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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 wit

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.)
cortesoft 10y ago
I don't think that is the argument the author is trying to make. Obviously, the 'aggregated' performance of the managers will match the index, minus the fees (assuming every stock is in the index, and there is no adverse selection). So basically, the argument is that having an active fund manager is increasing your risk while also increasing your potential reward. The expected value is average, while the volatility is higher. While you might think this is an insignificant conclusion, I don't think this fact is obvious; most people aren't expecting that choosing an actively managed fund is increasing their risk.
- OJRbberg 9y ago
  Knucklehead author here -- happy to see all the smart discussion on this thread here. Your point here is indeed one of the main takeaways. For all practical purposes the sum of active manager performance = the index. But given the probability that the active manager you pick won't beat the index (in large part determined by skewness, the academics cited would argue), is indeed the risk you introduce by taking this route. Thanks to all for reading and arguing. O

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.)

cortesoft 10y ago

I don't think that is the argument the author is trying to make. Obviously, the 'aggregated' performance of the managers will match the index, minus the fees (assuming every stock is in the index, and there is no adverse selection). So basically, the argument is that having an active fund manager is increasing your risk while also increasing your potential reward. The expected value is average, while the volatility is higher. While you might think this is an insignificant conclusion, I don't think this fact is obvious; most people aren't expecting that choosing an actively managed fund is increasing their risk.

OJRbberg 9y ago
Knucklehead author here -- happy to see all the smart discussion on this thread here. Your point here is indeed one of the main takeaways. For all practical purposes the sum of active manager performance = the index. But given the probability that the active manager you pick won't beat the index (in large part determined by skewness, the academics cited would argue), is indeed the risk you introduce by taking this route. Thanks to all for reading and arguing. O