Friday thoughts on risk

I have no real idea whether yesterday’s attempt to get all serious was a success, but it got more comments than anything else, and I’m all out of stupid economics ideas, so here’s another seriously held opinion of mine. Apologies for the fact that the following will be incomprehensible to all but three people in the world, all of whom have already heard it from me already:

The “equity risk premium” is worse than useless as a measure of anything at all.

(Quick primer to bring the dunces at the back of the class up to speed: the “equity risk premium” is the number which you occasionally hear talking heads spout on CNBC or such like to explain why the market’s through the floor/roof this year. It became popular about the time that the “Price/Earnings ratio” went out of fashion because it made the fatal error of telling people that stocks were overvalued when they were. Here’s an article going over the territory. You might note that the ERP is often calculated as the difference between the “earnings yield” on equities and the yield on government bonds. Smart readers will notice that the earnings yield is the reciprocal of the PE ratio, and that in effect, the new more scientific Equity Risk Premium is a linear transformation of the old, unscientific PE ratio which it was meant to replace. Nobody who has any familiarity with economics will be remotely surprised that this didn’t ring any bells at all.)

The interesting thing about the Equity Risk Premium is that, in its analytically rigorous form, it has nothing to do with equities and very little to do with risk. Let me explain:

It’s nothing to do with equities. The way that people describe the ERP is that they characterise it as the premium that people demand to hold a risky investment, as opposed to a risk-free one. Which would be fine, except that they then go on to estimate it as the difference in yield between a share of common stock and the yield on a ten year government bond. And this carries the implication that ten year government bonds are a risk free investment. Which they aren’t. Check out this chart. If you got in and out of ten year government bonds at the wrong time, you could have been absolutely carried out. Ten year government bonds are only a risk free investment if your holding period is precisely ten years (remember this point because I come back to it below). In actual fact, there is a risk premium embedded in the return on every security except cash.

It’s nothing very straightforward to do with risk. The basic problem with the ERP is that it’s a classic business school kludge. It’s derived from the Capital Asset Pricing Model, an extremely elegant application of quadratic programming to the problem of optimising a portfolio of risky securities over a fixed time period. That’s the problem with the CAPM; it’s intrinsically a two-period model and most of the simple, intuitively appealing features of the model (the ERP among them), are highly dependent on the assumption that there are only really two time periods; period 1 when you set up the portfolio and period 2 when you liquidate it and consume the proceeds. This ties in to what I mentioned above; there can only be a truly “risk free” rate in the context of a two period model, because interest rates change at all maturities from day to day.

Obviously, people have patched up the CAPM into a multi-period form, but a) the form that’s in common use and which is taught on MBA courses is the simpler version and b) the more rigorous explicitly multi-period model is a lot more ambiguous in a lot of its interpretation. For a start, it doesn’t deliver a single, unambiguous ERP in the way that we would want it to; the premium at any given time is dependent on investors’ expectations about their future consumption and investment plans. When you couch it in this way; that the ERP is what investors want because they don’t want to be caught with their money tied up in securities when they might want to consume it, then what you get, IMO, looks less like a “risk premium” and a lot more like Keynes’ (very ill-understood) concept of a “liquidity preference”.

But in any case, what is the big deal with the Equity Risk Premium anyway? As I mentioned above, in most empirical applications, it’s either a linear transform of the PE ratio, or it’s a pure piece of historical reportage; what equities earned in history treated as if it were a good estimate of what was expected ex ante when everyone knows that it wasn’t. Or to put it another way, since the demise through neglect of the Diamond-Water Paradox, economists haven’t really concerned themselves so much with the “true value” of anything in goods markets, so why do they seem to be so god damned hung up about the Equity Risk Premium, which if it isn’t a purely backward looking summary, is surely an attempt to tell us what the “objective” cost of bearing risk is?

I think it’s best to answer that question by putting forward my own pet theory: there is no such thing as the “price of risk”, because there is no such entity as “risk”, defined homogeneously. There is my risk, and your risk, and they aren’t comparable, aggregative or commensurable. In fact, there isn’t even “my risk”; all there is is “my risk right now”, and there is a price of “my risk right now”, which is the price that somebody will charge me in order to convert the particular investment which I am worrying about into the only risk-free security, cash.

But hang on … isn’t “the price that somebody will charge in order to convert a security into cash” just “the sale price of that security”?

Well yes.

Basically, I’m coming round to the view that securities prices (and much else in economics) are non-ergodic. There aren’t parameters like the Equity Risk Premium which can be used to rationally price anything (NB: this isn’t to say that these are unstable parameters which change over time; that’s would be much less of a problem. Describing the system as “nonergodic” means that the parameters which could describe the evolution of the system over time don’t exist at all.) As I mention below, lots of important economic quantities can’t be measured in a non-question-begging way, and this is just one more Damned Problem; it’s very arguable that many important economic phenomena just are Damned Things that happen to be that way because they happened to get that way.

And there we have it. Because Paul Samuelson, the Grand Old Man of Economics, set it down on tablets of stone that “economics is only a science if the world is ergodic“. I personally think this was dead wrong, but lots of people (particularly, economists with physics-envy) believe him. If the world isn’t ergodic, then there isn’t much point in spending vast amounts of time and effort constructing models which rely on the assumption that it is. You have to resurrect the careers of people like Veblen and Olin who had the bad taste to make important points in plain language rather than as the conclusions of axiomatic systems. You might have to take seriously the possibility that Keynes meant what he said, rather than what Hicks and Samuelson said he said. All sorts of things become terribly difficult for those of us who have a lot of invested intellectual capital in mathematical economics as it has been taught over the last fifty years.

Which is why it’s considered to be much better for economists to continue saying things about risk, time and liquidity which are not only downright wrong and provably so, but also completely inconsistent with the claim of neoclassical economists that they don’t believe in normative value theories. After all, as with the capital controversy below, it is often psychologically easier to deal with a massive single inconsistency than with a lot of little difficulties.


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