Cinderella’s slipper

In addition, it’s easy to understand both how PEG factors are constructed and why they should be useful. As Peter Lynch, an outstanding US investor of the 1970s and ’80s, said in his investment best seller, One up on Wall Street: “A company with, say, a growth rate of 12 per cent a year and a PE ratio of six is a very attractive prospect. On the other hand, a company with a growth rate of 6 per cent and a PE ratio of 12 is headed for a come down. In general, a PE ratio that’s half the growth rate is very positive and one that’s twice the growth rate is very negative. We use this measure all the time.”

Yet in the world of financial academia PEG factors encounter a certain sniffiness. That might be to do with their definition. Recall that a PEG factor is a PE ratio divided by a growth rate in E. As such, it’s mathematically illiterate, like dividing apples by pears; sure, you can do the arithmetic, but the result might be meaningless.

It does not help that there is no clear definition of the specifics. Should the PE ratio be based on historic or forecast earnings? Which growth rate should be used – a historic rate, one for the current year or a rate averaged over several years?

Table 1 illustrates this dilemma, using some holdings from the Bearbull Income Portfolio. The data for the column headed ‘Historic PEG’ uses the most recent full-year earnings in the PE and the denominator is the growth of those earnings from the previous year. The forecast PEG takes the PE based on earnings forecast for the next full year and divides that by the growth rate in estimated earnings.

If earnings were not subject to violent swings then there should be little difference between the historic and forecast PEGs. Yet the ratios are all over the place. Obviously, if earnings are forecast to fall then the PEG factor becomes meaningless anyway, but in only one of 20 observations does the PEG factor drop out at the magical 1.0, the number that’s supposed to indicate shares that are fairly priced; the instance is the forecast PEG for Vesuvius (VSVS).

Most of all, however, academic reluctance to handle PEG factors lies with the difficulty of fitting them into an arbitrage pricing theory where value or price, cash flows and an interest rate must all act in unison so that a change in one will generate logical changes in the others. Difficult, but not impossible. Granted, fitting PEG factors into an arbitrage-pricing theory might be a bit like an ugly sister squeezing herself into Cinderella’s slipper, but it can be done, as Peter Easton, professor of accountancy at Notre Dame University in Indiana, has demonstrated.

To explain, take the example of Zytronic (ZYT) from the Bearbull fund. As with any piece of pricing theory, we need an interest rate, which is the return an investor expects from holding a security. To keep it simple – though still plausible – let’s assume 10 per cent. From that, it follows that, as Zytronic’s share price is 453p, then the ‘economic’ earnings it must generate – ie, the earnings that drop out of the price and the interest rate – are 45.3p for the coming year. To put that the other way around – an investor would pay 453p for the security if his required return were 10 per cent and he knew he would receive 45.3p of cash in the forthcoming year from holding it.

Yet, as Table 2 shows, there is a big gap between theoretical economic earnings and the accounting earnings forecast by City analysts. The challenge is to find the growth rate that will cause that gap to close in the coming years. That’s the implicit rate of growth that will justify a given PEG factor.

The first part is to quantify the excess earnings expected by analysts over and above the amount that would be generated at the 10 per cent required rate (see Table 2). For Zytronic, in the coming year that’s 4.9p. After that a quadratic equation is needed to find the PEG factor hidden in the data. But there is one lurking and, in Zytronic’s case, the rate of return that justifies it is 12.4 per cent.

If that provides an intellectual justification of sorts for PEG factors, the more important question is: are they any use? How well do they predict share price returns? Even to answer that tentatively means crunching a lot of data, which will take time. I’ll supply answers in the coming weeks.