The Million Dollar Active vs Passive Wager

Warren Buffett has a 10-year, $1 million bet with some fund-of-funds managers: he reckons that his investment in Vanguard's S&P 500 index fund will outperform their portfolio of five fund-of-funds. It's a pretty standard active vs passive bet, albeit for uncommonly large stakes; the interesting thing here is that the active side of the bet can be considered to be a fund-of-fund-of-funds, which is pretty crazy, even after accounting for the fact that the top level fund isn't going to charge any management fees.

It's crazy because diversification is bad for the active side of the bet:

Buffett offered to bet any taker $1 million that over 10 years and after fees, the performance of an S&P index fund would beat 10 hedge funds that any opponent might choose. Some time later he repeated the offer, adding that since he hadn't been taken up on the bet, he must be right in his thinking.
But in July 2007, Ted Seides, a principal of Protégé but speaking for himself at that point, wrote Buffett to say he'd like to make the bet - or at least some version of it.
Months of sporadic negotiation ensued. The two sides eventually agreed that Seides would bet on five funds of funds rather than 10 hedge funds.

Buffett's actually in better shape here than he would have been with the original bet: the five fund-of-funds, between them, are bound to invest in much more than just 10 hedge funds. And the more hedge funds which underpin the bet the greater the chance that Buffett is going to win. After all, the average fund-of-funds, net of all fees, is going to underperform the market as a whole. Even Buffett's opponents concede that:

Top hedge fund managers have surpassed market returns net of all fees, while assuming less risk as well. We believe such results will continue.
There is a wide gap between the returns of the best hedge funds and the average ones. This differential affords sophisticated institutional investors, among them funds of funds, an opportunity to pick strategies and managers that these investors think will outperform the averages.
Funds of funds with the ability to sort the wheat from the chaff will earn returns that amply compensate for the extra layer of fees their clients pay.

But of course the more hedge funds that these managers invest in, the harder it's going to be for them to invest only in "the best hedge funds" and "sort the wheat from the chaff".

So I think Buffett actually underestimates his chances when he says he has a 60% chance of winning the bet. And if he does lose, I think he'll lose not because the hedge-fund managers did particularly well, but because the S&P did badly.

This is one area where the fund-of-funds have a big advantage: while Buffett is confining himself to large publicly-listed US equities, his opponents have the entire universe of asset classes to choose from. If they simply invest in something a bit more globally diversified, and if the US stock market doesn't go anywhere over the next 10 years, then it's quite easy to see how the hedge-fund managers might win with no thanks at all to their alpha-generating prowess.

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