Price to book versus ROE analysis: A case of random numbers?

The comparison of return on equity with price to book (or the enterprise value equivalents) is a common form of analysis. Some investors claim that the often high correlation between these measures indicates the importance of return on capital. However, all is not what it seems.

This analysis is, in reality, a comparison of price earnings ratios. Adding capital employed may provide additional insight but remember that aggregate returns are most value relevant if they are a predictor of forward-looking incremental returns.


Many investors regard return on capital as a key measure of performance and many companies strive to increase returns, often including return on capital targets as one of their financial objectives. Therefore, it stands to reason that better businesses have higher returns and that consequently they should also have a higher valuation.

Price to book often shows significant correlation with return on equity

Analysts often demonstrate this link by comparing return on equity with the price to book ratio. In practice, this relationship is invariably positive and often shows significant correlation. This would seem to indicate that differences in return explain a large component of differences in valuation multiples. Representing the relationship graphically and plotting a regression line visualises this relationship. It potentially identifies under and over-valued companies; stocks below the regression line apparently undervalued, with a price to book ratio lower than would be expected considering the returns earned.

The two charts below are typically what you find in practice. The first shows Australian Healthcare stocks and the second European Luxury Goods. In both cases higher return is consistent with higher valuation multiples. You will likely find something similar for most sectors, although the exact relationship and degree of correlation will vary.

Australian Healthcare P/BV to ROE analysis
European Luxury Goods P/BV to ROE analysis
Source: Factset at 18 March 2021. Returns and multiples are based on consensus forecasts for years ending in 2023.

Some investors claim that this high correlation is an indication of the importance of return on capital in assessing value. We recently saw a claim that ROIC has the largest impact on valuation and, consequently, should be the key focus for investors. The reasoning was that 56% (the R2 of the regression line) of the variation in enterprise value to invested capital of S&P 500 companies is explained by differences in return on invested capital.

Although return on capital is an important metric in equity analysis, we do not believe that the P/BV v ROE analysis offers as much explanation of value differences as some might believe. The main reason for this is that the analysis is, in reality, a simple comparison of price earnings ratios.

The analysis reflects differences in price earnings ratio

You will notice that the book value of equity appears as a component of both ROE and P/BV. This means that the charts above are, in effect, a comparison of price and earnings but scaled by the book value of equity. The location of companies on the chart is an indication of their price earnings ratio, with higher P/BV for a given ROE, indicating a higher PE ratio. In fact, we can add PE lines to the chart to illustrate. At each point along the red lines companies have the same PE ratios, albeit with different capital employed and hence differing combinations of ROE and P/BV.

For example, Richemont and Burberry have a similar price earnings ratio of just above 25x but with very different equity shareholders’ funds relative to both profit and value. Hermes on the other hand has a return on equity similar to that of Burberry but a much higher valuation, with nearly twice the price earnings ratio.

European Luxury Goods P/BV to ROE analysis with added PE ratio indicators

For this sector, the slope of the regression line of P/BV versus ROE seems to approximate a price earnings ratio of around 30x. Those companies below the regression line have a PE below 30x and those above have higher PE ratios.  If the regression line were forced through the origin, the slope of the line would be a version of an unweighted sector PE ratio.

Random numbers will also produce high correlation

The observed correlation in a P/BV to ROE chart is actually driven by a combination of how consistent PE ratios are within the sector and by the spread of observed ROEs. Even random figures for the book value component of each metric can produce high correlation.

In the interactive model below, we have replaced book value for each company in the European Luxury Goods sector with a random number. The randomised book values are selected so that the range of price to book value is somewhere within the actual range observed for the sector. Each time the chart is refreshed, or this page reloaded, a different set of book values for each company is selected.

Interactive model: European Luxury goods analysis with randomised book values
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You will notice that each set of random numbers that are generated almost always produces a positive relationship between P/BV and ROE with generally significant correlation. The price earnings ratios for each stock are the same as the earlier real values because the random number generation only affects book values. As there is some similarity of PE ratios across the sector, the (random) spread of book values and ROE produces the apparently good correlation. However, this is an illusion.

Correlation statistics should always be used with care

The correlation statistic (R2) measures how close the data points are to the regression line. In our P/BV versus ROE analysis, R2 measures how much of the variation in the price to book ratio can be explained by differences in return on equity. However, these statistics should come with a health warning. If, for example, one company in the dataset has a very low book value of equity, perhaps as a result of aggressive asset write downs, and others have a high book value, then that one outlier will skew the R2 metric.

You may notice an outlier appear in the random book value generation (just refresh the chart a few times) where one or two companies have very different ROE relative to the rest of the sector. In this case the correlation tends to be much higher. However, the correlation measure may not be reliable in such situations.

If these charts merely indicate high or low PE ratios does the inclusion of book value of capital employed provide additional insight? We think that it can.

How should return on capital affect value?

Return on capital is an important metric in equity analysis. It provides insight into management performance, profitability and the efficiency of utilising capital. However, the relationship between return on capital and value is complex. Returns can differ, and for a specific company can change, for a variety of reasons, each of which can have a different effect on value.

A higher return on equity due to higher profit, as long as that increase is sustainable, will likely lead to a higher price and hence a higher price to book ratio. The value gain may be still higher if the improved profitability also leads to a higher profit multiple being applied.

Equally, a higher aggregate return arising from a more efficient management of capital, such as reduced investment in working capital, may produce an immediate gain from the released investment and a further gain if this improved return also translates into higher future returns on new investment and, consequently, better cash conversion. However, not all increases in return are necessarily positive for value.  For example, impairing assets produces an increase in ROE but does not release capital or directly increase future returns. Indeed, it may indirectly indicate reduced future returns, thus resulting in reduced value.

In valuation it is important to differentiate between a current aggregate return on historical investment and a forward-looking incremental return on future incremental investment.

Return on capital is most value relevant where it predicts future incremental returns

The traditional (aggregate) return calculation is simply current or forecast profit divided by invested capital. For return on equity this is earnings attributable to equity shareholders divided by equity shareholders’ funds. While this measures a current return, the investment on which it is based is a sunk cost which, therefore, cannot directly affect value. An aggregate return is only relevant for valuation if it provides evidence of future performance or is a predictor of incremental returns.   

An incremental return is the increase in profit in a given period divided by the increase in invested capital. The increase in capital represents the additional investment in the business, which is the difference between profit and cash flow in a DCF analysis. Therefore, a high incremental return indicates a low incremental investment and a higher cash conversion – the difference between profit and cash flow. Because it is cash rather than profit that ultimately drives value, this incremental return on capital is a key value driver. In many models the incremental return is not an explicit input, but it is nevertheless always implicit in the assumptions for capital expenditure and growth.

Incremental returns are a key input in the target multiple models we have featured in previous articles. In the target equity multiple model below, we have added a target price to book multiple and aggregate ROE input1We featured this model in our article Price earnings ratios – DCF in disguise. The version in this article includes the additional price to book calculation.. If you change the incremental ROE input this affects both the target price earnings and price to book multiples. This is because the input directly impacts the underlying DCF value used to derive the target multiples. However, the aggregate ROE input only affects the target price to book multiple because historical investment affects the book value component but does not directly affect the underlying value. In our model we have separate inputs for aggregate and incremental returns. If aggregate returns are a predictor of incremental returns, the aggregate ROE would affect value and PE ratios as well as price to book.

While forecast incremental returns are a key value driver, it is important to note that a historical incremental return on capital can be very volatile and difficult to interpret. This is because the change in profit may not solely be driven by new investment. For example, a profit increase due to improved margins could result in a very high incremental return that is not related specifically to new investment.

Interactive model : Target equity multiples

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For further explanation about this model, and the underlying DCF calculation on which it is based, see our article Price earnings ratios – DCF in disguise. For EV multiples see Interactive model: Target enterprise value multiples.

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Remember that the model derives target multiples. If the aggregate ROE increases due to higher profit then, even though the profit multiple may not change, price will increase simply because that same multiple is applied to higher profit.

The model illustrates how price to book is almost certainly correlated with aggregate returns, but this does not necessarily mean that these returns are a key driver of value.

Although the investigation of returns is important in analysis and valuation, you should be mindful of the accounting problems that can make returns difficult to compare and interpret. Accounting is based on a mixed measurement model with incomplete and inconsistent recognition of assets, particularly intangibles.2For an explanation of intangible asset accounting and a discussion of how the lack of intangible asset recognition can affect equity analysis, including the classification of stocks as ‘value’ or ‘growth’, see our article Intangible asset accounting and the ‘value’ false negative

Return on equity versus return on invested capital

We have focused on return on equity and equity multiples; however, a similar analysis can also be applied from an enterprise value and total invested capital perspective. As we have said in previous articles, we generally have a preference for enterprise value-based analysis and valuation metrics. Equity returns and multiples are impacted by financial leverage differences and are more susceptible to accounting measurement issues.

However, everything we have said about P/BV versus ROE also applies to an EV/IC versus ROIC analysis. In effect, these charts are a comparison of an EV/EBIT or EV/NOPAT multiple (depending whether you measure returns pre or post tax) and do not necessarily indicate the dominance of aggregate return on invested capital as a driver of value.

Insights for investors

  • A price to book versus ROE chart is, in reality, a price earnings ratio analysis. High correlation merely indicates that the stocks have similar PE ratios and/or a range of returns.
  • Measures such as ROE are a useful component of equity analysis but remember they reflect historical returns and are based on a sunk cost. They will only directly affect value if aggregate returns are predictive of future incremental returns or future performance.
  • It is important to understand why returns differ and change. Higher ROE due to more efficient utilisation of assets is very different from higher ROE due to accounting measurement differences or asset write-downs.
  • Using enterprise-based measures removes differences in equity multiples caused by financial leverage and may reduce some accounting distortions. However, an EV/IC versus ROIC chart is also, in effect, a profit multiple comparison; either EV/EBIT or EV/NOPAT.
  • Be wary of high correlation (R2) being given as an indication of the quality of some analysis. The relationship may not be what it seems, and outliers can create misleadingly high correlation.

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