Go for stocks with high return on equity but low price-to-book ratio

ONE way to value a company is to ascertain how much abnormal earnings - that is, earnings above the cost of its capital - it will be able to generate in the future. This stream of abnormal earnings is then discounted to its present value. Add that number to the current book value of the capital and you arrive at how much the company is worth.

This way of calculation has intuitive appeal. It implies that if a company can earn a rate of return that is equivalent to its cost of capital, then investors should be willing to pay no more than the book value for the stock.

Book value is the original capital invested by the company in its various assets to start up its business after taking into account depreciation.

On the other hand, if the company is able to generate earnings above its cost of capital, then investors should be willing to pay more than the book value of its assets. Conversely, if a company's net earnings cannot even cover its cost of capital, then investors will only invest in the company if it is trading below its book value.

We can see how much the market is valuing a company by comparing the market value of its equity, that is its market capitalisation, with the book value of its equity.

So if a company's market cap is $100 million, and the book value of its equity is $50 million, then this company is trading at two times its book value. This measure is also referred to as the price-to-book (PTB) ratio.

A PTB ratio of two times implies that investors are confident that the company can earn significantly above its cost of capital for a sustained period of time.

We can actually derive the formula for PTB from the abnormal earnings formula. The latter says that to arrive at what a company's shares are worth, we take the current book value of its equity, and add the discounted future stream of net profits which is in excess of the cost of equity. The discount rate used is the cost of equity.

So if we scale the formula with book value on both sides, we get PTB value on the left-hand side, and abnormal return on equity (ROE), among other things, on the right-hand side.

This suggests that a company's PTB ratio is a function of three factors: its future abnormal ROE, the growth in its book equity, and its cost of equity.

Abnormal ROE is defined as ROE less the cost of equity.

Firms with positive abnormal ROE are able to invest their net assets to create value for shareholders, and as mentioned earlier, will have a PTB ratio greater than one.

Strong ROE-PTB links

The whole point of what has been said so far is to show that there is a strong relationship between PTB ratios and ROEs. Companies with high ROE should trade at higher PTB ratio compared with those with lower ROE.

So perhaps one way to spot mispricings by the market is to identify stocks with high ROE but low PTB ratio.

Will such a strategy pay off? Well, I did some back-testing and the results are phenomenal.

I download the ROEs and PTBs of all the companies listed on the Singapore Exchange from 1990 until 2007. These are the yearly numbers on Jan 1 of each year.

I then divide the ROE numbers with PTBs, and rank the stocks based on that number. The top-ranked stock would have the highest ROE relative to its PTB. The lower-ranked stocks would have low ROE and high PTB.

I then split all the stocks equally into 10 groups. The first group, or the first decile, is the top 10 per cent of stocks with the highest ROEs relative to their PTB ratios. The 10th decile comprises those with the lowest ROEs and highest PTB ratios. Then there's a group of loss-making companies.

Compounded returns

Assuming that an investor did this on Jan 1, 1990. Based on data from Thomson Financial Datastream, there were 39 stocks then. After ranking them, he invested $100 in the top four stocks with the highest ROE/PTB.

On Jan 1, 1991, he did the same screening again. Then he divested the initial four stocks and reinvested the proceeds into a new batch of stocks with the highest ROE/PTB.

And he consistently did that for the past 17 years. How do you think his $100 would have grown to? A whopping $34,048.

That's a compounded return of 41 per cent a year. The above calculations did not take into consideration transaction costs. If it did, a huge chunk of profits would disappear.

But the point is, there is a very clear relationship between stock returns and ROE/PTB. As can be seen from the chart, the top 10 per cent of companies with the highest ROE/PTB turned $100 into $34,048 in 17 years.

The next 10 per cent managed to grow the pot to $4,710 - that's still quite a decent 25 per cent a year. The following 10 per cent, or the third decile, managed $958 for a return of 14 per cent a year.

And as we move to stocks with lower and lower ROE/PTBs, the return shrinks correspondingly.

The fifth decile grew only 3.8 per cent a year and the 10th decile - the 10 per cent of the market with the lowest ROE/PTB - shrank the $100 to just $25. It is very clear from the findings that it doesn't make sense buying stocks with low ROE and high PTB.

This screening process takes into consideration the underlying earnings capacity of a company in relation to how the market is valuing the company. Those with high ROE but low PTB are clear cases of mispricing. That's why the back-testing shows such a phenomenal performance.

But of course, a firm's ROE is affected by such factors as barriers to entry in their industries, change in production or delivery technologies, and quality of management. These factors tend to force ROEs to decay over time. But since in the above testing, the holding period is just one year, the decay is not so much a factor.

So the next time you study a stock, look at its ROE relative to its PTB as well. If the ROE is high, but its PTB is high as well, then perhaps the good fundamentals have been reflected in the share price. However, if you find a stock with high ROE but relatively low PTB, then you may potentially have on your hands an undiscovered gem.