# Investment and luck

by on January 27, 2004

This is really Daniel’s department, but I’ve been waiting for Samuel Brittan to update his website with “his review”:http://www.samuelbrittan.co.uk/text173_p.html of John Allen Paulos’s “A Mathematician Plays the Market”:http://www.amazon.com/exec/obidos/ASIN/0465054803/junius-20 for a while, and he’s finally done it. The most bloggable point is borrowed — I think — from Taleb’s “Fooled by Randomness”:http://www.amazon.com/exec/obidos/ASIN/1587991845/junius-20

bq. In financial discussions you often hear how about Ms.X or Mr.Y who has had a consistently good record in beating the market indices. Paulos shows how such “successful” analysts can emerge purely by chance. Of 1,000 analysts, roughly 500 might be expected to outperform the market next year. Of these another 250 might be expected to do so well for a second year and 125 in the third. Continuing the series we might expect to find one analyst who does well for ten consecutive years by chance alone. But will she do better in the 11th year? Your guess is as good as mine.

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WillieStyle 01.27.04 at 4:58 pm

Doesn’t this just mean that you shouldn’t use a simplistic binary criterion to judge performance, lumping those who outperformed the market by 0.00001% with those who outperformed the market by 25%?

If you assume that broker performance will exhibit a normal distribution and select only those brokers who are atleast 1 standard distribution above the mean, then the odds of having a succsessful broker 10 years in a row simply by chance is
1 in 90,949,470 or there abouts.

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WillieStyle 01.27.04 at 5:00 pm

I’m sorry that should be “standard deviation” not distribution.

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Chris Bertram 01.27.04 at 5:06 pm

_select only those brokers who are at least 1 standard [deviation] above the mean, … 10 years in a row_

Do such creatures exist?

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wcw 01.27.04 at 5:08 pm

yes, luck. luck is also the major contributor to success in other fields of human endeavor. that said, you pretty much have to believe that investment skill exists. otherwise, markets are meaningless except as an internally consistent mechanism to eliminate arbitrage.

the tricky-if-not-impossible task is determining which outperformers actually have skill. simplistic market simulations almost always show luck swamping skill.

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WillieStyle 01.27.04 at 5:10 pm

Do such creatures exist?

Warren Buffet?
Besides, my post was purely theoretical.

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Matt 01.27.04 at 5:22 pm

Of course, better-than-average performance of any particular investor may just be random walking– but if there is a non-random component to investment (and you need to estimate the probability of that) then it makes some sense to find a good performer and try to do something similar.

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Matthew2 01.27.04 at 5:47 pm

It’s the reverse of that old scam (at least in the literature, I’ve not heard of it in real life) where the con-artist sends out 1000 letters to people telling them who will win tonight’s big football game, 500 team A and 500 team B. Then say team A wins; for next week’s big game he sends out 500 letters to those to whom he’d sent a letter saying team A would win, this time with 250 letters saying team C will win and 250 saying team D will win. And so on, until about 8 lucky recipients have received 7 letters each correctly telling them who would win that night’s big game. This time around you ask for money to continue your brilliant forecasting record…

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Odd Ray of Hope 01.27.04 at 6:07 pm

“you pretty much have to believe that investment skill exists. otherwise, markets are meaningless except as an internally consistent mechanism to eliminate arbitrage”

Financial markets can be efficient by properly pricing assets in light of available information and investor appetites, so the amount of forecasting skill available might not be related to efficiency.

Index funds allow us all to avoid the trickiness (and fees) of separating luck from skill.

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wcw 01.27.04 at 6:43 pm

efficiency can exist in the complete absence of investment skill; all that is required for efficiency is internal consistency and rapid communication. it is meaningful pricing that cannot exist if there is no such thing as skill. indexing, by ascribing utility to market prices, implicitly recognizes that investment skill exists.

it’s been a while since I looked into this, but a few years back an NBER working paper did a clever backwards look at what assumptions it would take to have zero investment in active management. hold on, let me Google..

here:
http://ideas.repec.org/p/nbr/nberwo/7069.html
“To justify such a zero-investment strategy, we find that a mean-variance investor would need to believe that less than 1 out of every 100,000 managers has an expected alpha greater than 25 basis points per month.”

now, 25 bp/mo outperformance is huge, and I am ready to believe that fewer than one in 10^5 investors has the latent potential to relize it. seems clear by the amount of active management that exists in the world that “the market” in this case believes otherwise.

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harry 01.27.04 at 6:45 pm

Not quite, since you can’t invest directly in an index, so fund managers use proxies (to minimise transaction costs). So even index funds vary around the performance of the index.

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Mike Kozlowski 01.27.04 at 7:06 pm

It should be fairly easy (given appropriate data) to determine if those long-term overperformers are beneficiaries of luck or skill. Given a 20-year period of data, look at the first ten years, and identify the consistent overperformers. Now compare the performance of that group versus the general market over the next ten years. If their performance was due to a string of luck, there’s no reason to expect that luck to continue for the next decade, so they should track the general market; if their performance was due to skill, they’ll continue to outperform in that second decade.

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Mats 01.27.04 at 8:10 pm

Thanks matthew2, I hadn’t seen that one, think it’s a brilliant illustration to Taleb’s point.

Then I think Taleb’s point actually has been discussed quite a lot in theoretical litterature – will a competitive market be efficient enough in identifying and sorting out the bad traders? If not, it won’t of course be much efficient in other ways either.

I think I saw an article a couple of years ago in Econometrica discussing this. The dominating idea then was (as I read it) that market mechanisms were to weak to separate skill from luck, leaving too good opportunities to dismal agents (traders) for the economy to root out (by selection) inefficiencies.

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Andrew Boucher 01.28.04 at 12:24 pm

“It should be fairly easy (given appropriate data) to determine if those long-term overperformers are beneficiaries of luck or skill. Given a 20-year period of data, look at the first ten years, and identify the consistent overperformers. ”

This of course isn’t necessarily true. What’s true of 10 years can also be true of 20. (Unless there’s something magical about 10-20 which you haven’t made clear, repeat your argument for 5-10.)

There can of course be trends even in long periods. There was roughly a 20-year bull market in the U.S. from the 1980s to 2000. So take the case of Goldman Sachs’ Abby Cohen, who was taken as a genius during this time because she would repeat, “Buy stocks.” Was her one-note luck or was it skill?

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dsquared 01.28.04 at 1:01 pm

I think that the point I’d make in response to this is that an individual analyst usually covers between 5 and 10 stocks, and analysts are typically assessed over periods of time much shorter than a year. If someone really did have a consistent track record of not making a bad call in ten years by pure chance, I think it would be way out in the tail of the distribution.

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Andrew Boucher 01.28.04 at 2:38 pm

“I think that the point I’d make in response to this is that an individual analyst usually covers between 5 and 10 stocks, and analysts are typically assessed over periods of time much shorter than a year. If someone really did have a consistent track record of not making a bad call in ten years by pure chance, I think it would be way out in the tail of the distribution.”

Show me *one* analyst who has not made a “bad” call over ten years covering 5 to 10 stocks.

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dsquared 01.28.04 at 3:43 pm

Yeh I know. The point I was sort of trying to make is that Paulos’ example very much depends on the low power of statistical tests and the likelihood of Type 2 errors when trying to find people who can pick stocks. In actual fact, there’s a lot more data to go on and I’d expect that it would be possible to find robust evidence that some people can pick stocks.

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