My answer to my own brain teaser

I was not fully satisfied with this post on equity market valuation, although it is clearly where my own best guess is. Equities are meh, not screaming cheap, outright and relative to bonds. I would rather own equities than bonds for the longer haul. Imagine that!

The problem with my post is that it does not quite get straight how to think about the earnings yield (EY)* in the S&P500. Is it by definition equal to the expected or required real return in equities, r+k, as an arbitrage relationship would seem to imply? Or might EY also be influenced by economic growth, which we might, stretching a bit, call g, attempting to apply the Gordon Growth Model?

I’m going to go ahead and say that confusion was not really my fault, because I was trying assess an argument that included that very confusion. But I ended up going with a kludge on the Gordon Growth approach, because it seems logically the least wrong, and (probably flukily) seems to fit the data okishly.

I figured I could do better with some help from the brainiacs in the Twitterplex, so I posed a brain teaser asking folks to resolve the tension there.  Crickets, almost. I think one problem with trying to speak with academics is that it takes a couple days to dissuade them from their view that a Wall Street type is probably stupid and not worth engaging.

So I got two answers, which were kind of funny in their dismissiveness. First, r is not g, you know. In fairness to that guy, who is a very good guy, he did mention that I did probably know.  Second, was a professor who said g has fallen only 1 percentage point, where my chart says 2. Besides, that too is not what I asked. In fairness to that guy, he may have got back with a better answer, but in a fit of very belated prudence I forced myself off Twitter so I will never know.

They say, if you want something done right you are going to have to do it yourself, even if you probably don’t know what you are talking about, as in my case. So here are my two cents.

First cent: an arbitrage relationship does indeed imply that the earnings yield is by definition equal to the expected real return.  However, it seems to me that that is just semantics, such that E must be defined (rather than simply measured) to generate that result.  Within this arbitrage framework E is that which makes the arbitrage rule so. But that E has the unfortunate weakness of not being measurable.

Second cent: this means that we have to use the logic of the Gordon Growth model and take some explicit account of growth.  But this is tricky. The Gordon Growth relation says that the dividend yield, not the earnings yield, is systematically related to the difference between the risk-free real interest rate and growth, k either held constant or backed out as actually our main interest.  It also says g refers to dividend growth, not potential economic growth.  My get around, scandalously worked up ex post, is to  ASSUME that the earnings retention rate, difference between earnings and dividends, is systematically correlated with the prospective gap between economic growth and dividend growth.  So long as I use the wrong measure of the yield in stocks I can also use the wrong g!  That rationalizes the calculation I show as the conclusion of my post. But man, is it ugly. It has the disadvantage of being supported by NO perspective. It is an ugly kludge that generates an equity premium that seems to behave roughly as we might expect.

Because of my second cent, I think you should probably use another approach to confirm or challenge the result of my crude calculation. Goldman Sachs produces a measure of the equity premium that models the dividend path directly, presumably taking account of the macro backdrop, but without reducing all that complexity to some proxy of g.  I no longer have access to that work, but if you do, I would encourage you to take a look. I think it is consistent with my take that equities are not screaming cheap here. I read that GS’s strategist is actually looking for a meaningful dip in the market, but I am not sure how much he relies on their measure of the equity premium in projecting that.

*I measure E as Shillerized operating earnings per share. But the arbitrage relation takes E conceptually, as true replicable earnings. So the awkwardness here is inherent and has nothing to do with Shillerization or choice of underling earnings series, although they are relevant on their own merits, as I tried to address in this more straightforward post.