Wednesday, June 09, 2010

Jeremy Grantham on Risk and Return

One of the heads of GMO, a large institutional money manager based in Boston, Jeremy Grantham, believes like I do that risk is clearly not related to returns, expected or actual. Cam Harvey, a pretty good representative of the financial academic establishment, noted on this blog that the problem was conflated by the fact that we do not see expected returns, nor expected risk, only actual returns. He was even stronger, saying "Finance theory says nothing about [risk and returns]. Our theory relates risk to "expected returns" not ex-post returns."

Now, he caught me being imprecise, so let me be clear: risk is not related to expected returns either. If, with data going back to 1927 in the US, and corporate bonds, currencies, dozens of countries, and with all that data, somehow 'expected' returns are so different than actual returns that they seem orthogonal, it's a rather strange thing. It's like saying one's investments will probably, in their lifetime, not be correlated with one's expectations. So, why waste time studying finance? If the world is that random, that diabolically unpredictable, apply the Serenity Prayer and focus on things were we can make a difference.

The notes that the absence of a robust, intuitive measure of risk that is supposedly omnipresent and important, reminds me of attempts to explain the mysterious absence of the aether in the 19th century, because this was the medium through which light and gravity traveled, it was supposedly everywhere. Like 'risk', no one could measure it, so ever more clever reasons were adduced as to why nature hides what is all around us. See this little piece on Fresnel's coefficient of aether drag, which all seems so reasonable, and uses differential equations (ie, it's science!). Fresnel was able to come up with an equation very much like special relativity, and thus matching reality, but using wrong assumptions, because a good mathematically oriented modeler can always get from assumptions to data if you give him enough time (the degrees of freedom are hidden within the functional form or algorithm). We have a glut of Fresnellian finance going on right now

Anyway, here's Grantham on risk and returns (expected&actual):

In fact, Quality stocks have outperformed the market since 1965 (when our quality data begins) ... On noticing this outperformance, embarrassingly late in my opinion, Fama and French adopted a circular argument rather typical of finance academics in the 1970 to 2000 era: the market is efficient; P/B and small cap outperform, ergo they must be risk factors. That the result in this case happens to get to the right result is luck. The real behavioral market is perfectly happy not rewarding “risk” when it feels like it, as is shown by the 70-year underperformance of high beta stocks. But this time it worked. Price-to-book, despite its low beta, is a risk factor because of its low fundamental quality and its vulnerability to failure in a depression. This is true with small cap as well. But what about “Quality?” This factor has outperformed forever. (The S&P had a High Grade Index that started in 1925 and handsomely outperformed the S&P 500 to the end of 1965 when our data starts.) Since the market is efficient, to Fama and French quality must be a risk factor! So, by protecting you in the 1929 Crash and in 2008, and by having a low beta for that matter, Quality as represented by Coca-Cola and Johnson & Johnson must be a hidden risk factor. Oh, I know: “The real world is merely an inconvenient special case!”


Unknown said...

The big question is what does Grantham mean by Quality. Is it a Zen and the Art of
Motorcycle Maintenance sort of Quality? Is it a backtested to find the winners kind of Quality? He fails to lay that out in his piece and even admits that the data can be assembled differently. Quality is an arbitrary concept that can be quickly revised. Suddenly BP isn't such a Quality company. If someone were to reverse-engineer their formula Coke wouldn't be such a Quality company. JNJ's Quality is in question as people trade down from their branded products. Whenever the investing public agrees that something is a Quality investment it's time to run the other way.

Anonymous said...

Don't French and Fama admit that they don't have a theoretical basis for equating their three factors with the stochastic discount factor? They just do so because the data say so...

Eric Falkenstein said...

Paul: he generates a pretty straightforward definition of quality, I don't know if its in there, but in other works. Basically, high earnings, low volatility.

openid: yes, but they still say it must be a risk proxy.

Will Ambrosini said...

I'm not sure why its calling me "openid".

Anyway, in the data it happens to be the case that correlations with FF factors was correlated with returns. Because this is what the SDF does in the theory, French and Fama say the factors are a risk proxy. They don't have a iron-tight theory connecting the factors to the SDF but they have decent hand waving.

By the time the three factors papers where written it was pretty clear simple CAPM didn't tell us what the heck SDF was in the data, i.e. it wasn't the market portfolio. The factors papers were NOT an attempt to bolster those old academic risk models. (BTW, isn't it Fama that wrote the paper putting the final nail in the old models' coffin?) These papers where written in an effort to get closer to identifying what, in the data, the SDF is.

While practitioners just want a good pricing model (empirical or theoretical), academics want a good story that elucidates the underlying mechanisms and match the data. The SDF/risk models do the former but are weak on the latter. The three factors do a good job at pricing, but we're not exactly sure why.

The aether was superseded by a better story of the mechanisms of gravity and light. (BTW, you don't think special relativity requires assumptions?) Similarly, if we're going to replace risk as a story about pricing assets, it has to be with a theory not with empirical regularities found in the data.

(I've been a lurker for a while and I just want to add this observation...) Your ideas on relative returns are not an alternative to the risk story, they are a novel measure of risk. You spend a lot of effort fighting the ideas of academics, but a slight change in your rhetoric puts them in your camp. Academics would be very open to a measure of risk that is better grounded than the three factors, say, and still able to do a good job pricing.

Eric Falkenstein said...

Will: well, I'm saying risk, as I define it and think it is perceived, is not priced, and my ssrn paper goes over why this is true in an equilibrium (it can be derived via arbitrage or utility theory). Risk still exists, as anything deviating from the broadly diversified 'consensus' portfolio, but it's like idiosyncratic risk in standard theory, diversifiable, so unpriced. I actually tried to get this published, but was given all sorts of contradictory criticism, like being wrong and obvious, or without any empirical support (my SSRN paper mention about 20 risk-return lacunas), one said what I was saying was 'like saying the earth was flat' (absurd, I think he was implying); or saying great but use this new conception of risk to show how those taking more risk get higher returns (which was exactly not my point). So, I stopped trying to resubmit elsewhere (no one asked for a revision).

Will said...

Thanks for your reply. I'm not able to download your paper for some reason... but from browsing your videos, you often define risk as correlation with the market portfolio. This measure of risk hasn't been "in" for quite a while. At other times you make reference to "intuitive" measures of risk (e.g. small business people have risky returns). I don't have to tell you how dissatisfying this measure of risk is.

Academics are looking for a better measure of risk (i.e. the object in data that coresponds to the SDF in theory). This is because they are satisfied with their abstract pricing theory as it is intuitive and because it uses so few assumptions (i.e. just that people can form expectations and they can contemplate small changes to their portfolio). These two facts, I'm wagering, explain all the feedback you got from the reviewers where the variation in feedback depends on which fact the reviewer thinks is more important.

Eric Falkenstein said...

Well, seeing part of my videos can be confusing, because when I critique the standard model, I mean 'risk' to mean what various people mean by 'risk', and I don't parenthetically say 'false' every time before I say risk. So, for Markowitz it was correlation with the market, for Roll it was 'the market including lots of important stuff we can't measure', for Cox-Ingersoll-Ross it's the difference in our marginal utility, basically, the SDF, for APT, it's various manifestations ofthe SDF via the SMB and HML factors. If you caught a page or two, I might have been discussing these various conceptions of 'risk', each of which I think aren't meaningful, but useful for expository purposes.

I agree the standard model makes sense, a nice try, it's just wrong, because it doesn't explain anything, and lots of other information say a utility function that is independent of status is inferior to one that centralizes status.

Anonymous said...

People in 2000 perceived tech stocks to be low risk and got low (negative) returns. In late 2008 financials were considered risky, they produced high returns. (Now let's talk about US treasuries today ...)
Just anecdotal observations, of course.

Dave Pinsen said...

Interesting post. Without the aether, science was left with action at a distance, which remains a metaphysical puzzle, no?

Re, quality, and risk and stock performance, Piotroski's F-Score research would seem to support you and Grantham.

paul b said...

Eric, you sight anecdotal evidence that “risk” is not rewarded. I sight anecdotal evidence that effectively no one can beat the market as strong evidence that the CAPM holds. The argument is simple. Assuming people want to maximize wealth over any period, if you have a better portfolio (including trading strategies) people will tend to hold that portfolio until it becomes the market portfolio.

Given your theory of asset pricing what portfolio would you hold and why?

p.s. I really liked you post on Arthur Brooks on happiness. That’s why I read you blog everyday.

Huskercr said...


Is the "rejected paper" you mentioned a few comments ago available somewhere? Thanks.

vonjd said...

@Eric: What do you think about the so called "volatility risk premium" in options or volatility products like variance swaps?

walt said...

Your wrote: "...a good mathematically oriented modeler can always get from assumptions to data if you give him enough time (the degrees of freedom are hidden within the functional form or algorithm)."

Here is an absurd example: