# Valuation Stretch: an Alternate Measure That Avoids Market-Wide Influences

### Introduction

Value models look for investment opportunities by discounting future cash flows, comparing current valuation multiples to historic multiples, or comparing multiples of various stocks within a cross section. Irrespective of the approach, the premise is always that the return potential is related to how far away the market value is from an estimated ‘fair’ or peer valuation. A measure of this potential – referred to as ‘valuation stretch’ – provides an expected future return from value models; such a measure of expected return is not easily available for other models, such as momentum or quality.

In this paper, we examine two different ways to measure the valuation stretch for cross-sectional equity valuation models, which is Man Numeric’s principal approach to valuation models. We find that a popular and intuitively simple measure can be clouded by market moves, so we propose an alternative that is unaffected by market-wide price moves and able to separate the return potential of cheap and expensive stocks.

### Cross-sectional valuation stretch

The cross-sectional approach to value compares the valuation multiple of a stock against that of its peers. While keeping our analysis broad, we will focus in this article on the price-to-earnings1 multiple – but all of the ideas we highlight here are also applicable to other valuation ratios such as price-to-book or price-to-sales. The expectation of a value investor is that cheap and expensive stocks will eventually converge in valuation. Importantly, value investors assume that this convergence will occur primarily through price moves, generating returns for the investor. This assumption is important because if cheap and expensive stocks converge through earnings deteriorating for the former and appreciating for the latter, the value investor would likely be disappointed.

The cross-sectional valuation stretch is a measure of that extent of cheapness or expensiveness. The wider the spread, the greater the return potential from value under the assumption that convergence will be driven primarily by price moves.

There are two questions one can ask about the valuation stretch to build intuition about the behavior of the value model. The first is to ask why valuation stretch rose or fell in the past and whether such moves were driven by changes in prices or earnings (in other words, is it because cheap companies became cheaper or because their earnings improved?). The second question is, given the current level of the stretch, what is the potential return for the value model? In this article, we will mostly focus on this second question.

### Traditional measure of the valuation stretch

The traditional measure of valuation stretch for industry-relative valuation models is to first industry adjust the earnings yield (by subtracting the industry average E/P from the E/P of each stock) and then take the difference in earnings yield between stocks that are cheap and expensive respective to their industry peers. A wide stretch indicates more potential for the yield differential to contract in the future, with correspondingly greater potential returns for the value investor.

For a US universe (largest 2,000 to 3,000 stocks by market cap, varying over time, using monthly sampling2), we see that such a measure of stretch widened during the tech bubble, the Global Financial Crisis (‘GFC’), and the European Sovereign Crisis (Exhibit 1). These were each followed by periods of attractive returns from value models.

#### Traditional Valuation Stretch calculation in two steps

Step 1:

Ind-adj E/P= (E / P) stock – (E / P) industry average

Step 2:

##### Exhibit 1. Traditional valuation stretch for a US universe

Source: Man Numeric, 2017. For illustrative purposes only.

An artefact of this method of calculation is how market-wide price moves impact this measure. Market rallies compress the stretch, while market declines expand the stretch (Exhibit 2). One can speculate about whether the resultant changes in stretch are indicative of future return potential of value, but there is no disputing that market-wide price moves make it difficult for us to compare the relative magnitude of the stretch over time. The bull market during the tech bubble narrowed the stretch, and the bear market during the GFC widened the stretch, making one wonder whether the value opportunity in 2008-2009 was greater than what was seen in 1999-2000 (Exhibit 1).

##### Exhibit 2. Stylized example of the impact of market-wide price moves on the traditional valuation stretch measure
Price Earnings P/E E/P
Cheap stock  $100$10  10  10.00%
Expensive stock  $200$10  20  5.00%
After a 20% market-wide price rise…
Cheap stock  $120$10  12  8.33%
Expensive stock  $240$10  24  4.17%
After a 20% market-wide price fall…
Cheap stock  $80$10  8  12.50%
Expensive stock  $160$10  16  6.25%

Source: Man Numeric, 2017. For illustrative purposes only.

### A measure that is untouched by market moves

If the stock’s price-to-earnings ratio were to converge with that of the median ratio of the industry, and if that convergence were to occur only due to price moves, this ratio would be the expected return from being long the stock and shorting the industry median – an industry neutral expectation of value returns.

To work through this example, let the stock’s current earnings and price be ES and PS0, respectively. Let the industry median earnings yield be EPi. The future price, PS1, at which the earnings yield of the stock would match that of the industry, would then be:

Es / Ps1 = EPi

I.e., Ps1 = Es / EPi

To get to that new price, the stock’s return would have to be:

Ps1 / Ps0 = Es / (EPi x Ps0) = (Es / Ps0) / EPi.

In other words, the expected return from a price-driven convergence is simply the ratio of the earnings yields. This can serve as an alternate measure of valuation stretch.

#### Proposed Valuation Stretch calculation in three steps

Step 1:

Ind-adj E/P= (E / P) stock – (E / P) industry average

Step 2:

Long-side expected return = Ind-adj EP|75th percentile - 1

Short-side expected return = 1 - Ind-adj EP|25th percentile

Step 3:

Valuation stretch = Total return from long- and short-sides

We see two advantages of this approach. First, it is not influenced by market moves (referring back to Exhibit 2, one can see that the ratio of the earnings yield in the last column remains the same irrespective of market moves). Second, one can get an estimate of the return from the long- and short-side of value separately (by first taking the ratio for each stock and then focussing on the 75th and 25th interquartile break points).

For the US universe described earlier, this new valuation stretch (Exhibit 3) shows the same three periods of larger value opportunity3: the tech bubble, the GFC, and the European Sovereign Crisis periods. But there are two important differences. First, without the effect of the market-wide price moves, it appears that the tech bubble period provided the most opportunity, while the GFC time period appears more muted (in contrast with what was seen in Exhibit 1). Second, the most recent time period (starting around May 2014) shows an elevated level of opportunity – an opportunity that may have been compressed in Exhibit 1 by the roughly 39% rise in the US markets over that time.

##### Exhibit 3. Alternative valuation stretch for a US universe

Source: Man Numeric, 2017. For illustrative purposes only.

If we look at the long- and short-side expected returns separately, we see greater opportunity on the long-side during the GFC (Exhibit 4) – consistent with the intuition that cheaper names continued to get cheaper during that time period. Looking at historical short opportunities in value, the tech bubble, with runaway glamour names, seems to have been the best time. We also observe that the widening opportunity in the latest year or two is limited to the long-side.

##### Exhibit 4. Long- and short-side opportunities

Source: Man Numeric, 2017. For illustrative purposes only.

#### Why not use the entire tail instead of the breakpoints?

A variation of the alternate method is to use the average expected return of the cheap and expensive quintiles, instead of using inter-quartile breakpoints (Exhibit 5). This has the advantage of capturing all the information in the tails (similar to how a value portfolio is typically constructed with many stocks in each tail). To prevent this calculation from being corrupted by outliers, we included only those stocks with price-to-earnings ratio greater than an arbitrarily chosen threshold of 3. The choice of this truncation may impact the magnitude of the long-tail returns – a higher threshold would reduce the skew towards larger long-tail returns than what is seen here (notice how long-side expected returns are larger than those from the short-side in Exhibit 5). A take-away here is that any time tail information is used in such calculations, interpretations are subject to the arbitrariness of truncation.

##### Exhibit 5. Long- and short-side opportunities

Source: Man Numeric, 2017. For illustrative purposes only.

### Comparison of the two methods

A quick way to compare the traditional and alternative approaches is to Z-score each with its own full period mean and standard deviation (Exhibit 6). The difference between the two during the tech bubble and GFC can be seen once they are plotted on the same scale.

##### Exhibit 6. Comparing the two methods

Source: Man Numeric, 2017. For illustrative purposes only.

A more interesting question when comparing the two approaches is: which is more intimately tied to value model performance? The question is not about predicting future value model performance, but about the connection between coincident changes in the stretch and returns of the value model. After all, widening stretch should coincide with negative value model performance, and narrowing stretch with positive. The proposed method does better in this regard (Exhibit 7), when comparing changes over a one month periods or changes over rolling 6-month periods4 (where we should be mindful of overlapped sampling).

##### Exhibit 7. Correlation between coincident changes in the valuation stretch and returns to a value model based on the same value metric. The proposed method has closer connection with the performance of the value model
1-month changes  -0.57  -0.71
6-month changes (incl. overlaps)  -0.69  -0.86

Source: Man Numeric, 2017. For illustrative purposes only.

Simulated realized value model returns over time (Exhibit 8) show that returns were comparable during the post-tech bubble and the post-GFC periods. This is consistent with the comparable opportunities for the two periods as indicated by the alternate method (Exhibit 2) and in contrast with the dominant opportunity during the latter period as indicated by the traditional method (Exhibit 1).

##### Exhibit 8. Simulated rolling 6-month returns realized by a value model driven by industry-adjusted E/P over an all capitalization US universe. This is the same valuation metric and universe in earlier exhibits. Returns shown are over six month subsequent to the date on the x-axis.

Source: Man Numeric, 2017. For illustrative purposes only.

### Valuation stretch across various regions

In the US small cap universe (names smaller than the largest 1,000 by market cap), in contrast with the large cap universe (largest 1,000 by market cap), the alternate method reveals how the valuation stretch has been widening since May 2014 through the recent past, a time period that has seen various value models struggle in this space (Exhibit 9). In the US large cap universe, the proposed approach highlights only the tech bubble over all other periods (Exhibit 9). It is possible that limiting ourselves to the largest 1,000 names causes valuation opportunities during the GFC to fall through to a small cap universe and avoid capture in this larger cap universe. It is also worth noting that the value opportunity among small caps is greater than the opportunity among large caps (Exhibit 9), commensurate with the historically higher risk/reward characteristics of value among smaller capitalization names.

##### Exhibit 9. Alternate method for US small cap and large cap universes

Source: Man Numeric, 2017. For illustrative purposes only.

When applied to Japan and Europe (note that the counts of stocks vary over time from 600-1,000 per region) universes, we see that in both cases the tech bubble emerges as the dominant historical opportunity (Exhibit 10). There also seems to be a secular decrease in the extent of available opportunity in Japan over the past 20 years, which could be a result of increased hunting of value opportunities by investors or of structural changes in the marketplace.

##### Exhibit 10. Valuation stretch in Japan and Europe

Source: Man Numeric, 2017. For illustrative purposes only.

The value opportunity as reflected within the largest 1,000 names in the developed world (Exhibit 11) is driven by the shape of events in US Large, Japan, and Europe. It is perhaps not possible to compare the magnitude of return today (or in the past several years) to what was seen about 20 years ago – changes in market structures (cross ownership, capital flow constraints, etc) may have brought us to more modest – but still appetizing – potential returns.

##### Exhibit 11. Valuation stretch in a global large cap universe (largest 1,000 names in the developed world by market cap)

Source: Man Numeric, 2017. For illustrative purposes only.

### Summary

Among stock selection models, value models enjoy an advantage of offering visibility into future return potential, though not on the timing of when that expectation may come to fruition. A traditional measure of valuation stretch based on earnings yield serves to quantify the extent of value opportunity in any cross section, but has the potential to be corrupted by market-wide price moves. We find that an alternative measure based on expected potential return may reduce the impact of this pitfall and has historically had a more intimate connection with value model returns.

1. We use Man Numeric’s measure of forward-looking earnings throughout this article.
2. We take the difference between the 75th and 25th percentile of earnings yield. This difference of inter-quartile breakpoints helps us avoid any distortion due to extreme values in the tails that can result from stocks with outlier earnings estimates.
3. It is interesting to note that there is always a positive expected return to value. The optimist will view this as a sign that it is always a good time to bet on value. The pragmatist will view this as an sign that naïve value approaches pick up on entrenched anti-growth or pro-leverage biases that will never come to fruition – and will look to refining value with risk adjustments.