The P/B-ROE Valuation Model

The price-to-book (PBV) v return on equity (ROE) model became famous after Jarrod Wilcox published a research paper on it in 1984. The paper gave a theoretical basis for PBV through some formula manipulation. When you take the dividend discount formula (Price=Dividend per share/expected return – growth rate) and make a few substitutions or manipulations, you arrive at a formula for PBV: PBV=(ROE-g)/(r-g).

The formula shows that PBV has three factors influencing it: ROE, growth rate g and expected return r. Unlike many theoretical theories, this one happened to have an empirical basis for it as well. Jarrod Wilcox showed that when a regression involving PBV and ROE was performed, a neat line of best fit could be drawn.

This has stood the test of time as well. Recent empirical evidence also confirms this relation with a few additions. Aswath Damodaran has done research on this too and shown a similar relationship. However, he makes a few additions. Because ROE can be amplified through leverage, a proxy for risk has to be utilized in regression as well. Along with a regression of PBV, ROE and Standard Deviation (SD, as a proxy for risk), he simultaneously performs regression of the same variables with an addition of expected growth in EPS – which can be a bit arbitrary.

Enough of the theoretical mumbo jumbo, let’s look at some graphs for a relief.

The above graph is one of the regressions Jarrod Wilcox ran in his study. Unbelievable, right? And below is a regression Aswath Damodaran ran in 2012 for US banks. It shows a similar trend with a bit more variation.

Now, when Wall Street found out about these cool ideas, they ran with it. How? Well, if a share has a high ROE and PBV, it’s likely to be fairly priced. So is a share with a low ROE and PBV. However, if there’s a share with a low ROE but high PBV, then according to the above ideas, the market is paying too much for the share, so it is overvalued. SHORT IT!

On the contrary, if there’s a share with a high ROE but low PBV, then the market is underpricing it. GO LONG! Many traders made strategies from this analysis. Go short on all the low ROE high PBV shares or go long on all high ROE low PBV shares.

The best tactic seems to hedge it both ways. Go long on high ROE low PBV shares and short on low ROE high PBV shares. Why? Because if the market sways one way or the other, the risk is reduced.

However, among all this, the key thing to note is that the PBV-ROE model is a relative valuation method. The trader is taking advantage of relative mispricing of securities. It is not a fundamental investment option which can be kept in the long run.

Another thing to note is R-squared in the regressions. In Damodaran’s regressions, when a PBV-ROE regression was run, R-squared was 60%. When SD was added to the regression, the R-squared rose to 79%. You can add expected growth to the mix as well which could increase R-squared but the expected growth metric is arbitrary so the regression can become less reliable.

Due to these reasons and the fact that on average, the shares should converge to the PBV-ROE standard, trades have to be made on a higher sample of securities to remain profitable.

But how does this model fair in the Pakistani stock market? The graph below shows the regression for 17 of the 20 publicly listed banks (three were excluded due to negative equity or losses). A trend is there but it’s not as strong.

When you compare the regression with current PBV of the banking shares, you see that AKBL, BOP and NBP are significantly undervalued (shown below). But at the same time, you notice that neither of these three shares pay dividends.

Once you add dividend yield to the regression, R-squared goes up to 62% showing that dividend yield is a key variable. Now, Meezan Bank seems like the most undervalued share (shown below). While JS Bank and Bank of Khyber seem to be the most overvalued shares.

But do you see the issue with this exercise? The regression can be quite imprecise based on which variables you choose as part of your regression. The other issue is the viability of some of the variables. For instance, we used SD as a proxy of risk. Is that a suitable variable especially since high ROE can be achieved through leverage. And high ROE leads to high PBV, so would the model be reliable?

Despite these limitations, if you create trading strategies with a large sample, you should generate some profits. But note, this is not a long-term investing strategy. For long-term strategies, one has to look at the earnings potential of a company. In this case, PBV and ROE seem to be poor metrics due to various reasons mentioned both in this blog and previous blogs.

In addition to this, there are other models which offer better long-term strategies. But more on that in a later blog.