10 ms·

An overlooked statistical concept shows why it’s so hard to beat a benchmark

79 points by bookbild 10y ago

beezle 10y ago
Have to call BS on this article. The same failure to beat will apply to RSP, an equal weight s&p 500 that has outperformed the traditional cap weighted index.
- DennisP 10y ago
  The article's main claim is that if you want to do well, you need to buy a large number of stocks. It used the S&P as an example but didn't claim that it was the best possible large portfolio.
tgb 10y ago
Huh this seems like a poor explanation to me. It doesn't argue that active investment will be worse than index over the long run, just that it will be worse most of the time in the short run. But I'm not investing in the short run, so I don't really care. What does this say about their long term expected behavior? I suspect the usual argument about fees will prove more relevant over the long term.
soVeryTired 10y ago
Their argument is that most stocks are mediocre, with a handful of big winners mixed in: that means building a portfolio of hand-picked stocks is likely to underperform since it will probably miss the best stocks. But there's a symmetry argument there that the article misses. Surely I can make a portfolio that tracks the market, but excludes a handful of stocks I think are going to be lousy. Because I have most of the market in my portfolio, I'm likely to hit the big winners, and with high probability I'll ditch losers. To build on their poker chip analogy, what if there are four $10 chips, one $100 chip and I pick four chips each time instead of two?
- madcaptenor 10y ago
  But the distribution of returns isn't symmetric. With the losers, you can lose at most 100% of your investment; with the winners, you can make a lot more.
  - sten 10y ago
    That's for stocks. You can always short and potentially have no limits for your loss.
- notahacker 10y ago
  This assumes your judgement on which stocks you think are going to be lousy is better than the market's overall. There might be rare occasions when that's justified (that company had major organizational issues when you worked there last month that aren't widely known, your technical knowledge means you know that hyped product probably doesn't work). But the rest of the time, you're just as likely to lose money overestimating how lousy the stock is as gain it. The $100 chip might well be the one you (and many other stock pickers) think is trending downwards until it pulls off that unexpected achievement. That said, you're right that excluding from a portfolio is a lower volatility strategy and much safer than shorting the "lousy" stocks. If I have reason to believe $TECHSTOCK is about to have their lunch eaten by new competitors and leave it out of my portfolio I slightly outperform the market if I'm right, and don't lose my shirt if Google buys it.
- bluGill 10y ago
  the problem is there are 4 $10 chips, 1 $100 chip, and 3 $-50 chips. Pick a $-50 chip and you are negative - note that in this market most chips will make you money, the total loses - I just picked my numbers at random. Now a good manager should be able to look at the signs: most companies that will lose money have plenty of warnings in their various (10k, 8q or whatever) reports, not to mention you can look at an industry and see trends that hit the bottom line. Should is key: many managers fail at this. However becareful when rating failures: the best managers long term have many years of below average performance - not just below market, below their peers are ultimately are not good. The best returns are from seeing a company that is doing bad now, but is going to turn things around in a few years (if you are a large enough you can even force this: buy enough of a company that you can change management). However this often means seeing that a turn around will happen sometimes in the next 5 years and waiting our 3 years of bad returns (and looking really bad!) before it happens. I cannot tell who the best managers are, except in hindsight though.
rodionos 10y ago
> equity benchmarks are so reliant on gigantic gains in just a handful of stocks that missing them Perhaps we're witnessing a shift towards an industrial model where a small number of players control disproportionate amounts of value added in their respective industries. I'd be interested to see historical data for Herfindahl indices for key verticals in the U.S., and globally.
peterbonney 10y ago
Skewness alone can't explain it, either. Imagine there are 100 stocks of equal weight in the index, and that 99 are going to underperform over the next year with only 1 outperforming. If there are 1,000,000 managers (with equal capital) each picking just 1 stock randomly to hold over that year, then yes, 99% of them will underperform the index and just 1% will outperform. But the aggregated performance of the managers will exactly match the index, minus fees. For skewness to factor into manager underperformance it must be coupled with adverse selection. I.e. it must be the case that the factors that contribute to that 1 stock outperforming are correlated with managers not wanting to own it just before it outperforms. That seems plausible, but goes against the argument that a truly random portfolio of stocks will underperform the index because of skewness (because truly random stocks are by definition not adversely selected).
- jessriedel 10y ago
  I agree with your observation that this Bloomberg writer is a knucklehead. "Number of managers beating the index" is obviously a silly metric since it matter by how much they win and lose, and an ideal random selection of stocks will obviously have the same expected value as the entire market. However, I think you (and the author) are missing a much simpler explanation for why skew is important: for fixed expectation value, variance is intrinsically bad for risk adverse investors. If you want to try and pick winners and losers in the stock market, you will have to become less diversified to do so. Since there are many ways to interconvert between additional expected return and risk (e.g. insurance), inducing an exchange rate between the two, there is a quantifiable cost for active management even when random. In yet other words: the cost of active management does not go to zero in the limit where the manager picks randomly and fees are ignored. Rather, as soon as you start picking you are accruing a cost through reduced diversification; you cannot come out ahead unless the size of your edge compensates for this non-zero cost.
- DennisP 10y ago
  Is it true that aggregated performance is low? Mostly I've just seen people say that the majority of managers have poor returns, without taking into account how well the best ones performed. (I agree there are plausible reasons for aggregate underperformance.)
nugget 10y ago
Active managers play a critical role in price discovery. We have traditionally had, and definitely still have, far more active managers than needed, but some number of them must survive in order to have a healthy market. Sometimes we lose sight of this in the (well-deserved) celebration of passive index investing. I'm interested in a few questions that only time will answer. First, what % of the market needs to be active rather than passive in order for healthy price discovery to occur? Is there an efficient frontier or stabilization point? Second, as passive indexes become the vast majority of public equity dollars, are there more opportunities for smart active investors to out-perform? (Given enough passive indexes as counterparties, it's theoretically possible for every remaining active manager to out-perform the market.) Third, in aggregate, what % of out-performance (if any) will active managers be able to take, as fees, in the future? (And what does it say about human psychology if it's >100%.)
- jessriedel 10y ago
  In the ideal case, the answer to your second questions seem to be obviously "yes"; the market in active managers will hit an equilibrium where their salary is paid by the additional info they bring. However, it seems clear from the current situation that the market is far from ideal since there have been too many active managers for decades. Whatever it is that allows them to persist (human overconfidence, salesmen, principal-agent problems) has not been eliminated, even if "word has gotten out" so that investors have began to develop a partial immunity against them. Knowing exactly where the new equilibrium will be requires a detailed understanding of that mechanism, which I don't think anyone has.
- dragontamer 10y ago
  While I agree with you that price discovery is useful... the facts of the situation mean only one thing: Active investing will decline until active investing is profitable. The price of stocks is dominated by human emotions in the short term after all (ex: Enron cooked the books as early as 1996... but didn't go bankrupt till 2001). Holding onto a "short" position for 5+ years is basically unheard of, especially in the context of a Stock whose price is skyrocketing. (You probably would have been margin-called during that runup). How many people would trust their "active investment manager" avoiding a hugely successful company with huge income growth? A quickly stock price and a good dividend? http://picker.uchicago.edu/Enron/EnronAnnualReport2000.pdf http://picker.uchicago.edu/Enron/EnronAnnualReport2000.pdf The fact is: even with perfect knowledge about which companies are good and bad (Perfect 20/20 hindsight), its still incredibly difficult to make cohesive arguments for or against particular companies.
knowno 10y ago
If many portfolios are similar, which a small group of values as a best candidate to appear in those portfolios then it is likely that they are not going to hit the big performers since they are playing a lottery. The soundness of the argument relies of what percentage of different values compose the typical portfolio.
hal9000xp 10y ago
Popular theories that investing in indexes is the best possible strategy are not self-sufficient. If there were no active traders, then nobody would trade individual stocks. In this case, there would be no indexes to invest. So markets stay in permanent equilibrium where active and passive investors are balanced out. More precisely, if there were too many active traders, it would be attractive to become a passive investor since markets are very efficient. If there were too few active traders, it would be attractive to become an active investor since markets are not very efficient. Yet despite of this simple truth, I constantly hear from seemingly serious people that only index investing is worth doing (i.e. random walk theories pop up regularly in the press). Beating index should be hard because it's a competition! And everybody is not supposed to be winner.
- qntty 10y ago
  I think the more reasonable claim is that it's highly unlikely that you will beat an index fund over a (say) 40 year period, so for the average investor who is investing for retirement, it makes no sense.
- jessriedel 10y ago
  You're talking to the wrong people. The idea isn't that all investors should be index investing, the idea is that all investors without special expertise should be index investing. This is a non-trivial statement because one might think (and people often argue) that active managers with expertise can beat indices, and therefore unsophisticated investors should just hire those people. The problem with this is that unsophisticated investors can't tell the difference between active managers who have a real edge (be it special insight, better computers, bigger brains, etc.) and those who do not. Insofar as an active manager can demonstrate convincingly to an unsophisticated outsider that they have an edge, the manager will be able to capture the excess value by commanding larger fees in the marketplace for managers. This would be a fine equilibrium for wise unsophisticated investors, but unsophisticated investors are not all wise. Various human biases and market failures mean that there are an excess number of active investors (i.e., a number above the equilibrium value in an efficient market), many/most of whom are leeches. This is the state we find ourselves in today. The reason the number of active managers is decreasing is because wisdom is diffusing, but we are not done. It goes without saying that "special expertise" involves a lot more than reading financial newspapers and considering yourself a smart person. It's about as hard to be able to compete at that level as it is to compete in professional sports. The big difference is that the heavy dose of randomness involved in investing allows more people to convince themselves that they are able to compete with the big boys, when almost none of them are. (The evidence that you can't compete with LeBron James at basketball is harder to ignore.)
rdlecler1 10y ago
In short, the same principles driving VC returns are driving public market returns with the exception that amongst top teir VCs there is effectively insider information which is illegal in public markets, hence no information asymmetry to bias returns.
- Nomentatus 10y ago
  Great point - actually, what the article leaves out is that investors are always competing with vast holdings held by insiders who by definition have insider information; and most of their trades based on that insider information are perfectly legal (inevitably.) Such as selling their positions. Passing on insider information other than to the public at large is what's legislated against.
savanaly 10y ago
This is a lot of words to say a very simple thing: if you measure a stock picker's performance on a binary scale (did they outperform the market, yes or no?) then you'll get different results from if you measured them on a scale that includes how much they under or outperformed the market by. It just so happens that for the stock market the former yields a result that makes the stock pickers look worse than the latter. The original paper, as far as I can tell, is saying nothing more brilliant than that for stock picking results, the median is lower than the mean. Hence, the "average" (aka median) stock picker underperforms an index (which is, after all, the mean).
andrewprock 10y ago
This reads a lot like: "The losers pay the winners. Not really a surprising result given that really good arbitrageurs will extract a lot of value until the game is discovered by the wider world.
deleted 10y ago
[deleted]

79 points by bookbild 10y ago

Have to call BS on this article. The same failure to beat will apply to RSP, an equal weight s&p 500 that has outperformed the traditional cap weighted index.

DennisP 10y ago
The article's main claim is that if you want to do well, you need to buy a large number of stocks. It used the S&P as an example but didn't claim that it was the best possible large portfolio.

tgb 10y ago

Huh this seems like a poor explanation to me. It doesn't argue that active investment will be worse than index over the long run, just that it will be worse most of the time in the short run. But I'm not investing in the short run, so I don't really care. What does this say about their long term expected behavior? I suspect the usual argument about fees will prove more relevant over the long term.

soVeryTired 10y ago

Their argument is that most stocks are mediocre, with a handful of big winners mixed in: that means building a portfolio of hand-picked stocks is likely to underperform since it will probably miss the best stocks. But there's a symmetry argument there that the article misses. Surely I can make a portfolio that tracks the market, but excludes a handful of stocks I think are going to be lousy. Because I have most of the market in my portfolio, I'm likely to hit the big winners, and with high probability I'll ditch losers. To build on their poker chip analogy, what if there are four $10 chips, one $100 chip and I pick four chips each time instead of two?

madcaptenor 10y ago
But the distribution of returns isn't symmetric. With the losers, you can lose at most 100% of your investment; with the winners, you can make a lot more.
- sten 10y ago
  That's for stocks. You can always short and potentially have no limits for your loss.
notahacker 10y ago
This assumes your judgement on which stocks you think are going to be lousy is better than the market's overall. There might be rare occasions when that's justified (that company had major organizational issues when you worked there last month that aren't widely known, your technical knowledge means you know that hyped product probably doesn't work). But the rest of the time, you're just as likely to lose money overestimating how lousy the stock is as gain it. The $100 chip might well be the one you (and many other stock pickers) think is trending downwards until it pulls off that unexpected achievement. That said, you're right that excluding from a portfolio is a lower volatility strategy and much safer than shorting the "lousy" stocks. If I have reason to believe $TECHSTOCK is about to have their lunch eaten by new competitors and leave it out of my portfolio I slightly outperform the market if I'm right, and don't lose my shirt if Google buys it.
bluGill 10y ago
the problem is there are 4 $10 chips, 1 $100 chip, and 3 $-50 chips. Pick a $-50 chip and you are negative - note that in this market most chips will make you money, the total loses - I just picked my numbers at random. Now a good manager should be able to look at the signs: most companies that will lose money have plenty of warnings in their various (10k, 8q or whatever) reports, not to mention you can look at an industry and see trends that hit the bottom line. Should is key: many managers fail at this. However becareful when rating failures: the best managers long term have many years of below average performance - not just below market, below their peers are ultimately are not good. The best returns are from seeing a company that is doing bad now, but is going to turn things around in a few years (if you are a large enough you can even force this: buy enough of a company that you can change management). However this often means seeing that a turn around will happen sometimes in the next 5 years and waiting our 3 years of bad returns (and looking really bad!) before it happens. I cannot tell who the best managers are, except in hindsight though.

rodionos 10y ago

> equity benchmarks are so reliant on gigantic gains in just a handful of stocks that missing them Perhaps we're witnessing a shift towards an industrial model where a small number of players control disproportionate amounts of value added in their respective industries. I'd be interested to see historical data for Herfindahl indices for key verticals in the U.S., and globally.

peterbonney 10y ago

Skewness alone can't explain it, either. Imagine there are 100 stocks of equal weight in the index, and that 99 are going to underperform over the next year with only 1 outperforming. If there are 1,000,000 managers (with equal capital) each picking just 1 stock randomly to hold over that year, then yes, 99% of them will underperform the index and just 1% will outperform. But the aggregated performance of the managers will exactly match the index, minus fees. For skewness to factor into manager underperformance it must be coupled with adverse selection. I.e. it must be the case that the factors that contribute to that 1 stock outperforming are correlated with managers not wanting to own it just before it outperforms. That seems plausible, but goes against the argument that a truly random portfolio of stocks will underperform the index because of skewness (because truly random stocks are by definition not adversely selected).

jessriedel 10y ago
I agree with your observation that this Bloomberg writer is a knucklehead. "Number of managers beating the index" is obviously a silly metric since it matter by how much they win and lose, and an ideal random selection of stocks will obviously have the same expected value as the entire market. However, I think you (and the author) are missing a much simpler explanation for why skew is important: for fixed expectation value, variance is intrinsically bad for risk adverse investors. If you want to try and pick winners and losers in the stock market, you will have to become less diversified to do so. Since there are many ways to interconvert between additional expected return and risk (e.g. insurance), inducing an exchange rate between the two, there is a quantifiable cost for active management even when random. In yet other words: the cost of active management does not go to zero in the limit where the manager picks randomly and fees are ignored. Rather, as soon as you start picking you are accruing a cost through reduced diversification; you cannot come out ahead unless the size of your edge compensates for this non-zero cost.
DennisP 10y ago
Is it true that aggregated performance is low? Mostly I've just seen people say that the majority of managers have poor returns, without taking into account how well the best ones performed. (I agree there are plausible reasons for aggregate underperformance.)

nugget 10y ago

Active managers play a critical role in price discovery. We have traditionally had, and definitely still have, far more active managers than needed, but some number of them must survive in order to have a healthy market. Sometimes we lose sight of this in the (well-deserved) celebration of passive index investing. I'm interested in a few questions that only time will answer. First, what % of the market needs to be active rather than passive in order for healthy price discovery to occur? Is there an efficient frontier or stabilization point? Second, as passive indexes become the vast majority of public equity dollars, are there more opportunities for smart active investors to out-perform? (Given enough passive indexes as counterparties, it's theoretically possible for every remaining active manager to out-perform the market.) Third, in aggregate, what % of out-performance (if any) will active managers be able to take, as fees, in the future? (And what does it say about human psychology if it's >100%.)

jessriedel 10y ago
In the ideal case, the answer to your second questions seem to be obviously "yes"; the market in active managers will hit an equilibrium where their salary is paid by the additional info they bring. However, it seems clear from the current situation that the market is far from ideal since there have been too many active managers for decades. Whatever it is that allows them to persist (human overconfidence, salesmen, principal-agent problems) has not been eliminated, even if "word has gotten out" so that investors have began to develop a partial immunity against them. Knowing exactly where the new equilibrium will be requires a detailed understanding of that mechanism, which I don't think anyone has.
dragontamer 10y ago
While I agree with you that price discovery is useful... the facts of the situation mean only one thing: Active investing will decline until active investing is profitable. The price of stocks is dominated by human emotions in the short term after all (ex: Enron cooked the books as early as 1996... but didn't go bankrupt till 2001). Holding onto a "short" position for 5+ years is basically unheard of, especially in the context of a Stock whose price is skyrocketing. (You probably would have been margin-called during that runup). How many people would trust their "active investment manager" avoiding a hugely successful company with huge income growth? A quickly stock price and a good dividend? http://picker.uchicago.edu/Enron/EnronAnnualReport2000.pdf http://picker.uchicago.edu/Enron/EnronAnnualReport2000.pdf The fact is: even with perfect knowledge about which companies are good and bad (Perfect 20/20 hindsight), its still incredibly difficult to make cohesive arguments for or against particular companies.

knowno 10y ago

If many portfolios are similar, which a small group of values as a best candidate to appear in those portfolios then it is likely that they are not going to hit the big performers since they are playing a lottery. The soundness of the argument relies of what percentage of different values compose the typical portfolio.

hal9000xp 10y ago

Popular theories that investing in indexes is the best possible strategy are not self-sufficient. If there were no active traders, then nobody would trade individual stocks. In this case, there would be no indexes to invest. So markets stay in permanent equilibrium where active and passive investors are balanced out. More precisely, if there were too many active traders, it would be attractive to become a passive investor since markets are very efficient. If there were too few active traders, it would be attractive to become an active investor since markets are not very efficient. Yet despite of this simple truth, I constantly hear from seemingly serious people that only index investing is worth doing (i.e. random walk theories pop up regularly in the press). Beating index should be hard because it's a competition! And everybody is not supposed to be winner.

qntty 10y ago
I think the more reasonable claim is that it's highly unlikely that you will beat an index fund over a (say) 40 year period, so for the average investor who is investing for retirement, it makes no sense.
jessriedel 10y ago
You're talking to the wrong people. The idea isn't that all investors should be index investing, the idea is that all investors without special expertise should be index investing. This is a non-trivial statement because one might think (and people often argue) that active managers with expertise can beat indices, and therefore unsophisticated investors should just hire those people. The problem with this is that unsophisticated investors can't tell the difference between active managers who have a real edge (be it special insight, better computers, bigger brains, etc.) and those who do not. Insofar as an active manager can demonstrate convincingly to an unsophisticated outsider that they have an edge, the manager will be able to capture the excess value by commanding larger fees in the marketplace for managers. This would be a fine equilibrium for wise unsophisticated investors, but unsophisticated investors are not all wise. Various human biases and market failures mean that there are an excess number of active investors (i.e., a number above the equilibrium value in an efficient market), many/most of whom are leeches. This is the state we find ourselves in today. The reason the number of active managers is decreasing is because wisdom is diffusing, but we are not done. It goes without saying that "special expertise" involves a lot more than reading financial newspapers and considering yourself a smart person. It's about as hard to be able to compete at that level as it is to compete in professional sports. The big difference is that the heavy dose of randomness involved in investing allows more people to convince themselves that they are able to compete with the big boys, when almost none of them are. (The evidence that you can't compete with LeBron James at basketball is harder to ignore.)

rdlecler1 10y ago

In short, the same principles driving VC returns are driving public market returns with the exception that amongst top teir VCs there is effectively insider information which is illegal in public markets, hence no information asymmetry to bias returns.

Nomentatus 10y ago
Great point - actually, what the article leaves out is that investors are always competing with vast holdings held by insiders who by definition have insider information; and most of their trades based on that insider information are perfectly legal (inevitably.) Such as selling their positions. Passing on insider information other than to the public at large is what's legislated against.

savanaly 10y ago

This is a lot of words to say a very simple thing: if you measure a stock picker's performance on a binary scale (did they outperform the market, yes or no?) then you'll get different results from if you measured them on a scale that includes how much they under or outperformed the market by. It just so happens that for the stock market the former yields a result that makes the stock pickers look worse than the latter. The original paper, as far as I can tell, is saying nothing more brilliant than that for stock picking results, the median is lower than the mean. Hence, the "average" (aka median) stock picker underperforms an index (which is, after all, the mean).

andrewprock 10y ago

This reads a lot like: "The losers pay the winners. Not really a surprising result given that really good arbitrageurs will extract a lot of value until the game is discovered by the wider world.

deleted 10y ago

[deleted]