How is the multiple P / VPA per segment?

Periods of stress in the market, with high volatility and uncertainties ahead tend to produce very negative effects on stock prices. That you already know, or rather, that you already feel.

In situations like these, the price of a share may differ from its value in different degrees and intensity. At this point, some investors start looking at indicators, usually the result of accounting variables, to try to measure any possible opportunities.

Multiples are given for these indicators , which are nothing more than a relationship, and in general a ratio, between the price of a share and another business variable.

When creating a multiple, a company’s value is compared with other key information about its business to identify investment opportunities.

In this text we are going to focus on a specific multiple: the P / VPA , which is nothing more than the ratio of the share price to its book value per share. In the international literature, the indicator is known as Price-To-Book Value or Ratio (P / BV or P / B).

As Arruda (2015) points out in his study Multiples and its determinants: a study for the Brazilian stock market : “The difference between the book value and the market value of a company has always drawn investors’ attention, since if the value market value is well below book value, this firm is probably undervalued and therefore there may be an opportunity for investors to buy it ”.

Most companies have a P / VPA greater than one, which means that their market value is higher than their book value. Even so, in times of crisis, the use of the multiple can also show a little more of the investors’ irrationality.

In general, investors will pay a “premium” above the book value if the company is expected to have sufficient earnings in the future. Thus, these gains justify a market value above the book value.

The usual is to evaluate the multiple companies by company and thus calculate the indicators between firms in the same sector, but here we are going to show a broader, less usual way.

We will illustrate how the multiples of the entire sector would be, considering the individual multiple of each company for its participation within its segment.

The objective here is not to illustrate the difference between sectors, as each has a characteristic that would weaken the usefulness of this comparison, but rather to illustrate the evolution of these sectors over time, especially in periods of crisis (2009, 2014-2016) and bonanza (2019 ).

Of course, it is also important to note that searching for comparable firms in the same segment has its limitations, especially when the firm under analysis operates or is influenced by more than one sector.

In general, companies showed a strong increase in their multiple after the 2014-2016 crisis, with emphasis on the Mining, Commerce, Travel and Leisure sector. In turn, non-cyclical consumer companies showed a reduction in the indicator (with emphasis on ABEV3).

In the case of Commerce, notice the effect of the 2009 crisis and then the 2010 boom, when the economy grew by around 7.5%, with a strong presence of consumption. On the other hand, look at how the Telecommunications sector is constant throughout the analysis period, which we agree, was full of ups and downs.

The oil, gas and biofuels sector, on the other hand, suffered a lot during 2014-2016, even below 1, showing a higher book value than the market, reflecting obviously a collection of scandals and risk aversion of national companies linked to the sector .

Trying to find the determinants of P / VPA

The interest here is to take advantage of the studies by Albuquerque (2009) entitled “ Study on Multiples and Determinants of Price-to-Book-Value ”, in addition to the one already mentioned at the beginning of the text, the study by Arruda (2015).

After following the same methodology as the author, using an econometrics tool called panel regression in a model with random effects (I know, the name is ugly, no need to worry), it was possible to relate how the quarterly evolution of the P / VPAs around 65 companies.

The model was influenced by the indicators used in the study: i) net margin; ii) number of trades, iii) payout (proportion of profit distributed to the shareholder); iv) ROE (return on equity) and v) beta (a risk measure, which measures the sensitivity in relation to a market portfolio). I take the opportunity to add some macro variables such as: i) exchange rate ; ii) Selic rate ; iii) Gross Domestic Product (GDP) .

In this way, we preliminarily arrive at the results below.

The coefficient tries to signal the effect of that variable on the multiple P / PVA. Its reading to the letter is a little more complex, so I prefer that the reader pay more attention to the signal. The column called p-value is a statistic that the lower, the better the confidence in the result (in general, below 0.1 is interesting, although preferable below 0.05, meeting some other criteria and desired tests).

Thus, there is a strong importance of return on equity (ROE) , net margin and payout (proportion of profit distributed to shareholders) on the evolution of P / PVA, two important information that investors can look at when evaluating a company for this indicator. Events that affect these variables tend to greatly impact the evolution of the multiple.

Still, an interesting point is how some macro variables and the Ibovespa affect these indicators. While the model suggests a positive effect of GDP and Ibovespa itself, the dollar and Selic seem to have the opposite effect. The fear indicator, VIX , would have a negative impact, but in this case there is greater uncertainty as to whether the indicator really has any practical effect (the absence of a direct effect was to be expected).

It is difficult to say exactly which variable in the multiple (the share price or equity) each variable impacts more, risking the suggestion that the expectations of the macro variables produce a more intense effect on the share price in the short term, being much more sensitive to the effects of market sentiment.


The big point is that most accounting indicators take a little longer to compile and disseminate, leaving it up to experts to try to estimate what happened and, based on this estimation, decide whether the price is much above or below the equity value.

Thus, the study here tries to at least leave a “pocket rule” for you to understand what should happen with the indicator, in general, when there is a change in the macro scenario.

An economic crisis tends to have a negative effect on the multiple, with the share price falling much faster in the very short term than the company’s own profit or relevant accounting indicator. This could be intuitive in a way, but I try to give a little more statistical strength to this intuition.

The next step is to assess how these indicators affect each company and how much more sensitive it can be in relation to its own segment, which can generate insights when it comes to differentiating and choosing an action within a specific sector.


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