Black Swans and Fama French data

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AzRunner
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Black Swans and Fama French data

Post by AzRunner » Sun Jan 27, 2008 7:26 pm

Having just finished Nassim Nicholas Taleb's The Black Swan I thought I'd raise one of the central points that Taleb makes in his book, namely, given the extent of Black Swans in financial markets, how can we trust any theory or hypothesis that is based on Gaussian statistics?

Thus the Fama-French three factor model based on regression analysis of the stock market since 1926, per Taleb, is useless since its whole apparatus is based on a normal distribution of returns.

One possible way that I can see that investors can still rely on the FF data is to say that the black swans are part of the data and that it is only a model, but it has explained 95% of the past data.

Of course Taleb would likely counter that history will not repeat itself and the market is far, far riskier than Gaussian statistics imply.

Thoughts?

Norm

PS: I highly recommend Taleb's book since it provides a wealth of information about risk and uncertainty.

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Post by nisiprius » Sun Jan 27, 2008 9:05 pm

I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.
--Ecclesiastes 9:11
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Post by Opponent Process » Sun Jan 27, 2008 9:52 pm

well, yes I'd agree. but I'd never try to argue against an SV tilt. I for one am extrapolating on the idea that stocks will outperform bonds. I just don't feel as sure about SV or any other box. One of those boxes will surely outperform for the next 50-100 years. might be SV, SG, LG, whatever.

it's also why I could never argue with that Hocus guy and his TIPs portfolio.

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Post by tetractys » Sun Jan 27, 2008 10:35 pm

Yes, life is a risk. On the one hand markets have behaved in a certain way that has followed the impetus of human nature. On the other hand, markets have been wiped off the map every so often.

EMH is far from proven; it's a model for investors to follow, a device, and nothing more. It contains no reliable prediction of the future; but only demonstrates what might be expected if certain fragile conditions persist. Even so, with all Teleb's routing of this conundrum, he isn't able to improve on it.

Selah, Tet

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Post by larryswedroe » Mon Jan 28, 2008 7:53 am

the three factor model doesnt have anything to do with fat tails or normal distributions
The model says that the returns are explained by the exposure to those factors--that should be the case whether there are fat tails or not.

On similar topic Sharpe Ratios are only relevant if the returns are basically normally distributed

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Post by nisiprius » Mon Jan 28, 2008 8:34 am

Keep in mind that the normal distribution usually arises as a result of the central limit theorem. If you are observing something, and what you observe is caused by multiple factors--each of which can be treated as a separate variable and if (two big ifs)

--the contributing variables are independent of each other

--the variable you're observing is simply caused by the addition of all of those contributing variables

then the thing you're observing will have the normal distribution and all of the statistics based on them will apply.

A statistics professor once said in class that "independence" is the assumption that's almost always violated. And it has a devastating effect. You see this in analyses of accident probabilities, for example. Someone will figure that a certain industrial accident can't occur unless all four pumps fail, and the chances of any pump failing are one in a thousand, ergo the chances of all of them failing are one in a trillion. Then the accident actually happens in real life and it turns out that they all were relying on a single backup generator. Or a maintenance worker changed the oil on all four of them at the same time and used the wrong oil. Or the handles that control all four of them were right next to each other on the control panel and someone bumped all four of them at the same time with his elbow...

The additivity can be a problem, too, and it can be misleading because many things are linear over small ranges. That leads to variables that look normally distributed near the center, because everything is in the small-variation range and everything is additive or nearly so and the central limit theorem is doing its stuff, but huge departures from the normal distribution out in the tails--departures that aren't obvious when plotted because, you know, 0.001% and 0.00001% look about the same!
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Post by Robert T » Mon Jan 28, 2008 11:48 am

.
On the subject of outliers and implications for portfolio choice here are some extracts from one of Grantham’s Letters to the GMO Investment Committee titled “The Wile E. Coyote Market”. I have put my take-away message upfront. The letters are available on the GMO website (although you have to register but it is free). Hope this is useful.

On outliers:
  • The longer the time period, the more ‘normal’ the distribution (mean revision): “Exhibit 4 shows the distribution of a daily price series compared to a normal distribution. It appears oddly and interestingly to have a very large number of very small changes, more than you would expect. But the real action is with the outliers. 1987 was an 18-sigma event; the sun would have to cool down completely before you would expect to see one of those based randomly on the distribution of the other 99.9% of all days. These outliers have enormous implications for decisions such as leveraging and selling options. You take home a nice profit year after year, and over 10 years it can look ‘riskless,’ and then, bang – you’re dead. Some hedge funds have an element of this selling insurance imbedded in them, so caveat emptor. Exhibit 5 shows a distribution of yearly returns. Now we only have to deal with a measly one in 3,000 year ‘random’ event in 1931 and note that the other end is 1932 – not a complete accident and enough to materially narrow the distribution of 2-year returns, but space does not allow an extra exhibit. Exhibit 6 shows the 30-year distribution and it is now a normal distribution! From the last point we covered on mean reversion, we know that it has half the range that would have been expected from the daily volatility, but it is still a normal distribution. And one in which all the outliers have disappeared.”

    The available historical data may omit outliers experienced in other parts of the world (e.g. irreversible, permanent market loss in 1919 Russia when mean revision does not work). He suggests being more conservative than would be justified by historical data. “It must also be remembered that although all the outlier events disappeared in these 30-year holding periods in the last 80 years, the actual experience may well have been lucky for the U.S., the U.K., Denmark, and a few others. For Czarist Russia the market risk did not work out so well. Germany also took its licks both in hyperinflation in the 1920s and in World War II. We have only one flight path in history to study, and it could have been a much less successful one. The safest procedure is to take all relevant examples, not just the U.S., as a measure of future outliers. Having said that, the overwhelming majority of event risk was reduced by the passage of time and mean reversion. The U.S. recovered from the depression as if it had never occurred. Japan caught up, and Germany recaught up with Europe after the destruction of WWII. Only when irreversible, permanent loss of market value occurs (e.g., 1919 Russia), can mean reversion not work its magic. It is hard to mean revert from zero. This point, importantly I think, always argues for being more conservative than would be justified by historical data only.”
On portfolio choice:
  • He suggests adding bonds (20%) can significantly reduce short-term portfolio volatility without much cost to returns. “There are several reasons, though, for owning bonds, especially a mix of nominal and real or inflation protected bonds. An annually rebalanced 80/20 stock/bond portfolio only reduces return by 0.22% from the 100% equity portfolio if the last 80 years of data are adjusted to give a ‘modern’ 2.8% risk premium, yet it reduces short-term volatility or risk by about 20%. This is a real bargain if we allow for even a small possibility of some outlying catastrophe specific to some organization – the college burns down and the treasurer forgot to pay the insurance premium – or more likely some general equity setback of a hitherto unrecorded sort like a 20-year Japanese- type mini depression.”
Robert
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Post by daniel » Mon Jan 28, 2008 12:04 pm

Great post Robert T!
It is nice to see a well founded opinion that shows that the black swans are really more important to people that are highly leveraged or take risky bets. For a conservative, well diversified investor, time will smooth out the outliers -- unless the event is catastrophic but perhaps you will have other things to worry about in that case :-)

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Post by edge » Mon Jan 28, 2008 1:01 pm

Thanks Robert.

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AzRunner
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Post by AzRunner » Mon Jan 28, 2008 1:22 pm

Thanks for the responses. Per the Grantham information, Stay the course seems to be the message unless you do get to zero, such as Russia in 1919.

Another good take-away is to always figure that things can be worse than what the historical data suggests, a point that Taleb makes a number of times.

I am so steeped in the Diehard philosophy that it is difficult for me to change course even if that were truly the way to go. Taleb's approach may be easier to implement for someone who truly is extremely fearful of black swans and total ruin in the financial markets. That might motivate a search for a wide range of wildly speculative bets while keeping the bulk fo their portfolio in short-term treasuries.

Norm

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Post by dcarpenter » Mon Jan 28, 2008 1:35 pm

larryswedroe wrote:the three factor model doesn't have anything to do with fat tails or normal distributions
The model says that the returns are explained by the exposure to those factors--that should be the case whether there are fat tails or not.

On similar topic Sharpe Ratios are only relevant if the returns are basically normally distributed
I had understood Fama and French's work to be an extension, if you will, of modern portfolio theory. Taleb's book is explicitly a repudiation of MPT. He says that without returns that are normally-distributed you no longer have MPT. If Taleb is correct in what he says, then MPT is seriously flawed to say the least; so how might that affect investing approaches based on Fama-French? In a Talebian world, where as Bill Bernstein (I think,) said, diversification fails you when you need it the most, what then?

Not that I can see any application for Taleb's conclusions! Much less accept them uncritically. As far as I could tell he has nothing usable at all to offer in MPT's place. You can't fund a retirement by betting on black swans.

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cost matters

Post by Murray Boyd » Mon Jan 28, 2008 2:34 pm

nisiprius wrote:A statistics professor once said in class that "independence" is the assumption that's almost always violated.
And how! That was a great post.

For us normal investors none of it matters too much. Even if the standard deviation and correlation matrix stuff doesn't work like magic, stocks and bonds and diversification still work pretty well.

And like Jack Bogle says, you can only control costs:

http://www.vanguard.com/bogle_site/sp20060101.htm

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