This is a slightly extended “director’s cut” of a post written for CFA Institute Enterprising Investor.

Warren Buffett sometimes says things that seem . . . contradictory.

For example, in the “You don’t have to be a genius to be a great investor” category:

He loves tweaking academic proponents of the efficient market hypothesis (EMH):

And yet Buffett also says most people should steer clear of active investing: Like those same gullible investment professionals and misguided EMH proponents, he recommends low-cost index funds.

[To his own self-selected trustee] My advice to the trustee could not be more simple: Put 10% of the cash in short-term government bonds and 90% in a very low-cost S&P 500 index fund. (I suggest Vanguard’s.) I believe the trust’s long-term results from this policy will be superior to those attained by most investors — whether pension funds, institutions or individuals — who employ high-fee managers.”

How can Buffett say passive investing is best for most people and also an “enormous advantage” for active investors like him? If it helps everyone else, how can it also help him?

The opposite view is sometimes described as the “suckers at the poker table” hypothesis — the theory that an increase in passive investing is bad for active investors like Buffett because the fewer suckers there are to fleece, the less profit there is for smart active investors.

So which view is right? The “suckers at the poker table” theory, or Warren Buffett, who says passive investors make his job easier? And how can Buffett be right while at the same time saying most people should invest passively?

Let’s do a simple thought experiment: What would happen if everyone was a passive investor except Warren Buffett?

As is often the case, we find that Buffett is way ahead of everyone else. He is both correct and self-serving. Anyone can use an index to match the market on a holding period–return basis, and yet Buffett can still crush everyone else on a money-weighted basis.

A brief theoretical digression: The Grossman-Stiglitz paradox holds that you can’t have a perfectly efficient market because that requires someone to be willing to arbitrage away any inefficient price. But arbitrageurs have to get paid. So they will only step in if they’re compensated for their time, data services, research, compliance, office rent, overhead, and an adequate after-tax, risk-adjusted return.

So markets tend toward an equilibrium where prices are boundedly efficient, where there is no more mispricing than at the level that would make arbitrage profitable.

The set of all investors is the market itself and, in the aggregate in any given period, earns the market return. The subset of index investors, by virtue of owning the market portfolio, also earns the market return. To make the indexers and non-indexers add up to the market, the non-index investors in the aggregate must also earn the market return.1

In the aggregate, those “arbitrageur” active investors aren’t making any excess profits! Before expenses, they are matching the market, and after expenses they are underperforming.

In order to have any profitable active investors, it seems you need overconfident, “dumb” active money that loses money trading against the “smart” arbitrageurs. And that doesn’t make much sense. It implies the persistence of a class of irrational investors. If there’s a tug of war between smart money and dumb money, and a priori the dumb money is as strong as the smart money, and it’s to the smart money’s advantage to trick the dumb money whenever possible, why should that make prices efficient?

It sounds like a theory of irrational traders and not very efficient markets.

Let’s see if a thought experiment can shed some light:

What happens if passive investors take over the market so there is only one active investor left: our hypothetical Warren Buffett?

Let’s disregard, for now, changes in the composition of the index. We only have Buffett trading with passive investors. The passive investors just want to enter and exit the whole market. They don’t want to trade individual stocks or a non-market-weighted portfolio. And there are no other active investors to trade with other than Buffett, who makes a bid-ask market for the index, selling when it’s above his estimate of fair value and buying when it’s below fair value.

A somewhat trivial example, which should be familiar to those who have done the CFA curriculum on holding period vs. money-weighted returns:

 Cash Flows Index Fair Value (%Chg) Index Price (Premium/ Discount) Passive Investor 1 Passive Investor 2 Dumb Investor 3 Dumb Investor 4 Warren Buffett Corporate Issuance Year 0 $100.00 100.00 (0%) (1,000) (1,000) (1,000) (1,000) – 4,000 Year 1$ 105.00 (5%) 94.50 (-10%) – (1,000) – 945 (1,000) 1,055 Year 2 $110.25 (5%) 121.28 (28.3%) – (1,000) (1,000) (1,000) 1,283 1,717 Final value$ 115.76 (5%) 115.76 (0%) 1,158 3,337 2,112 955 – Holding period return 5.0% 5.0% 5.0% 5.0% 5.0% Money weighted return (IRR) 5.0% 5.4% 2.7% -5.0% 28.3%

• The index fair value grows at 5% per year.
• It starts priced at fair value in Year 0, in Year 1 it trades at a 10% discount, in Year 2 at a 10% premium, and then finally returns to fair value in Year 3.
• The holding period return, which ignores flows, is 5%, matching the index.
• Passive Investor 1 buys $1,000 worth of stock in year 0, never trades thereafter, and has holding period and money-weighted return of 5%, the market return. • Passive Investor 2 buys$1,000 worth of stock each year and has a money-weighted return of 5.4% as a result of automatically buying more shares when they are cheap and fewer when they are expensive.
• Dumb Investor 3 panics when the market goes to a 10% discount and doesn’t buy that year and ends up with a 2.7% money-weighted return.
• Dumb Investor 4 panics even worse, sells when the market goes to a 10% discount, and ends up with a -5.0% money-weighted return.
• Warren Buffett stays out of the market until it trades at a 10% discount, sells at a 10% premium, and ends up with a 28.3% money-weighted return.
• Corporate issuance is included as a reminder that there are two sides to the market and overall cash flows in and out have to net to zero.2

If you examine any individual year, everyone here is a passive investor in the sense of always holding the index.

Everyone gets the same 5% holding period return, which ignores flows.

But on a money-weighted, risk-adjusted basis, of course, the returns are very different, and our Warren Buffett crushes the market.

One way of looking at it is Buffett times the market, increasing the size of the overall pie when the odds are in his favor, shrinks it when they aren’t, and outperforms without necessarily taking anything from the other investors, who earn the market return in each holding period.

Another way of looking at it is to consider the whole scenario as one holding period during which Buffett took advantage of people who were selling low and buying high. Effectively, our Warren Buffett sets a floor under the market when events or cash flows make the passive investor inclined to sell excessively cheap and sets a ceiling when the market gets expensive.

Even though everyone here is passive in a given year, if you think of the entire scenario as one holding period, only someone who owns the index and never trades is really a passive investor. Everyone else is buying high or selling low within the period.

The key point here is, the only person who is a passive investor is the one who never trades. That person is guaranteed the market return. Even if you are just re-investing dividends, there’s no guarantee of how well you will execute. As soon as you trade, you are at risk of being exploited.

On a sufficiently long timeline, the probability of being a completely passive investor goes to zero. If you’re planning to invest for an objective other than buying and holding forever, you have to make decisions about when and how much to invest and when and how much to withdraw.

Eventually you have to make an active investment decision, and at that point the shrewd investors are lying in wait. Everyone eventually has to pay Charon to cross the river Styx.

It gets even better for Buffett when you incorporate index changes.

An IPO comes out. The IPO is initially not in the index. Our hypothetical Warren Buffett sets the IPO price. He doesn’t have anyone to bid against or anyone to trade with besides the issuers since the stock is not yet in the index. Being an accommodating fellow, he sets the price at fair value minus his margin of safety, illiquidity discount, etc.

The IPO eventually gets added to the index. Indexers have to buy the stock. Buffett solely determines the price at which it gets added to the index. In his obliging manner, he sets it at fair value for a liquid index stock plus a reasonable convenience premium.

What a sweet deal! Pay a steep discount for any security not in the index and demand a big premium when it goes into the index. Similar profits are available when securities exit the index.

Going back to the Grossman-Stiglitz paradox, the arbitrageur active traders can do pretty well, even without the existence of a large pool of permanently underperforming “dumb money,” which is unnecessary and illogical.

They pull a bit of Star Trek’s Kobayashi Maru scenario by going outside the bounds of picking stocks from within the index, by timing the market, by charging a toll for the more passive investors to enter and exit the index.

The “suckers at the poker table” paradigm goes astray because there isn’t some exogenous fixed size of the investment pie investors are fighting over. The returns are endogenous: They are in part determined by how smart the investors are, how well the capital in the economy is allocated, and by everything else that impacts economic and market outcomes.

The performance pie is not fixed. When someone invests in an early Apple or Google, are they stealing performance from someone else? Was Ron Baron stealing performance from someone else when he funded Wynn as a startup? He’s creating something that eventually goes into the index…pulling a bit of a Kobayashi Maru by redefining the index.

When Buffett invested in Goldman Sachs during the crisis is he stealing performance from someone else? You could argue Goldman Sachs made excess returns on his investment, it gave them opportunities no one else had, and benefited all shareholders. Buffett pulls a bit of a Kobayashi Maru by expanding the investable market when it’s cheap, instead of taking it as a given fixed pie. 3

Smart money going into appropriately priced investment opportunities grows the whole pie. Dumb money going to bad businesses shrinks the pie. Once it’s not a strictly zero-sum game, you don’t need “suckers at the poker table” to outperform. Sufficiently smart money creates its own suckers.

The more extreme advocates of passive investing go astray, I think, in concluding that passive investors can always match active investors.

See for instance, Sharpe. His mathematical proof that indexers always match the market is, of course, correct insofar as the passive investor who does nothing, gets the market return. But as soon as you trade, you’re an active investor in that period (Sharpe’s footnote 4). And the spread you have to pay to transact is the gain of the active player on the other side. So passive performance = active performance, but only because the passive investor has to briefly become an active investor in order to get fleeced.

Sharpe’s proof is correct on an accounting basis, but tautological and not fully descriptive of market reality. In order for the passive investor to match the market in practice, he must be able to trade in size at the market price and not allow himself be exploited. Which is not a bad assumption at small scale but gets harder as the passive investor gets bigger. (Sharpe hand-waves past this in footnote 3, saying trading makes the math more complicated but doesn’t change the basic principles. But if passive trading is big enough to move the market, if effective trading spreads are sufficiently large, that can no longer be true.)

Passive investors cannot always have a free option to match the market, unless the other side gives it to them. The outcome is an equilibrium. When few people are passive, indexers get to match the market and free ride with the people who do the research and set the prices. On the other hand, when many are passive and few are active, there are mispricings, and when indexers have to trade, for instance around big dividends, corporate actions, index changes, rebalancing, seasonal cash flows, economic developments that necessitate cash flows, they can be exploited because they herd.

It’s a little absurd to take a fanatical view about indexing. Active vs. passive is a continuum, from matching the market portfolio and never trading, at one extreme, to finding big bets where you have an edge and trading often, at the other extreme. Anyone who trades inside your time frame is active and giving you an option to potentially eat their lunch if they’re willing to trade at a favorable price, and on a long enough time frame no one can be completely passive forever. What one should be fanatical about is expenses, after-tax risk-adjusted returns, keeping it simple, and avoiding mistakes _ all of which are good arguments for indexing.

There are many useful parallels between investing and poker. You have to zig when everyone else zags. Simple strategies can be exploited. You have to use a meta strategy, like a mixed Nash equilibrium.

Unlike poker, investing is not a zero-sum game. Dumb money is not the primary driver of returns for most strategies, and “suckers at the poker table” is not a useful analogy for most long-term investors. There is always a game beyond the game, where the best players astutely redefine the game to find an edge.

Efficient market proponents make the point that there ain’t no such thing as a free lunch, in the form of persistent pricing inefficiencies that provide excess risk-adjusted returns. But in a sense, indexing is yet another attempt to find a free lunch … the indexer gets a free ride on efficient prices determined by everyone who does their homework. Like all free lunches, this one also goes away if enough people take advantage of it.

Takeaways:

• If sufficiently few people index, indexing is a free lunch: same performance with lower costs.
• If you can index and never trade, you are guaranteed the index return (without reinvesting dividends).
• Nobody can be totally passive forever. Everyone has to trade sometime. Even re-investing dividends, rebalancing has a cost.
• Everybody can’t be passive, someone has to take the other side of each trade.
• If enough people index, and have to trade, they can be exploited.
• As indexing increases, herding increases, correlation increases, overall volatility increases. 4
• The math that proves indexers can always closely or perfectly match the index performance, doesn’t add up when the indexer has to trade, and trades are big enough to move markets.
• Instead, there’s a Nash-like mixed strategy equilibrium: too little passive, passive can exploit active, too much active, active can exploit passive.
• Dumb money doesn’t become smart money because it indexes. It just finds another way to lose. There is always a game beyond the game.
• If most people are bad at active management, it’s better for them to be mostly passive, trade as little as possible, choose active decisions only at market extremes. And if a few people are pretty good at active management, it’s better for Buffett if they don’t compete with him at his own game. Although I doubt many good active investors have been deterred by academic passive zealotry.
• And finally, everybody likes a good Buffett angle, even if it’s a MacGuffin for a boring discussion of limits of active v. passive.

This benefited from discussion with Will Ortel of CFA Institute and Wes Gray of Alpha Architect.

1. This accounting excludes issuers of stock, who are kind of important. Companies are net distributors of cash to their stockholders. They pay dividends and they on net buy back stock, these days. So everyone cannot be a passive investor in the S&P and reinvest dividends. If they tried, something would have to give. Investors would bid up stocks until someone capitulated and started selling, or companies started issuing stock, or something. When it’s not a zero-sum game, reasoning from accounting identities tends to be misleading.

2. Here’s a thought exercise: do you think the issuers are on balance generally timing their corporate actions efficiently, issuing high and buying back low? Does it matter? Answer (I think): On any finite time period, of course it matters! If companies are acting efficiently over time, generally selling stock when it’s expensive and buying it back when it’s cheap, that is bad for whoever took the other side of that trade. The shareholders on the other side have a lower return than the market average. The company has a lower effective cost of capital than long-term market averages would suggest. And the shareholder who holds indefinitely and never trades gets a benefit.

Going back to footnote 1, this is another reason active=passive only with simplifying assumptions of ignoring issuance and distributions and trading, which are rather significant to returns and properly functioning capital markets.

(If any good research summary on how well capital transactions are timed, I would love to read about it. À priori I would guess IPOs and LBOs tend to be not advantageously timed for public shareholders; dividend adjustments tend to lag market developments; buybacks tend to be distorted by management incentives around return on equity and stock options; cash mergers, not sure. )

3. When someone invests in an early Microsoft, they are partly creating wealth, partly taking it from e.g. IBM shareholders. Similarly when Buffett invests in GE on the cheap, he is partly increasing the pie for everyone, partly giving himself a better deal at the expense of everyone else. The beauty of a properly designed free market is that everyone has to harness creativity for the benefit of all to gain something for themselves.

4. These seem the most plausible first-order approximations. The reasoning is that as active investors turn passive, flows are more correlated, the inside bid-ask from the remaining active investors can only get wider, and a given flow has a bigger impact on price. But if the one Warren Buffett who is left changes his mind daily on intra-index relative prices more than the exiting investors did, you could conceivably see an increase in intra-index volatility.