This is really Daniel’s department, but I’ve been waiting for Samuel Brittan to update his website with his review of John Allen Paulos’s A Mathematician Plays the Market for a while, and he’s finally done it. The most bloggable point is borrowed — I think — from Taleb’s Fooled by Randomness
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.
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.
I’m sorry that should be “standard deviation” not distribution.
select only those brokers who are at least 1 standard [deviation] above the mean, … 10 years in a row
Do such creatures exist?
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.
Do such creatures exist?
Warren Buffet?
Besides, my post was purely theoretical.
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.
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…
“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.
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.
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.
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.
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.
“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?
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.
“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.
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.
À Gauche
Jeremy Alder
Amaravati
Anggarrgoon
Audhumlan Conspiracy
H.E. Baber
Philip Blosser
Paul Broderick
Matt Brown
Diana Buccafurni
Brandon Butler
Keith Burgess-Jackson
Certain Doubts
David Chalmers
Noam Chomsky
The Conservative Philosopher
Desert Landscapes
Denis Dutton
David Efird
Karl Elliott
David Estlund
Experimental Philosophy
Fake Barn County
Kai von Fintel
Russell Arben Fox
Garden of Forking Paths
Roger Gathman
Michael Green
Scott Hagaman
Helen Habermann
David Hildebrand
John Holbo
Christopher Grau
Jonathan Ichikawa
Tom Irish
Michelle Jenkins
Adam Kotsko
Barry Lam
Language Hat
Language Log
Christian Lee
Brian Leiter
Stephen Lenhart
Clayton Littlejohn
Roderick T. Long
Joshua Macy
Mad Grad
Jonathan Martin
Matthew McGrattan
Marc Moffett
Geoffrey Nunberg
Orange Philosophy
Philosophy Carnival
Philosophy, et cetera
Philosophy of Art
Douglas Portmore
Philosophy from the 617 (moribund)
Jeremy Pierce
Punishment Theory
Geoff Pynn
Timothy Quigley (moribund?)
Conor Roddy
Sappho's Breathing
Anders Schoubye
Wolfgang Schwartz
Scribo
Michael Sevel
Tom Stoneham (moribund)
Adam Swenson
Peter Suber
Eddie Thomas
Joe Ulatowski
Bruce Umbaugh
What is the name ...
Matt Weiner
Will Wilkinson
Jessica Wilson
Young Hegelian
Richard Zach
Psychology
Donyell Coleman
Deborah Frisch
Milt Rosenberg
Tom Stafford
Law
Ann Althouse
Stephen Bainbridge
Jack Balkin
Douglass A. Berman
Francesca Bignami
BlunkettWatch
Jack Bogdanski
Paul L. Caron
Conglomerate
Jeff Cooper
Disability Law
Displacement of Concepts
Wayne Eastman
Eric Fink
Victor Fleischer (on hiatus)
Peter Friedman
Michael Froomkin
Bernard Hibbitts
Walter Hutchens
InstaPundit
Andis Kaulins
Lawmeme
Edward Lee
Karl-Friedrich Lenz
Larry Lessig
Mirror of Justice
Eric Muller
Nathan Oman
Opinio Juris
John Palfrey
Ken Parish
Punishment Theory
Larry Ribstein
The Right Coast
D. Gordon Smith
Lawrence Solum
Peter Tillers
Transatlantic Assembly
Lawrence Velvel
David Wagner
Kim Weatherall
Yale Constitution Society
Tun Yin
History
Blogenspiel
Timothy Burke
Rebunk
Naomi Chana
Chapati Mystery
Cliopatria
Juan Cole
Cranky Professor
Greg Daly
James Davila
Sherman Dorn
Michael Drout
Frog in a Well
Frogs and Ravens
Early Modern Notes
Evan Garcia
George Mason History bloggers
Ghost in the Machine
Rebecca Goetz
Invisible Adjunct (inactive)
Jason Kuznicki
Konrad Mitchell Lawson
Danny Loss
Liberty and Power
Danny Loss
Ether MacAllum Stewart
Pam Mack
Heather Mathews
James Meadway
Medieval Studies
H.D. Miller
Caleb McDaniel
Marc Mulholland
Received Ideas
Renaissance Weblog
Nathaniel Robinson
Jacob Remes (moribund?)
Christopher Sheil
Red Ted
Time Travelling Is Easy
Brian Ulrich
Shana Worthen
Computers/media/communication
Lauren Andreacchi (moribund)
Eric Behrens
Joseph Bosco
Danah Boyd
David Brake
Collin Brooke
Maximilian Dornseif (moribund)
Jeff Erickson
Ed Felten
Lance Fortnow
Louise Ferguson
Anne Galloway
Jason Gallo
Josh Greenberg
Alex Halavais
Sariel Har-Peled
Tracy Kennedy
Tim Lambert
Liz Lawley
Michael O'Foghlu
Jose Luis Orihuela (moribund)
Alex Pang
Sebastian Paquet
Fernando Pereira
Pink Bunny of Battle
Ranting Professors
Jay Rosen
Ken Rufo
Douglas Rushkoff
Vika Safrin
Rob Schaap (Blogorrhoea)
Frank Schaap
Robert A. Stewart
Suresh Venkatasubramanian
Ray Trygstad
Jill Walker
Phil Windley
Siva Vaidahyanathan
Anthropology
Kerim Friedman
Alex Golub
Martijn de Koning
Nicholas Packwood
Geography
Stentor Danielson
Benjamin Heumann
Scott Whitlock
Education
Edward Bilodeau
Jenny D.
Richard Kahn
Progressive Teachers
Kelvin Thompson (defunct?)
Mark Byron
Business administration
Michael Watkins (moribund)
Literature, language, culture
Mike Arnzen
Brandon Barr
Michael Berube
The Blogora
Colin Brayton
John Bruce
Miriam Burstein
Chris Cagle
Jean Chu
Hans Coppens
Tyler Curtain
Cultural Revolution
Terry Dean
Joseph Duemer
Flaschenpost
Kathleen Fitzpatrick
Jonathan Goodwin
Rachael Groner
Alison Hale
Household Opera
Dennis Jerz
Jason Jones
Miriam Jones
Matthew Kirschenbaum
Steven Krause
Lilliputian Lilith
Catherine Liu
John Lovas
Gerald Lucas
Making Contact
Barry Mauer
Erin O'Connor
Print Culture
Clancy Ratcliff
Matthias Rip
A.G. Rud
Amardeep Singh
Steve Shaviro
Thanks ... Zombie
Vera Tobin
Chuck Tryon
University Diaries
Classics
Michael Hendry
David Meadows
Religion
AKM Adam
Ryan Overbey
Telford Work (moribund)
Library Science
Norma Bruce
Music
Kyle Gann
ionarts
Tim Rutherford-Johnson
Greg Sandow
Scott Spiegelberg
Biology/Medicine
Pradeep Atluri
Bloviator
Anthony Cox
Susan Ferrari (moribund)
Amy Greenwood
La Di Da
John M. Lynch
Charles Murtaugh (moribund)
Paul Z. Myers
Respectful of Otters
Josh Rosenau
Universal Acid
Amity Wilczek (moribund)
Theodore Wong (moribund)
Physics/Applied Physics
Trish Amuntrud
Sean Carroll
Jacques Distler
Stephen Hsu
Irascible Professor
Andrew Jaffe
Michael Nielsen
Chad Orzel
String Coffee Table
Math/Statistics
Dead Parrots
Andrew Gelman
Christopher Genovese
Moment, Linger on
Jason Rosenhouse
Vlorbik
Peter Woit
Complex Systems
Petter Holme
Luis Rocha
Cosma Shalizi
Bill Tozier
Chemistry
"Keneth Miles"
Engineering
Zack Amjal
Chris Hall
University Administration
Frank Admissions (moribund?)
Architecture/Urban development
City Comforts (urban planning)
Unfolio
Panchromatica
Earth Sciences
Our Take
Who Knows?
Bitch Ph.D.
Just Tenured
Playing School
Professor Goose
This Academic Life
Other sources of information
Arts and Letters Daily
Boston Review
Imprints
Political Theory Daily Review
Science and Technology Daily Review