It's not. The observers who argue P/E multiples should not justifiably significantly decline during periods of high inflation have missed two important points: (1) P/E multiples are multiples of

*nominal*not real earnings; and (2) the impact of taxes. Allow me to explain.

Suppose a company is earning a 10% RoE in a period of zero inflation. Both its nominal and real RoE is 10%. It is not growing, so it pays it all out as a dividend. Suppose the company trades at 1x book value, or 10x earnings (and a 10% yield).

Now let's take exactly the same company earning the same 10% real return on equity, but this time posit an environment of 10% inflation. The company's nominal RoE should now be 20% (to preserve the same 10% real RoE). Because the real RoE is the same, the company should still trade at the same 1x book (ignoring the impact of taxes - see below). However, this is now 5x earnings. In addition, in order to preserve the company's real asset base at a constant level, it will now need to retain half of its earnings, to grow its book value 10% a year (in line with inflation), reflecting nominal increases in working capital in line with inflation, as well as the higher nominal replacement cost of fixed assets as they depreciate and are replaced. The company's dividend payout ratio will accordingly drop to 50%, and it's dividend yield will remain the same - 10%. This is also a real yield, as dividends will rise 10% pa (20% nominal RoE x 50% retention rate), offsetting the impact of inflation.

This is the same company earning the same RoE, and yet the P/E multiple in the first scenario is 10x, and in the second 5x. The error made by observers is in using

*nominal*P/E ratios instead of

*real*P/E ratios. What ought to be done to work out a real P/E ratio, is to subtract the rate of inflation from the nominal RoE to derive the real RoE, and compare that real RoE to the company's P/BV. The formula should be as follows:

P/E real = Price-to-book / (Nominal RoE - inflation), or equivalently:

P/E real = Price-to-book / Real RoE

In our first example (10% RoE with zero inflation), we derive:

1.0x / (10% - 0%) = 1.0x / 0.10 = 10x

In our second example (20% nominal RoE with 10% inflation), we derive:

1.0x / (20% - 10%) = 1.0x / 0.10 = 10x

In other words, while it is true that

*real*P/E ratios should not decline during periods of high inflation (before adjusting for taxes - see below), it is absolutely true that

*nominal*P/E ratios should decline - indeed meaningfully so. It is amazing to me that no major academic I am aware of has ever recognised this reality and why, nor have most commentators, including many heavyweights of the investment world. It is merely insisted stocks' earnings are real and hence P/E ratios should not change.

This exercise is not purely theoretical, in a world where low inflation now prevails. A serious valuation mistake made by many investors based in developed markets when they invest in high-inflation emerging markets, is to seriously misprice stocks by not taking into account inflation differentials. Places like India have been an obvious example. I have seen many typically first-rate DM investors argue certain stocks in India are cheap at 20x P/E, because they are growing at 15% a year with 15% RoEs (3x book), but that growth was being struck in an environment of 6-7% inflation. The real RoE was closer to 8-9%; real EPS growth was 8-9%, and the real P/E was therefore closer to 35x. Would they pay 35x for a company with a 8-9% RoE in the US/Europe?

The difference between perceived value and actual value has been reflected in substantial currency depreciation over time (the Indian rupee has fallen from 40 vs. the USD to 70 since 2010, due to elevated inflation differentials,

*not*mean-reversionary currency volatility), which unsurprisingly given the valuations paid, has yielded poor returns over the past decade on a dollarized basis. "Our stock picks have performed well, we merely lost money on the currency", is a common refrain. Well, of course you did! You also see the same mistake made whenever you read a headline that says 'EM markets trade at a significantly lower P/E to DM', implying that that makes EM cheaper. Until you adjust for inflation, you cannot make such a proclamation.

The same is also true in reverse. Banks in the EU and low-inflation markets such as South Korea, for instance, have lower RoEs of 8-10%, vs 15% in places like India and Indonesia. But because inflation is so low in those former markets, the real RoEs are actually not that dissimilar. And yet banks' P/BVs in India/Indonesia are 2-5x, whereas they are closer to 0.5-0.7x in Europe/SK, as investors labour under a 'money illusion'. It's as if bond investors compared nominal bond yields/interest rates in Turkey of 15% vs. 2% in the US without taking into account the impact of widely variant rates of inflation. It's foolish, and yet the practice is fairly widespread.

The second reason why P/E multiples ought to decline in a higher-inflation environment (and

*real*P/E multiples this time) is the way taxes on investment profits/capital gains are typically levied. Typically taxes are payable on

*nominal*gains, instead of the more appropriate

*real*gains.

Consider again our initial example, but let's now also assume capital gains and dividend taxes are both 20%. In the first example (10% RoE; zero inflation), the nominal and real pre-tax return is 10%, and the after tax return is therefore 8% real and nominal. However, if inflation is 10%, nominal returns are now 20%, yielding a nominal after-tax return of 16%,

*which is only 6% real*. When inflation is high, the implicit tax rate on real returns significantly rises, and this justifies not only lower nominal P/E multiples, but lower

*real*P/E multiples as well.

This is a long-standing problem with the tax system. In my opinion, taxes on investment profits (both capital gains and interest - dividends alone are less of an issue) should only assess taxes on the real portion of the gain, netting off the change in CPI during the relevant period from the return. However, in practice this has not occurred and is unlikely to occur, which means lower real P/E multiples are also justified in high-inflation periods. When the nominal-to-real P/E adjustment is also made, it is clear that in combination,

*very significantly*lower P/E multiples are economically justified in periods of high inflation - particularly for investors subject to high rates of capital gains taxes.

Intriguingly, the reverse is also true. We are currently living in a low-inflation world (in developed markets). That means the quality of the nominal RoEs being reported by companies is now much higher than it has been in the past, and despite that fact,

*nominal*RoEs are currently also high in places like the US relative to historical standards (although this is partly offset by a higher portion of offshore earnings deriving from high-inflation economies - this is perhaps one reason why nominal RoEs are meaningfully above historical averages).

*This means significantly higher nominal P/Es are economically justified viz-a-viz historical averages*.

It is interesting that this reality is almost never taken into account by market observers/strategists, who simply compare current

*nominal*P/Es to historical averages, without taking into account the fact that rates of inflation have significantly fallen. They then simply conclude markets are expensive because nominal P/Es have risen above historical averages. Perhaps low inflation is one economically-justifiable reason why nominal P/Es are above historical averages?*

LT3000

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*That is not to say markets are not expensive. In many sectors/markets, they are. However, they are less expensive than they first appear relative to historical averages on account of lower inflation.*