Ronnie Shah has a new piece on low volatility investing (Residual Volatility and Average Returns, Dec 2012), and as he works for Dimensional Fund Advisors, I presume his take is consistent with that of the Dimensional management. As this would include Eugene Fama, Ken French, Robert Merton, Roger Ibbotson, Myron Scholes, and George Constantinides, I think it represents conventional academic financial wisdom about as well as any firm can.

The old guard continues to think nothing's wrong with the standard theory, a 3-factor model include a value and size proxies (ie, long high book-market/low cap, short low book-market/high cap) as well as the market (as in the traditional Capital Asset Pricing Model). The market factor does not work within equities, but 'explains' the relative premium in equity indices over bonds; the size and value factors explain, well, themselves (the size and value anomaly). That is, all factors are chosen to explain themselves! While the market factor has some theoretical justification, value and size proxy some factor we still, after about 30 years, haven't identified. That this is considered a logical, rigorous, theory highlights to me that smart people are willing to accept a lot of rationalization to keep their paradigm alive.

In any case, Shah's argument is that Low Volatility is not an anomaly because if you sort by residual volatility, among the high cap/value stocks, there's an insignificant difference between the low and high volatility stocks.

Methinks he's conveniently ignoring a lot of arguments, instead focusing on a simple statistic that, while logically correct, is rather selective. That is, minimum volatility portfolios taken

I haven't broken out a low 'residual volatility' portfolio because I think it's really total volatility that is the key, and so using residual volatility handicaps the results. Note that there's no beta premium, and so from a return perspective this doesn't hurt, and lower systematic volatility (ie, beta) is also a good thing for a portfolio.

More importantly, even if there's no low volatility premium, the fact you can generate the same return for one-third the beta, or total volatility, then anyone who believes in mean-variance optimization (as the Dimensional Star Chamber does) should love low volatility investing much more than value or small cap investing.

Lastly, just because high volatility stocks tend to be small cap, and have high spreads, does not mean they aren't good data points. It's true that you can't really arbitrage the poor returns on high volatility stocks because they are often illiquid, but note that lots of people own these stocks, and they seem strictly dominated in the sense of Rothschild and Stiglitz (Increasing Risk I, 1970). The fact you can't short them efficiently, still doesn't explain why anyone would own these as they do. Further, given their high transaction costs, the holding period should be long, and what really kills these stocks is the compounding, as their volatility is about 40%, which generates an 8% drag on geometric returns (Geometric Return=arithmetic Return-variance/2). That people buy these lottery tickets is impossible to reconcile with the model where people are maximizing a standard utility function.

This will be an example of Max Planck's dictum that science increases funeral by funeral, because these guys aren't about to give their standard model the root canal I think it deserves. As shown above, you can have meaningfully large opportunities that won't look statistically significant for 50 years, so, if you have a strong prior, there's no logical reason you have to give it up in this life.

The old guard continues to think nothing's wrong with the standard theory, a 3-factor model include a value and size proxies (ie, long high book-market/low cap, short low book-market/high cap) as well as the market (as in the traditional Capital Asset Pricing Model). The market factor does not work within equities, but 'explains' the relative premium in equity indices over bonds; the size and value factors explain, well, themselves (the size and value anomaly). That is, all factors are chosen to explain themselves! While the market factor has some theoretical justification, value and size proxy some factor we still, after about 30 years, haven't identified. That this is considered a logical, rigorous, theory highlights to me that smart people are willing to accept a lot of rationalization to keep their paradigm alive.

In any case, Shah's argument is that Low Volatility is not an anomaly because if you sort by residual volatility, among the high cap/value stocks, there's an insignificant difference between the low and high volatility stocks.

Methinks he's conveniently ignoring a lot of arguments, instead focusing on a simple statistic that, while logically correct, is rather selective. That is, minimum volatility portfolios taken

*within*the SP500, since 1998, generate a large 3.9% difference in annual returns with the SP500 (this is just multiplying the monthly returns by 12). Look at the results below (data are from here). That's statistically insignificant, however, given standard t-stats, and if things continue, will become significant around 2050. Such is the nature of financial time series.I haven't broken out a low 'residual volatility' portfolio because I think it's really total volatility that is the key, and so using residual volatility handicaps the results. Note that there's no beta premium, and so from a return perspective this doesn't hurt, and lower systematic volatility (ie, beta) is also a good thing for a portfolio.

More importantly, even if there's no low volatility premium, the fact you can generate the same return for one-third the beta, or total volatility, then anyone who believes in mean-variance optimization (as the Dimensional Star Chamber does) should love low volatility investing much more than value or small cap investing.

Lastly, just because high volatility stocks tend to be small cap, and have high spreads, does not mean they aren't good data points. It's true that you can't really arbitrage the poor returns on high volatility stocks because they are often illiquid, but note that lots of people own these stocks, and they seem strictly dominated in the sense of Rothschild and Stiglitz (Increasing Risk I, 1970). The fact you can't short them efficiently, still doesn't explain why anyone would own these as they do. Further, given their high transaction costs, the holding period should be long, and what really kills these stocks is the compounding, as their volatility is about 40%, which generates an 8% drag on geometric returns (Geometric Return=arithmetic Return-variance/2). That people buy these lottery tickets is impossible to reconcile with the model where people are maximizing a standard utility function.

This will be an example of Max Planck's dictum that science increases funeral by funeral, because these guys aren't about to give their standard model the root canal I think it deserves. As shown above, you can have meaningfully large opportunities that won't look statistically significant for 50 years, so, if you have a strong prior, there's no logical reason you have to give it up in this life.

## 5 comments:

Some observations about bank regulations in the conclusion of this new Atlantic article:

http://www.theatlantic.com/magazine/archive/2013/01/whats-inside-americas-banks/309196/

relevant to EF’s 12/30 post.

Falkster, the last thing these people want to admit is that their "theory" has amounted to little more than a 50 year mathturbatory yank fest. Too much prestige on the line to fully correct this massive whopper anytime soon. And when it is corrected, it will require full extraction - not a root canal.

It's a another case of identifying the assumptions you have to accept for your models to work, then ignoring the fact that those assumptions aren't being met. With MVO it's normal distributions/quad utility/stable inputs, With option pricing, it's constant variance, with CAPM,it's IID. Economists love equilibrium models, but the real world doesn't cooperate.

Agreed, but that's no excuse for the improper use of "begs the question"

http://begthequestion.info/

I'm a laissez-faire linguist content to accept some vernacular misconceptions, though I draw the line at "irregardless."

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