The Price/Earnings Ceiling

From the valuation approach described previously, we can look at the earnings yield of a broad index such as the SP 500 and invert the growth formula:

earnings yield = dividend yield + growth rate

to obtain:

P/E = 1/(dividend yield + growth rate)

To put an upper bound on the P/E ratio, we want a lower bound on the yield + growth rate. Generally speaking, the total returns on capital (for equities, that would be growth rate and dividends) have been the GDP growth rate over the period. That is one of Kaldor's "stylized facts", which actually says that returns to capital as a fraction of GDP are the same over time, and that therefore the growth rate will be the same. Now, that doesn't need to be in equity, it could be in other forms of capital, but over time, it's hard for the equity returns to outgrow the total returns.

If you don't like the Kaldor argument, then notice that GDP = GNI, so that if national incomes are growing at g, people will be willing to accept effective bond rates of a little below g, so that the premium for equity should be a little higher than that. So that gives g as the expected returns from capital.

So that gives a long run upper bound (actually approximate equality) for the P/E multiple for the equity market as a whole. Obviously the variance is large :) Going forward, output growth may continue to slow.

Suppose you think a GDP growth rate of only 4% (nominal) is warranted over the next 20 years. In that case, the average P/E multiple would be at most 25, but there is a good chance that the equity markets wont like such a low yield, and money will shift to other forms of capital.

This surprises people who associate "high multiples" with growth stocks, but that is only to the degree that their multiple is higher than that of the index. The economy as a whole grows with GDP, as does the return to equity capital as a whole. Some specific returns may be more highly valued, but if the entire index is more highly or lowly valued than the yield available for the economy, then you are looking at a bubble or arbitrage opportunity. Historically 10 years has been long enough for this to unwind, and 20 years certainly has.

The larger the deviation, the more difficult it is to maintain earning growth as the company grows. For the SP 500 as a whole, if it is a constant share of capital, then the multiple will increase in absolute terms as yields fall.

It is usually better to buy when earnings are collapsing, but in this case you look at "smoothed" 10 year earning multiples (i.e. the current price divided by the average real earnings over the last 10 years). This would allow you to not be fooled into thinking that a high multiple is expensive, when in reality the denominator is abnormally low. Alternately, smoothing will not let you think that anything goes -- for example the July 2009 multiple was 117 -- and the market kept climbing.

FYI, in July '09, the smoothed P/E multiple was about 18. Not cheap by any means, and certainly not sustainable, unless you are assuming something along the lines of a dividend yield of 2% and nominal earning growth rates of 3.5% going forward. In that case, it might not have been a bad idea to buy. Just be aware that a high multiple is only justified on a long term basis only if we experience a secular growth collapse that also would also result in long term bond yields falling to well below 3.5% as well. Such an environment might not fare well for equities.