## How EPS and P/E ratio affects share prices

### How EPS affects share price

There are few things in this world that are more heavily studied than financial markets. Computational finance and analysis can be incredibly interesting. Yet, for all this financial analysis, there is surprisingly little quantitative data available for people. For this article, we’ll be looking at how P/E ratio, or price to earnings ratio, affects the future share price of a stock. Sure, many people automatically assume that the lower the P/E of a stock is, the better value the stock represents. This makes all the intuitive sense in the world. If you’re presented with a stock for \$20 per share, and the company generates \$1 per share each year, you have a P/E of 20. Now say you’re presented with another stock for \$20 per share, but that company generates \$2 in profits per share each year, for a P/E ratio of 10. Which represents the better value?

### Starting with the EPS

Instead of going directly to P/E ratio, for reasons we’ll soon go over, it’s better to start with earnings per share. For the top 500 volume stocks on NASDAQ, I’ve collected all the earnings data for each quarter from 1998 to 2013. I also have the shares outstanding data, along with the daily price data for all the securities. Using this data, I gathered the earnings per share by totaling the earnings for the most recent 4 quarters, and dividing by the number of shares outstanding. So now we have the cash earned for each share. To normalize all the different stocks, I divided that by share price. So please note, for the duration of this article, EPS is really EPS divided by the share price. This gives us the X-axis, which is basically the percentage of each share price generated in the last year. There is a heavy concentration around 5%. For the Y-axis, I decided to choose the share price exactly 1 year into the future. However, to normalize that against overall market performance, I made the Y-axis the share price change in 1 year, minus the gains NASDAQ made in the same timeframe. This gives us our first plot. For anyone interested, I use Mathematica for a lot of my analysis and data visualization, since it’s a very powerful tool.

### EPS analysis

Finally, we have some actual data, rather than subjective feelings. By the eyeballs, we can see that as EPS increases as a percentage of the share price, we appear to have a slightly greater chance for the stock price to outperform the NASDAQ. However, the data is heavily mixed. Just look at all the data points below the X-axis. Around half the data points are actually below the X-axis, meaning the stocks underperformed the NASDAQ. The one general conclusion we can make is that if you choose a stock by EPS alone, you have a roughly equal chance of the stock performing better than or worse than the overall market. So whenever you hear someone tout that a stock has a great EPS ratio, keep in mind this is far from a guarantee.

### Cleaning up the EPS data

When sorting and convolving the list with a simple average with a radius of 5, we can produce a much clearer graph that shows the actual trends. What we see is quite astonishing. Companies with an EPS ratio of 20, meaning that the company earns 20% of it’s share price in profits over the last year, perform quite well. On average, they can outperform NASDAQ by as much as 30%. Wow! Keep in mind that there’s very few data points there. However, the range from 8 to 14 does perform quite well. There is another stunning revelation. For companies that lose money, the more money they lose as a percentage of their share price in the last year, on average, the better the company will perform against the NASDAQ. This is quite amazing. On average, a company that loses money performs better on average than a company that earned 6% of it’s share price in the last year. I never would’ve guessed, and that’s exactly why I decided to create some actual graphs rather than listen to reason and logic.

### The P/E ratio

With all the previous data, the EPS was normalized against the share price. This means all we have to do to get the P/E ratio is to invert the x-axis data. Ever wonder many finance websites list EPS as N/A for companies with negative P/E ratios? Well, this graph should demonstrate how useless negative P/E ratios are.

It’s still difficult to make out the trends in this graph. We can go ahead and convolve the list with a simple average filter with a radius of 5, to produce the following graph. Here, we can see that, on average, stocks with P/E ratios of 12.5 or lower do perform quite well relative to NASDAQ. In fact, stocks with P/E ratios of 12.5 or lower perform around twice as well relative to NASDAQ as the stocks with a P/E ratio of 15 through 30. So yes, the general convention is correct in that, on average, stocks with lower P/E ratios tend to perform better than those with higher P/E ratios. The keyword here is ‘on average’. As the scatter plots show, it’s no guarantee, and many stocks with low P/E ratios still perform worse than the overall market. If you buy one stock, good luck, you’re still in a casino. But if you buy 20 stocks or more, you can substantially improve your chances of outperforming the market. That’s why diversification is often the key to success.