Why the Zero-Sum Game Gives Indexing an Edge

Elizabeth Tammaro: Bob would like to know how the stock market is a zero-sum game. And, Scott, I believe you have some information to provide an answer there.

Scott Donaldson: Well, great, and that’s really an important question, I think, in light of certainly the overview that Walter just gave about indexing in general and how it works and why some of the success factors are there; but, generally, the zero-sum game is very, very important from an indexing standpoint because, really, I think the success of indexing is grounded in that theory for a few reasons. And, one, if you think about starting from the premise or the understanding that every day or every minute the market, or all the holdings in a particular market that are being held by investors, aggregate up to become that market and create a return for that market is basically the concept of a zero-sum game.

So if you think about it simply, every transaction in the stock market or the bond market has a buy and a sell transaction. Somebody thinks that they’re going to buy a stock or a security because the forward-looking performance, in their mind, looks to be good. At the same time, you have somebody deciding to sell that at a particular price meaning they think there are better opportunities out there, right, so a buy and a sell.

So from a performance standpoint, [for] every dollar-weighted excess return that outperforms the stock market, there has to be a corresponding dollar-weighted excess negative return. So dollars that win have to be offset by dollars that lose. It’s a mathematical certainty and just the way that the market operates.

So all of the active managers out there that say, in their marketing literature, “I’m going to outperform, or we’re going to try to outperform the market,” everybody cannot outperform the market. It’s an impossibility based on the zero-sum-game theory. And I actually have a chart I think I’d like to go to that might help explain this just a little bit better.

impact-costs-investor-returnsSo here, you see a chart, basically two hypothetical bell-curve distributions, okay, of the returns of the stock market. This curve on the right is the before-cost distribution of the market return. So if you’ll see, the market return here in the middle is the average return for an investor before cost: You have 50% of the dollars outperforming, and you have 50% of the dollars underperforming the market that achieves that return.

However, in reality, okay, we all know that investors have costs associated with investing. There’s expense ratios when investing in mutual funds. In trading individual securities, there’s potentially commissions. There’s bid-ask spreads. And, actually, one type of cost that a lot of people forget about is actually taxes, which can be a very, very, a huge cost.

So if you think about equal dollars outperforming before and equal dollars underperforming the market from the zero-sum-game frame point, if you add cost in, what it does is shift the distribution of market returns to the left. Now you have the average investor return after cost here, which is significantly less than the original, okay. And now you have only this portion, this shaded portion, of investors who have actually outperformed the market after cost. Before it was all of this, now it’s only this. Now you have a significantly more than half of investors’ dollars underperforming the market on an after-cost basis.

That is why indexing works because indexing seeks to keep your return as close to this line as possible by keeping costs and transactions low. The closer you stay to that before-cost, market return line, the more individual investors you’re going to outperform.

Elizabeth Tammaro: Yeah, I think that’s a helpful visual. Thanks.

Scott Donaldson: And it’s interesting. How does that translate to the real world, okay? If you try to take this theory and apply it, if you look at the returns of active managers versus their corresponding benchmarks or index funds over the last say 15 to 20 years, about 70% of active managers have underperformed their benchmark over 15 and 20 years. That’s a significant percentage.