Posts filed under “Mathematics”

Reports of the death of mean reversion are premature

James Montier is a member of GMO’s asset allocation team. Prior to joining GMO in 2009, he was co-head of Global Strategy at Société Générale. Mr. Montier is the author of several books including Behavioural Investing: A Practitioner’s Guide to Applying Behavioural Finance; as well as Value Investing: Tools and Techniques for Intelligent Investment; and The Little Book of Behavioural Investing.

In between longer think pieces for GMO, James publishes at Behavioral Investing, which he describes as the “application of psychology to finance and the home of an investing skeptic.”



Note: This was originally written for the FT, but they seem to have gone the same way as so much media and are dumbed down these days – they said it was too technical (after sitting on it for more than a week).


Reports of the death of mean reversion are premature

In a recent article [1] Richard Clarida and Mohamed El-Erian of PIMCO argued that the ‘New Normal’ offered at least five implications for portfolio management.

I. Investing based on mean reversion will be less compelling

II. Risk on/risk off fluctuations in sentiment will continue

III. Tail hedging becomes more important

IV. Historical benchmarks and correlations will be challenged

V. Less credit will be available to sustain leverage and high valuations

Implications IV and V seem pretty reasonable to me. However, reports of the death of mean reversion are premature. I fear that the authors are confusing the distribution of economic outcomes with the distribution of asset market returns. The distribution of economic outcomes may well turn out to be flatter, with fatter tails than we have previously experienced.

However, asset markets have long suffered such a distribution; it has proved no impediment to mean reversion based strategies. In fact, the fat tails of the asset market have provided the best opportunities for mean reversion strategies. For instance, in equity markets the fat tails associated with unpleasant outcomes (poor returns) have generally occurred as high (sometimes ludicrously high) valuations have returned towards their ‘normal’ level, and the fat tails which we all love (good returns) have occurred as low valuations have moved back towards more ‘normal’ levels.

As long as markets continue to follow the second implication (as they have done since time immemorial) and flip flop between irrational exuberance and the depths of despair, then mean reversion (at least in valuations) is likely to remain the best strategy for long-term investors. (This also highlights the apparently contradictory nature of the first two implications that the authors point out). We don’t require long periods of time at equilibrium for mean reversion strategies to work, rather (and considerably less onerously) we simply require markets to pass through the equilibrium periodically.

As always, investors need to be mindful of the context of their investment decisions. It is always possible that we are standing on the brink of a shift in the level to which asset valuations mean revert. But that has always been the case. Only careful thought and research can work to try to mitigate the dangers posed by this threat. After all, if investing were both simple and easy, everyone would be doing it.

The third implication that tail risk hedging will become more important is and always has been true (much like the second implication). The prudent investor should always pay attention to tail risk – the new normal doesn’t alter that.

Ever eager to please, the ‘engineers of innovation’ (or should that be the ‘architects of destruction’?) are happily creating products to serve the new bull market in tail risk. Deutsche Bank is launching a long equity volatility index, while Citi has come up with a tradeable crisis index (mixing equity and bond vols, swap spreads and structured credit spreads). Strangely enough, Bloomberg reports that PIMCO is planning a fund that will protect investors in the event of a decline greater than 15%. Even the CBOE is planning a new index based on the skew in the S&P 500.

However, any consideration of the purchase of insurance should not be divorced from a discussion of the price of the insurance. Cheap insurance is wonderful, and clearly benefits portfolios in terms of robustness. However, the key word is that the insurance must be cheap (or at very worst fair value). Buying expensive insurance is a waste of time. I used to live in Tokyo and was constantly amazed that the day after an earth tremor the cost of earthquake insurance would soar, as would the demand!

You should really only want insurance when it is cheap, as this is the time when no one else wants it, and (perversely) the events are most likely. Buying expensive insurance is just like buying any other overpriced asset … a path to the permanent impairment of capital. Rather than wasting money on expensive insurance, holding a larger cash balance makes sense. It preserves your dry powder for times when you want to deploy capital, and limits the downside.

So buy insurance when it’s cheap. When it isn’t and you are worried about the downside, hold cash. As Buffett said, holding cash is painful, but not as painful as doing something stupid!

In summary, the new normal may pose some issues for investors who have never bothered to study history (which is, of course, littered with many, many ‘new normals’). However, for those with perspective, prudence, patience and process, many of the same ‘eternal’ rules are likely to govern the game as they always have, come rain or shine. In essence, many of the implications are less the new normal, and more the old always!

[1] Uncertainty changing investment landscape, Market Insight, 2 August 2010

Category: Investing, Mathematics, Valuation

Tax Cut Changes

chart courtesy of CNN/Money > This chart is pretty stark in terms of who gets hit the hardest in the expiration of the Bush Tax cuts. But this comparisons isn’t all that informative — how many of each of these taxpayers are there? What is the total amount of tax dollars collected in each grouping?…Read More

Category: Mathematics, Taxes and Policy

Mandelbox Zoom

This will blow your minds Mandelbox Zoom from hömpörgő on Vimeo music: Dajuin Yao -­ Satisfactio­n of Oscilla­tion hat tip boingboing

Category: Mathematics, Weekend

Skill vs Luck

Legg Mason’s Michael Maubossin looks at the difficulties in untangling outcomes that are based on skill or luck or both as applied to the universe of investing. His conclusions? • The outcomes for most activities combine skill and luck. • Separating skill and luck encourages better thinking about outcomes and allows for sharply improved decision…Read More

Category: Investing, Mathematics

Presidential Stock Picks

There is a BusinessWeek article that notes “Shares of companies whose CEOs dine with Obama outdo the S&P.” I have a quote in that I would like to clarify: “Just a coincidence? Only partly, says Barry Ritholtz, CEO of equity research firm Fusion IQ. Losers don’t get asked to hang out with the President, he…Read More

Category: Mathematics, Really, really bad calls, Trading

“Saving” Social Security

“There is no trick. We can’t promise to work less, raise pensions and erase deficits.” -French Labor Minister Eric Woerth > The issue of government debt seems to be coming up a lot news lately. Courtesy of the credit collapse and economic recession, Deficits are front page news. Classic balance budget advocates are reiterating their…Read More

Category: Mathematics, Politics, Taxes and Policy

Mathematicians – Not Economists – Should Run the Fed

“A number of folks are expressing growing concern about potential overbuilding and worrisome speculation in the real estate markets, especially in Florida . . . Entire condo projects and upscale residential lots are being pre-sold before any construction, with buyers freely admitting that they have no intention of occupying the units or building on the…Read More

Category: Federal Reserve, Mathematics

Tax Burden on Various Americans

David Leonhardt has two good tax related pieces (an article, and a blog post) that shed some light on who pays how much taxes in the US. The full article, Yes, 47% of Households Owe No Taxes. Look Closer., is noteworthy for this truism about the tax burden.  It is rather informative: “There is no…Read More

Category: Mathematics, Taxes and Policy

Government’s Share of Economy, 1950 to 2075

Peter Boockvar dug up these fascinating charts from this CBO report from 2002.

What really surprised me is how consistent the US economy has been for most the latter half of the 20th century: About 20% of GDP. It starts about 19%, peaks at about 23% then falls back to about 18 and a half%.

Note that this data is before the Bush’s Prescription Drug Act or Obama’s Health Care bill.

Federal Outlays, 1962 to 2001

(As a percentage of GDP)


Charts via CBO, Perot Charts

More charts after the jump . . .

Read More

Category: Economy, Mathematics

Long Term Growth in US Labor Force

Despite my association with the Bear camp, and my belief that we are most likely in a long term secular bear market, I actually am an optimistic guy. The future is never as dire looking as the survivalists make it out to be. Even though I know the cyclical bull rally within the longer bear…Read More

Category: Economy, Mathematics