is no discernable correlation between PE and stock price over all S&P 500 stocks over the long run.

Let’s take a look at a larger sample: the Russell 2000. Here’s the same plot for the Russell:

```
OLS Regression Results
===============================================================================
Dep. Variable: lt_avg_daily_change R-squared: 0.000
Model: OLS Adj. R-squared: -0.002
Method: Least Squares F-statistic: 0.1474
Date: Mon, 28 Dec 2020 Prob (F-statistic): 0.701
Time: 12:34:02 Log-Likelihood: 2152.5
No. Observations: 397 AIC: -4301.
Df Residuals: 395 BIC: -4293.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0011 0.000 10.072 0.000 0.001 0.001
start_pe -2.436e-06 6.35e-06 -0.384 0.701 -1.49e-05 1e-05
==============================================================================
Omnibus: 142.124 Durbin-Watson: 2.073
Prob(Omnibus): 0.000 Jarque-Bera (JB): 415.558
Skew: 1.698 Prob(JB): 5.79e-91
Kurtosis: 6.687 Cond. No. 33.8
==============================================================================
```

### Is there a correlation between P/E ratio and stock price in a sector/industry?

Many professional investors use PE with an industry or among competing companies to find “value” stocks. Theoretically, the stocks with a lower PE in an industry should see a larger stock price increase than those with a higher PE.

In order to test this, we first tried to look at each sector of the S&P 500, and grouped stocks into sectors. However, breaking up the S&P 500 into sectors resulted in too few stocks per sector to get any meaningful result.

So instead, we will look at the Russell 2000 components.

Again, we see nearly 0 r-squared values for each of these industries. So we can conclude that within industries, there is no exploitable correlation between PE ratio and future returns.

In the graphs above, we chose the PE ratio from early 2010, and looked at returns since then. However, looking at other timeframes results in a similar conclusion.

### One takeaway: Very high P/E ratios are less likely to result in significant long-term returns

There is one thing we can take away from the graphs, however. In nearly every example, companies that had a very high PE ratios were unlikely to have high long-term returns.

If we identify all companies with PE ratios of 35+, we can see that very few have high long-term average returns compared to the rest of their industries.

This leads to a hypothesis: *companies with very high PE ratios tend to have lower returns than their peers.*

Let’s test that hypothesis. To do that, we calculate the probability that the long-term returns are above industry average given that the starting PE is greater than 35.

Using our Russell 2000 data, we find that Pr(LT returns > industry avg|PE > 35) is between 30-40%. So if we eliminate companies with PE ratios over 35 in a stock screen, we have a reasonable chance of being correct.

This also holds true for S&P500 companies, with similar percentages.

## Conclusion

So is there a relationship between P/E ratio and future stock price? Yes, but it’s not as strong as you would think. And it’s not quite as useful as the investing books suggest. In our next article in this series, we will look into whether there this relationship can be exploited to trading purposes.

## No Comments