When valuing a company, one of the most commonly used approaches is Valuation Multiples. But within this approach there are different ratios that can be used, so the question is: **which of them is the best?** In this post we will compare three of the best known ratios: **P/E** (Price-to-Earnings), **P/B** (Price-to-Book) and **P/S** (Price-to-Sales).

## What are Valuation Multiples?

Valuation multiples are used to approximate the value of a company, looking at how similar companies (same line of business or industry) are valued by the market. A valuation multiple is comprised of two components:

**Numerator**: valuation metric (Equity Value or Enterprise Value)**Denominator**: financial metric (Earnings, Sales, EBITDA, …)

Depending on the numerator used, a distinction is made between two types of multiples: Equity Multiples and Enterprise Value Multiples. In this post we are going to focus on the former.

### Equity Multiples

They are based on dividing the market capitalization (price of the company) between different financial metrics. So the higher the ratio, the more expensive is the stock and vice-versa. The four best known ratios are:

**P/E (Price-to-Earnings)**: it compares the price of the stock with its earnings (net income) from the last twelve months (LTM). It is the most famous fundamental ratio.**P/E10 (CAPE, Cyclically Adjusted Price-to-Earnings)**: it is the same as P/E but using the average earnings from the last 10 years, in order to smooth fluctuations in corporate profits. It is also known as the Shiller P/E ratio.**P/B (Price-to-Book)**: it compares the price of the stock with its book value (total assets minus total liabilities). It is commonly used for banks.**P/S (Price-to-Sales)**: it compares the price of the stock with its sales (renevues) from the last twelve months. It is commonly used for companies that have losses.

## S&P 500 valuation

In this section we are going to see the historical multiples for the S&P 500 index since 1995, adjusting for survivorship bias: only aggregating, for each date, the ratios of the S&P 500 components in that date.

### P/E (Price-to-Earnings)

As we can see in the next chart, using only the LTM earnings does not seem to be a good idea for calculating the Price-to-Earnings ratio, as in crisis periods earnings falls to practically zero, making the ratio to soar despite falling stock prices (cheaper stocks).

For a long-term analysis it is more useful to use the Cyclically Adjusted Price-to-Earnings (CAPE) ratio rather than using the current P/E ratio.

### P/E10 (CAPE, Cyclically Adjusted Price-to-Earnings)

The CAPE charts looks much less noisy, and more coherent, than the previous P/E chart. And we can say that the S&P 500 is currently strongly overvalued from a corporate earnings point of view, as we are at P/E levels above 40, which have not been seen since the Dotcom crisis…

### P/B (Price-to-Book)

The P/B ratio is currently near the Dotcom crisis levels, indicating an overvalued market, too.

### P/S (Price-to-Sales)

Last but not least, the P/S ratio is currently at all-time highs, suggesting a very expensive market in relation to the current total revenues of the biggest USA firms.

## Which ratio is better?

The million dollar question: which ratio is better? **Which one is more accurate predicting future returns?**

Of course it is not an easy question. But we are going to try to give some insight by analyzing the correlation of each of the ratios with the future return of the S&P 500. That is, for each day we are going to see what has been the return of the S&P 500 in the next 261 business days, and we are going to build a time series with all these returns. This would be the time series “to predict”. We start from the premise that when a ratio has high values the expected market returns should be low, and vice-versa.

The table below shows the historical correlation of each of the above ratios with the S&P 500 one-year forward returns.

As expected all ratios have a **negative correlation**, which confirms that when a ratio takes high values it indicates that the market is expensive/overvalued and is more likely to have low returns, and when it takes low values it is more likely that the market rises.

But we see a big difference between the predictability of the ratios. **The P/E10 (CAPE) is the one that manages to better “explain” the future returns. **On the other hand, the P/E (Price-to-Earnings) is the worst predictor, which was to be expected given that its historical curve was not very coherent.

### Best window

You are probably wondering what would happen if we try to predict the return of the S&P 500 in less than a year, will the CAPE ratio still be the best one? What if we use a higher window, will all ratios still be negatively correlated?

Relax, as a Quant I could not pass up the opportunity to do a GridSearch over the window parameter (even though we know that it usually leads to *overffiting* hehe). Here are the results:

We see that the P/E10 (CAPE) ratio is still the ratio that best “explains” future returns, regardless of the size of the window. The other conclusion we can draw from the last chart is that fundamental ratios perform better in the long term than in the short term. Although, as the reader can imagine, it is one thing for the P/E10 to have a correlation of -0.90 with the 5-7 year return, and quite another that this -0.90 could be converted into a profitable, robust and applicable strategy. Spoiler: it is not as easy…

## Next steps

In this post we have focused the analysis on calculating the aggregated fundamental ratios of an index, the S&P 500, but what would happen if we carry out the analysis at company level? And on a sector level? Are all the sectors of the S&P 500 overvalued? If you are interested in knowing the answers to these questions, stay tuned!

## related posts

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