Another day, another controversial subject within investment management I am taking on. In this post I discuss and hope to dismantle an oft-repeated missive about active management. Namely, that active management is zero sum. For brevity’s sake, I propose the acronym of AMIZS (pronounced, “amazes”) as a stand in for “active management is zero sum.”

AMIZS is Logical…Right?

Here are the assumptions of the logical argument put forth for why active investment management theoretically must be zero sum.

1. Let’s assume that the split of passive vs. active invested funds is 55:45.
2. Now we can write an equation giving the total return of the market portfolio as a weighted sum of the passive and active segments:

market return = ( 0.55 * passive return ) + ( 0.45 * active return )

3. Passive investors hold the market portfolio, right? So, the passive return must be equal to the market return. Thus, the equation reduces down to:

market return – ( 0.55 * market return ) = 0.45 * active return

or

0.45 * market return = 0.45 * active return

thus,

active return = market return

But, this is before the costs of active management. Shazbut! So, after the total costs of active management, the active return must be less than the market return. Drop the mic. This argument is simple, perfectly logical, and irrefutable, right? Wrong. Here’s why.

Question the Assumptions

Sadly, the above argument is endlessly and smugly repeated by the press, by academics, by passive managers, and even by some active investors (e.g. Ray Dalio). But just like any logical argument, if the logic is sound then the only way to defeat the logic is to question the assumptions. Let’s take on the assumptions, shall we?

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Assumption 1: “Market” Constitution

Just like Shakespeare is endlessly quoted, but rarely read, so it is for the original paper that defined CAPM, from whence the concept of the Market comes. Most quoters of AMIZS have never read the original paper. Most important to our discussion is Sharpe’s definition of “The Market.”

It was first described by Sharpe in the Journal of Finance in 1964’s “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk.” Sharpe’s definition of “the Market” when outlining the Capital Market Line is “The model of investor behavior considers the investor as choosing from a set of investment opportunities that one which maximizes his utility.” At no point does he constrain his definition to an index, or a benchmark, or anything, really. Just, “a set of investment opportunities.”

The affect of this is that any investment may be held by an investor. Not just stocks. Not just bonds. Not just ETFs. Not just options. But also, your grandmama’s silver set, molybdenum, your home, a sports card collection, artwork, a classic car, and on and on.

Functionally, this means that no one, in theory, can possibly access the entirety of The Market. Because it is impossible to own all assets. Thus, while AMIZS is true, this is also true of passive management. Crucially, and I do mean crucially, this is only true in theory. After all, what benchmark serves as a true proxy for The Market? Not one. So, even your preferred and very broad proxy for The Market is zero sum because it is also a subset of the Market.

Because functionally no one can own the entirety of The Market, in order to beat my competition, including a benchmark, all I need to do is to possess one more, or one less asset than the benchmark, as defined. Further, all I have to do is to be over- or under-weight one asset in the defined benchmark.

Sadly, the investment business has evolved such that a benchmark, such as the S&P 500 is considered The Market. It is not. In fact, it was used as a proxy for The Market in the 1970s for entirely practical reasons.

You see, back in the day there was limited access to mainframe computers. There was no access to calculators, because they had not been invented. Therefore, a large stock market benchmark served as a stand-in for The Market.

But now we have benchmarks, style boxes, tracking error, and the like to ensure that The Market remains stunted and small in concept. And our industry swallows this whole and chooses to compete on these grounds.

Last on this point, if you think about it, all assets composing The Market, are going to approximate something like economic growth or productivity growth.

Assumption 2: Same Strategy

AMIZS assumes all investors have the same strategy. Presumably, to beat the market. But, Sharpe defines it very differently, “Investors are assumed to prefer a higher expected future wealth to a lower value, ceteris paribus.” He goes on to assert that investors exhibit risk aversion and choose assets that have lower expected volatility relative to their expected returns for investments. Note: I did not directly quote Sharpe on the risk part because he defines multiple terms mathematically.

Let’s do a check in with reality. The investment management industry is massively fragmented. Small cap value. Mid cap core. Large cap growth. Short duration phlegm bonds. Etc. AMIZS ignores that different investors have different strategies. Why? I don’t know, but it is also not my place to question investors’ decisions to have different strategies. But the fact is that it is entirely possible for multiple strategies to be satisfied within the constraints of The Market.

Here is an example. A small cap value manager buys a stock whose valuation is less than that of her benchmark. It appreciates, delivers alpha, and soon violates the constraints valid for her benchmark (e.g. valuation and capitalization). Not wanting to be accused of style drift she sells the stock to a mid cap core manager. He is happy to buy it because his estimation is that it is likely to continue its price appreciation and the stock meets his benchmark’s valuation and capitalization constraints. Turns out, he was right. Yay! In turn, he sells the asset on up the style box to another manager with another strategy in the large cap space.

Now, from the perspective of The Market, the first two managers have experienced the zero-sum (but only in theory) described by active management detractors. But, in reality, because they have different strategies the managers are satisfied, and so are their investors.

Assumption 3: Same Goals

Oh, speaking of investors…not every investor has the same goals. What if they have different goals? What if one investor, A, prefers rapid capital appreciation to pay for a boat, and another prefers a steady source of income, investor B, to partially deliver retirement income?

If investor A is successful and buys an early stage growth company and experiences the capital appreciation needed, she sells her stock. But, what if in the interim the stock becomes a steady grower/cash accumulator and starts to pay a dividend? If investor A sells to investor B, how (except in theory) is this a zero-sum activity?

Assumption 4: Same Time Horizon

The same logic described in Assumption 3 is easily extended to differences in investors’ time horizons. An investor who is approaching retirement, investor A, has a shorter time horizon than someone just entering their income-earning years, investor B. Investor A may sell a chunk of his equity portfolio, probably the portions with the highest cost basis (tax efficiency, and all that) as a part of an asset allocation rebalancing. Investor B, in turn, may buy some of those equities. Again, how is this a zero-sum activity, except, in theory?

Conclusion

I could go on with this line of thinking, but to summarize. AMIZS assumes a homogenous market and a homogenous investor. Where exactly is there evidence of either of those things, except, in theory?

Furthermore, the original framers of modern portfolio theory and CAPM did not frame their arguments in terms of returns. Really? Yes, really. In fact, the whole enchilada rested on the Utility Theory of von Neumann and Morgenstern. In other words, the theory rests on the assumption that different investors are trying to maximize their utility. Whatever that means. Fascinating.

So please let us abandon the unquestioned, oft-repeated, pithy heuristic of AMIZS. Like most heuristics they are intellectual germs leading to head colds. And you don’t want a sick head do you?

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