Warranted Stock Market Valuations and the Price-Earnings Equation Once Again

It can be shown http://delong.typepad.com/sdj/2007/05/a_teaching_note.html that the "right" way to value the stock market is with the price-earnings equation:

P = E/[r - (1/θ - 1)ρ]

Where E are the earnings--the sustainable permanent cyclically-adjusted, and correctly accounted for Haig-Simons earnings--paid on the index, r is the appropriate real rate at which to discount cash flows of the riskiness of the stock market, θ is the payout ratio of dividends to earnings, andρ is the wedge (which may be posititive or negative) between the appropriate external real interest rate r and the internall rate of return the firm can earn on its reinvested earnings.

If we are willing to assume that ρ is close to zero, than this equation is approximately:

P/E = 1/r

The price-to-permanent earnings ratio is one divided by the market's expected discount rate.

Mark Gongloff presents the ratio of prices to a ten-year lagging average of earnings for the S&P 500--the idea being that the ten-year moving average irons out transitory fluctuations in profits and gives you permanent earnings.

This is not quite right. This gives you permanent earnings five years ago. To get permanent earnings today you have to grow the average by five years of the trend growth rate of real earnings--which has been 6% per year over the past twenty years. The current value of 28 for the price-to-moving-average-of-lagged-earnings ratio corresponds to a price-to-permanent-earnings ratio today of roughly 21, and to a current r of4.8% per year.

That looks pretty good when compared to current Treasury TIPS real interest rates of 0.6% per year for five years, 1.31% per year for ten years, and 1.81% per year for twenty years. It's not the six percent per year average equity premium of days of yore. It is, however, at least half that. If you are a buy-rebalance-and-hold investor--and you should be--equities are still looking good.

But that's not the way the mind of Wall Street works. Exhibit: Mark Gongloff:

Ahead of the Tape - WSJ.com: [A] look at a stalwart measure of cheapness -- the price-to-earnings ratio -- from various vantage points suggests stocks might be dear.... The Standard & Poor's 500-stock index trades at 15 times forecast operating earnings this calendar year. But that's not much of a deal when compared with the 60-year average of about 12.... Other takes on P/E lead to a still-more-bearish conclusion. When measured against the past 12 months' reported earnings, the S&P 500's P/E ratio jumps to about 21, above its 60-year average of roughly 16.

Benjamin Graham and David Dodd... suggest weighing prices against earnings averaged over a period of as long as 10 years. On that basis, the S&P 500 today trades at roughly 28 times reported earnings. That's lower than the peak of about 48 at the height of the dot-com bubble, but hardly a bargain; for the past 60 years, that P/E ratio has averaged about 21....

James Montier, global equity strategist at Société Générale, said his screening had uncovered a rich vein of short-selling opportunities. "If one finds lots of shorts, and not many longs, it suggests that the market is generally overvalued," Mr. Montier says....

"Are there securities where valuations are high? Absolutely," says Tim Ghriskey, chief investment officer at Solaris Asset Management. "But we do not have the risk we had in 2000, where valuations were at historic extremes."

Surely not. But we're not at a low extreme, either.

It's just worth pointing out that whenever the stock market is at valuation ratios that Gongloff and company consider "normal" then equities are an absolutely amazing deal relative to all kinds of bonds

Comments

[Finance attorney]

Equities are indeed an absolutely amazing deal. But you can't prove it with P/E ratios based on reported accounting earnings.

Accounting earnings are not economic earnings. Worse, they are not even consistent with themselves:

+ The definition changes -- often dramatically -- from time to time. (The treatment of lease payments, for example, has changed several times in the last 20 years.)

+ Even when the definition doesn't change, firms have discretion in deciding which principles to apply. (LIFO or FIFO?)

+ Different industries have incompatible principles. (The publishing industry has an idiosyncratic method of booking sales.)

Consequently, even if one assumes that accounting earnings measure something useful, one cannot make intertemporal comparisons.

[Ken Houghton]

He did stipulate Haig-Simons earnings:

http://en.wikipedia.org/wiki/Income#Full_and_Haig-Simmons_income

One might, though, quibble that theta, for most of those "historic" years, was closer to .04 than the current ca. 0.02, which produces an interesting change if rho is =not= zero.

[Matt]

The Gordon rule calculations are based on firms with increasing exposure to world trade, but the yield curve of interest rates is (more) limited to the USA. (The economic covering of the stock market and the covering of bonds do not match.)

So, we need to use global yield curves in part, complicating the argument because transaction costs and exchange rate volatility prevent smooth investments in foreign bonds.

Otherwise, Brad has right, in fact he is more than right because investment in stocks give us indirect access to foreign yield curves at lower cost than buying foreign bonds directly.

[Maynard Handley]

Doesn't this analysis assume a static world? It talks about "sustainable permanent cyclically-adjusted" earnings and incorporates no parameter describing the change of earnings with time.

An optimist would, then, surely say that this valuation model doesn't reflect reality because it doesn't incorporate the potential for growth.

More interestingly, a pessimist would say that it doesn't reflect reality because it doesn't incorporate the potential for earnings to go down substantially. (Everyone's willing to at least admit the possibility to things going horribly wrong in China, thereby dooming the entire country; few are willing to admit that possibility for US, let alone the entire world, in spite of peak oil, global warming etc.)

[David Lloyd-Jones]

.

This cute formula relies on one of the most powerful notions in all of economics: equilibration at the margin. Obviously any well-run company will finance itself so that its marginal internal rate of return is the same as the interest rate in the external market. (The excellent Carol Loomis once wrote a hilarious article for Fortune on the fall of Lincoln National, I think it was: the bank's President thought that there as a plot behind the whole sorry mess, but he assured her that he always operated on the principle of lending at rates higher than his average cost of borrowing...)

What this P = E/[r - (1/θ - 1)ρ] stock-price analysis ignores is one of the most interesting things in th real world: what goes on in the intra-margin. (And thinking stoopidly about the intra-margin is what led Lincoln National down the tubes.)

If company A makes ten zlotys on the first frammel it makes, while company B makes only three on its first whingwhiffle, but they both make M%, the market rate, on the second and last one they put out, obviously company A is worth more, even though the formula makes them look the same. Everybody is notionally the same at the margin.

I was once at the Center for the Study of Democratic Institutions in Santa Barbara for the morning, and then left just as Kenneth Arrow was arriving for lunch. The rush of the Center's Fellows at his limousine resembled nothing so much as the mob of teeny-boppers when the Beatles showed up at Maple Leaf Gardens, which I witnessed that same year.

What makes the horse race is that horsies are all different.

What makes the Tote board is that bettors and hence betting crowds are all different.

.

[a]

There may be more people who can borrow at low rates and invest at higher rates today vs. other times such as the 1980s when interest rates were higher. You can find a lot of low beta stocks that have yields of around 5%+ when you factor in stock buybacks in addition to cash dividends.

What if "inflation rate" varies by person? for example, a person with a heavy proportion of education and health expenditures may think inflation is higher than someone with a relatively low proportion of spending going toward education and health expenditures (and thus a different real rate of interest).

reasons not to buy equities:
there are a fair amt of people who do not want to get squeezed (eg, have to sell too much stock in a down market) and thus people may not want to invest in equity.

also, you may fear that interest rates (nominal at least, possibly real) in the U.S. are inevitably going to go much higher at some point in the future, which may change the attractiveness of equities.

people are making relatively more money (net) running privately held businesses (see most recent buffett annual shareholder letter)

[Cranky Observer]

> This cute formula relies on one of the most
> powerful notions in all of economics:
> equilibration at the margin. Obviously any
> well-run company will finance itself so that
> its marginal internal rate of return is the
> same as the interest rate in the external market.

I am approaching 25 years in manufacturing companies of various types; 7 of them IIRC although several of those with multiple divisions (30 in one case); most US-centric but one highly international; started with the type of manual labor job Hillary seems to think she knows about; staff, management, and consulting positions: and I have not ONCE encountered an organization that operates in the hyper-rational, mathematical manner that most posters here seem to believe is the norm in actual business. In fact the most successful of the places I have worked deliberately drove out anyone who attempted to make decisions in that manner in favor of people willing to spend long hours with the customer then make decisions intuitively.

I have also worked extensively in business information systems and associated data warehousing and I can tell you with absolute certainty that 97% of the organizations in the world have no bloody idea what their marginal cost is for /purchased paperclips/ much less the product that they make.

Cranky

[Matt]

http://www.finfacts.ie/stockperf.htm

According to a University of Michigan study, an investor who stayed in the US stock market during the entire 30-year period from 1963 to 1993-7, 802 trading days-would have had an average annual return of 11.83 %. However, if the investor missed the 90 best days while trying to time the market, the average return would have fallen to 3.28% per annum.

The trick works for long integration times, 800 trading days, but the bulk of advance comes from about 100 days, or one eighth of the investment period.

Investing since 1990 would have returned a much bigger value, but that was a period of rapid global expansion.

If one invested from 1920 to 1980, the relative returns from bonds and stock says one dollar would get you about $30 from stocks and about $5 from bonds. Inflation adjusted. However, from 1990 the ride of globalization would make you rich, who would of known?

Good site for comparing bonds and stocks.

http://investorsfriend.com/asset_performance.htm

[Neil B.]

But, there's no "right way" in the actual predictive sense to value the stock market. Prices there are based so much on self-exciting momentum movements, they are a sort of economic vaporware since how much you earn is not just based on dividends but how much you can sell it for, which it based on how much the next person thinks he can sell it for etc. - it's a hall of mirrors, there is no "rational" analytic way to figure this. Bro in law Kevin Rock and other sharp analysts try to derive such formulas (I was even happy to provide him some complex number integrations for this effort) but it just isn't like mechanical physics, it is more like chaos theory or worse.

BTW, the recent trading in futures/derivatives has surely brought up the market (versus the producer source price, note little media coverage) price of oil beyond simple supply/demand in the face of peak oil, see for example http://www.financialsense.com/editorials/engdahl/2008/0502.html and http://hsgac.senate.gov/public/_files/052008Masters.pdf

[wil]

Cranky has it right. As far as I can tell, the only people who use models of this type in the real world work on Wall Street (or some reasonable facsimile thereof), trying to predict what results the people doing the actual work will realize. Not that such behavior is inappropriate - it gives the producers benchmarks to target, and creates a rational market.

[zak822]

Cranky, you were so on the money in your post. And saying "I have not ONCE encountered an organization that operates in the hyper-rational, mathematical manner that most posters here seem to believe is the norm in actual business" is priceless.

The difference between how business really gets done and the way economists say it gets done can be striking, with real world consequences. It's something that should get a lot more discussion than it does.

Wil noted that it creates rational markets, so there's nothing really inappropriate about it. I'm not so sure, but I'd like to hear more about it.

[David Lloyd-Jones]

Cranky,

The point of my post was simply that I thought the formula, like all formulas, is inappropriate for giving a recise value of equities.

However I stand by my "Obviously any well-run company will finance itself so that its marginal internal rate of return is the same as the interest rate in the external market." Two reasons:

First the naturalistic one: whether people plan to follow the law of gravity or not, they *will* follow it. Over time organizations with marginal costs of capital higher or lower than their own marginal productivity of capital at the margin will go to the wall.

Second, organizations with treasurers or CFO's who do not come pretty close to this aim are simply not well run. It's like "mechanics who let their tools rust are not good mechanics." There are rules for adequate performance, and that one is the one for corporate treasurers.

[Neal]

In the same sense that "inflation is contained", it depends on how it is measured and who is doing the measuring.

For instance, from the Financial Times 5/21/08:

(quote)

The world’s leading banks have stepped up pressure to relax controversial accounting rules with a new plan aimed at breaking the “downward spiral” of huge writedowns, emergency fundraisings and fire-sales of assets.

The proposals on “fair value” accounting by the Institute of International Finance, an alliance of 300-plus companies chaired by Josef Ackermann, Deutsche Bank’s chairman, would enable financial companies to cushion the blow of financial crises by valuing illiquid assets using historical, rather than market, prices.

(end quote)

So what does this say about the valuation of these companies and their stock? This is happening all over.

The market is not just composed of optomists, it is composed of blind optomists.

[Mark Gongloff]

Actually, though I don't presume to be a mind-reader, "the way the mind of Wall Street works," in my limited experience, is holding firm to a belief that equities are a good deal pretty much all of the time, except at rare moments of absolute panic. I guess my mind works a little differently than that: I think they're not always necessarily such a great deal, and I think they're not a better deal now than they have been, on average, in their history.

Obviously reasonable people can disagree, and low interest rates indeed might make stocks a better deal. But interest rates aren't the final arbiter of that controversy. If they were, then U.S. stocks would have been a terrible deal in 1982 and Japanese stocks would have been a great deal in 1998.

[Darren]

Cranky, when I started my economics education (after years in IT), I too was hostile to the use of mathematical modelling that did not take institutional and information realities into account. However, I am beginning to think some of my hostility was misplaced.

Firstly, simple equations governing the behaviour of stylized corporations are only meant to be approximations. It's a *model*. All models are false. Some, hopefully, are useful.... with a handful of equations you can describe a dynamic system that kinda, sorta, looks like the vastly more complex real world, and that's useful. Drawing welfare implications from that same handful of equations is much more problematic, and that's where economics really tends to crap the bed IMHO, but that's another argument.

Secondly (and this is more speculative) a corporation need not consciously recognize what it is doing in order to behave in a certain way. To extend DLJ's natural argument, corporate structures could have evolved such that the end result is to behave in a way governed by a few simple equations. To borrow an analogy from the excellent Richard Dawkins: a bat's echo-location system involves the bat squeaking, listening to the echos, and inferring where the obstacles are (all in the presense of thousands of other squeaking bats). That little bat-brain must have some US military grade signal processing built in. Does the bat need to know how it does what it does? No. It just evolved: bats that are able to do this find food, bats that can't do this bump into things and die. Perhaps corporations evolve the same way :)

[Chris]

I think that DeLong and Gongloff rely on the assumption that earnings fall through to outside, passive, minority investors. One of the great problems of recent years is that executives and other insiders have extracted great wealth from their companies. Why should an OPMI get a 4.8% earnings yield in the equities market when corporate bonds provide more yield?