# Price-to-earnings ratio in the UK large-cap market

Academics, economists and practitioners have contributed a significant amount of research into the value factor. As such, there is an established consensus conclusion that buying relatively cheap stocks will yield higher returns. The amount of books, academic papers and investment philosophy persuading investors to buy cheap is staggering, and some of the most distinguished names in the industry have popularised this style.

Traditionally, multiples have been used as an indicator of valuation in different ways, using a variety of fundamentals to assess ‘fair value’. One of the most depended upon across different sectors is price-to-earnings (P/E). Historically this has been indispensable information to value stock pickers, and had become the gold standard on value. Like all valuation multiples, there is no requirement for a forecast. For this reason, this premium has been labelled an anomaly to the efficient market hypothesis. Rather than questioning the robustness of the P/E relationship, we wanted to challenge the immortality of valuing stocks using past earnings information and have a closer look at whether there is still scope for outperformance using this style systematically.

The literature on this subject is vast, and the P/E factor has been a hot topic of research at least since the 1960s. Conclusions on the subject have varied but do also maintain similar findings, accumulating a consensus. Early findings such as Nicholson (1960) who proposed that companies with low (historic) P/E ratios tend to yield higher returns over the long term and concluded with the explanation that ‘The purchaser of common stocks may logically seek the greater productivity represented by stocks with low rather than high price-earnings ratios’. This statement might in other words suggest that investors should prefer companies that generate higher (earnings) yields. Academics and investors have for decades named the contribution to returns the ‘value premium’ and have supported Nicholson’s conclusion at least of a positive relationship. Fama and French (1998) observed similar findings and observed value stocks outperforming growth in 12 out of 13 developed markets. Basu (1977) concluded that ‘while the efficient market hypothesis denies the possibility of earning excess returns, the price-ratio hypothesis asserts that P/E ratios, due to exaggerated investor expectations, may be indicators of future investment performance.’ Shiller (2000) extends the theory with the idea that value is explained and indicated by an aggregated P/E ratio over the trailing 10 years on a macro level. This assertion argues that short-term historical data is a noisy signal and that the premium is explained by lower prices rather than short-term changes in earnings, which mean revert.

Despite the concrete evidence displayed over the last 60 years, perhaps there is scope to challenge several facets of these theories on recent data. Firstly, the value premium discussed above relies on using past information which will have already been digested by the market. Is there still a premium in historical data? Secondly, with this in mind, what are the behavioural implications and how have they changed? Why does the premium only reward in the long term and can this trend continue? In particular, the aim of this research will be to focus on these relationships from a systematic perspective.

## Systematic valuation of equities

Over what period should an investor hold a stock? Magnus Pedersen (2014) in his paper outlines an approach for valuing equities using ratios such as P/E and Price/Book, computing a regression against returns over different periods with the aim of estimating the future return across multiple periods and quantifying the probability of the result continuing. Rather than attempt to devise a valuation formula, this technique applied to the P/E ratio might indicate the time horizon of returns that are most related to P/E. In the below figure, each chart shows a scatter plot of the P/E ratio and future returns of the largest companies in the UK for each month since 2001. The P/E ratio is calculated using the historical price and the calendarised earnings per share (EPS) over the historical trailing 12 months.

Figure 1: Scatter plots of historic 12 month P/E ratio (calendar adjusted) vs nominal return %.

Source: Bloomberg, Thomson Reuters

Figure 1 shows four scatter plots of P/E and return for 1, 3, 5 and 10 years (non-annualised). At first over 12 months we see a lot of noise, 3 years an inverse slope starts to appear, 5 years this becomes more organised and over 10 years there is a clearer inverse relationship where the colours are somewhat separated showing some sort of cointegration between the two. Each colour is one stock, showing that over 10 years many stocks have tended to perform better while their P/E is lower than when it is higher. It’s important to note that this reduction in noise is also a result in lower dispersion as the annualised volatility between stocks will reduce over a longer time horizon. This aside, the graphs do show some important differences between the long and short-term horizon. Over 1 and 3 years there is data in the top left (high returns and low P/E) which is much higher than the majority of the data. This would indicate that where there have been extraordinarily high returns, the P/E has been lower rather than higher. Of course where this is data from the same security, each point is not statistically independent and following an unusually high return, the P/E ratio should also increase. Looking at the 10 year chart there is no evidence of this and the effect that can be seen is that low P/E stocks have performed better than high P/E.

Another observation here is more easily identifiable in the 10 year chart: it appears that stocks idiosyncratically display a range of normal returns at higher and lower P/Es over the entire test. Conversely stocks maintain similar P/E ratios but with consistently higher or lower returns. In summary, despite the results being very noisy, there are visible linear trends all over the chart which suggests that we are not actually comparing something that is normalised with respect to the output returns we are likely to experience.

With this in mind, if we quantify this relationship cross-sectionally, i.e. ranking stocks by their P/E ratio, we might be introducing bias and noise. Why, because investors value equity in different ways and each sector differently. More to the point, equities have many different qualities (or flaws) that investors are willing to pay for, such as growth, intellectual property, high return on assets, mergers and acquisitions etc., and no individual factor is an absolute measure for intrinsic value. Therefore by ranking stocks cross-sectionally by one factor, we are automatically introducing bias of other factors. A systematic investor consistently buying low P/E stocks is not taking the conviction that they are buying stocks ranked by intrinsic value. Instead, they are taking the conviction that over a certain period buying low P/E stocks will tend to outperform high P/E stocks and they are taking advantage of the ability to rank a large number of stocks rather than researching a small number to great detail. The resulting choice of securities may then be taking advantage of a behavioural factor rather than witnessing a correction to fair value.

## Performance of P/E quantiles

To determine whether this hypothesis has held over the last 15 years, we have performed a similar analysis using baskets of stocks rather than trying to examine each individual time series. Stocks that have earnings (EPS) available for each month are ranked into deciles and quartiles, each quantile forms an equally weighted portfolio which is rebalanced monthly. The annualised performance of each decile over 2001 to 2016 is shown below.

Figure 2(i) Decile and 2(ii) Quartile of P/E vs. annualised return from 2001 to 2016 (cumulative)

Source: Bloomberg, Thomson Reuters. Performance is gross of transaction costs but net of income.

The results are interesting. Both tests do show that there is some trend between quantiles, however. Looking at the deciles, there are higher returns from lower deciles of P/E ratio and lower (negative) returns from high deciles, but to score this as 1^{st} decile – 10^{th} decile would not fully capture the inverse relationship. The bottom decile (lowest P/E) has performed very badly with the second lowest not far ahead. The highest returning stocks are from the third decile and the lowest from the 9^{th} decile. Visually, the relationship is noisy.

To try to overcome this, the same test was run using 4 quartiles in order to reduce the noise seen in high concentrated deciles (typically these would hold 10 stocks). With around 25 stocks in each basket and with the help of diversification there might be a cleaner trend. Surprisingly, though, the lowest quartile still produces returns that are in the bottom half. A closer look reveals that the 1^{st} decile is around 8x earnings; this perhaps is often too cheap and reflects anomalies to value. Another closer look at the data reveals that over time the boundaries of the quantiles do change considerably. Below is a plot of the boundaries that were used to calculate the quartile chart above.

Figure 3(i) value of quartiles and median p/e ratio. Figure 3(ii) value of mean p/e ratio. Both using dataset of stocks with earnings.

Source: Bloomberg, Thomson Reuters.

The above plots reveal more about the landscape of P/E ratio cross-section, particularly through the crisis in 2008. The P/E ratio of the market peaked at above 80x earnings in 2009 while these results show a much lower 35x. This is because we are only looking at companies with a P/E ratio available at each historical date – for a P/E ratio to be available the company must be generating positive earnings. The market P/E calculation aggregates all companies’ EPS regardless. Therefore we are focusing on companies that maintained positive earnings during 2008-2009, and while we can see evidence of both the selloff and then the increase in P/E (which naturally lagged), we know that effects of the whole market are not properly observed in this cross-section of data. To have a closer look at this, we can perform the analysis over periods of data and examine each calendar year.

Figure 4 calendar year returns from each decile.

Source: Bloomberg, Thomson Reuters. Performance is gross of transaction costs but net of income.

The table above suggests that in the short term there is little to no statistical significance that low P/Es outperform high P/Es. This is consistent with the noise seen in earlier charts. Some of this noise is due to the interference of the higher volatility visible at the extreme quartiles. The charts below demonstrate this.

Figure 4(i) mean calendar year return from each decile and 4(ii) standard deviation of calendar year return. 2001 to 2016

Source: Bloomberg, Thomson Reuters. Performance is gross of transaction costs but net of income.

The left hand chart shows the mean annual return of each decile and the right chart shows the standard deviation. The volatility chart is probably the most remarkable and tells us that there is a very clear increase in volatility towards the extreme deciles, particularly at lower P/E ratios. Does this indicate that there is naturally higher volatility in cheaper stocks, or is this evidence of excess volatility caused by stocks with lower P/E ratios correcting or outperforming? The higher volatility at higher P/E ratios would be explained by the same effect. To look at these results more closely, the same test is represented by monthly data, again using mean and standard deviation.

Figure 5(i) mean monthly return from each decile and 5(ii) standard deviation of monthly returns. 2001 to 2016

Source: Bloomberg, Thomson Reuters. Performance is gross of transaction costs but net of income.

Using monthly data there is hardly an improvement in the effect on returns. However, with a higher frequency of data the results for volatility have improved and confirmed that the effect on volatility is true at both extremes. This has outlined that stocks with an extreme P/E, despite being past information, exhibit anomalous behaviour compared to the rest of the market.

## Consistency of the P/E effect

The final test using the same data is to statistically measure how this effect has changed over time by applying a simple linear best fit to determine the extent of the relationship between P/E and return over rolling 12 months. Over time the relationship does change quite severely as shown below.

Figure 6(i) slope across each decile and 6(ii) R-squared coefficient. 2001 to 2016 calculated using 2 year moving average

Source: Bloomberg, Thomson Reuters. Performance is gross of transaction costs but net of income.

## Conclusions

Based on results, it is clear that stocks with a lower P/E over the last 15 years have outperformed stocks with higher P/Es; however, this exclusively holds over the long term. In the short term, this effect is often scarce and over several years there is little to no statistical significance. There is evidence that stocks with extreme high returns over 1 and 3 years have had lower P/E ratios. A logical observation of the historic P/E (trailing 12 months) is that when relatively low then, assuming that the earnings will continue or grow steadily, the price of that stock has over-reacted. The measure itself is therefore not necessarily a model of future events but an indicator of reaction. This therefore would complement Shiller’s use of the CAPE to remove additional noise that would distort this information. The ratio can also deviate due to increased earnings and a slow reaction from the market. In both cases the rationale behind buying is contrarian - that the stock is irrationally unpopular. The volatility results would suggest that the value is a result of an overreaction in price and the long-term returns would suggest that most of the value benefits the less extreme decile. Therefore some of the extra volatility in the 1^{st} decile must be attributed to another factor. Perhaps this is a reflection of the idea that an extremely low ratio tells us that something else has been priced into the stock, which is not displayed in the returns ranked by P/E decile. This is either that the market knows something about a future event, the stock is a value trap or there are other factors such as growth which drive the price and have discounted the value factor. These reasons might explain why there is anomalous behaviour to the trend, and would suggest that systematically there isn’t enough value in buying the 1^{st} decile.

Finally, looking at the consistency of these results, there seems to be a large amount of variation in the difference between the 1^{st} and 10^{th} decile and the relationship has even reversed for some periods. The cyclical behaviour of the factor as a whole has been noted, and is reflected in figure 6. However, this also reveals that more recently (since 2011-2012) the relationship has become slightly statistically insignificant and might suggest that the quality and availability of forward looking consensus estimates have increased, raising expectations of predictive data improving the general efficiency of the market. The effects described above might now be attributed to new information or forecasted earnings which are very different to the past 12 months. This has given the stock market an increased role of a leading indicator in economic/macro events, of which there has been a relatively high concentration in the last 15 years. The EPS data is actual and will naturally lag these events, perhaps a year after they have been priced in, and this will therefore distort the P/E ratio hugely.

In order to improve results and extend this research, a good avenue would be to look at how macro events affect valuations cross-sectionally and identify relationships using forecast data. Further to this there would also be scope to improve the quality of the value premium using more advanced techniques to normalise data.

**References**

Nicholson, S. (1960), ‘Price-Earnings Ratios’Nicholson, S. (1968), ‘Price-Earnings Ratios in Relation to Investment Results’

Basu, S. (1977), ‘Investment Performance Of Common Stocks In Relation to their Price-Earnings Ratios: A Test of the Efficient Market Hypothesis’

Fama, E and French, K. (1992), ‘The Cross-Section of Expected Stock Returns’

Fama, E and French, K. (1998), ‘Value verses Growth: The International Evidence’

Ball, R. (1978), ‘Anomalies in Relationships Between Securities’ Yields and Yield-Surrogates’

Ball, R. (1992), ‘The earnings-Price Anomaly’

Shiller, R. (2000), *Irrational Exuberance
*Shiller, R. (2002),

Anderson, K and Brooks, C. (2006) ,‘The Long-Term Price-Earnings Ratio’