The financial market is a vast arena where participants buy and sell securities based on their beliefs and financial needs. While some investors prefer active management, which deviates from market weights, others opt for passive management, which mirrors the market weights. The concept of active versus passive management has been a topic of debate for years, with many believing that active investors can outperform passive investors. However, the reality is that, on aggregate, active investors cannot beat passive investors. This is because active management is expensive and time-consuming, and the expenses incurred in performing active management, such as research, technology, marketing, and sales, reduce the returns for active investors. Additionally, the average performance of active participants in the market equals the market performance. On the other hand, passive investing is more cost-efficient and provides returns similar to the market. In this essay, we will delve into why, by definition, active investors cannot outperform passive investors.

To comprehend why on aggregate active investors cannot outperform passive investors, we will need to build on the below thought experiment:

Suppose there are 4 participants in a barter market, and each has grown 50 apples and oranges. That means there will be a fixed number of apples and oranges, 200 of each. Since there is a fixed supply, the participants meet when the market opens and decide which fruit and how many they want. All the buyers/sellers have an active preference displayed by their willingness to exchange apples and oranges. If they don’t have a preference, they will keep the 50 apples and 50 oranges they have grown.

Each participant can perform certain exchanges based on their preference. Here is one scenario:

• Participant 1: wants 40 apples and 60 oranges → gives up 10 apples for 10 oranges.
• Participant 2: wants 80 apples and 20 oranges → gives up 30 oranges for 30 apples.
• Participant 3: wants 60 apples and 40 oranges → gives up 10 oranges for 10 apples.
• Participant 4: wants 20 apples and 80 oranges → gives up 30 apples for 30 oranges.

Has the total market changed after the transactions? No, only the allocation of apples and oranges between participants has changed. Some prefer apples (Participants 2 & 3), so they have overweighted their allocation to apples. The reverse goes for Participants 1 & 4.

What is the average allocation to apples? Or oranges? The average (aka passive) allocation remains 50 of each (200 apples divided by 4 participants). Of course, the average has not changed. We shuffled things around based on preferences. How does this apply to financial markets which generate a return?

Markets are regular gatherings of people for the purchase and sale of something. The transactions must be voluntary, hence the term “free” market. However, each participant must assign a different value to what is exchanged. Otherwise, people will not transact. Further, whatever is sold on the market must be owned by someone.

Let’s look at the equity market now. We know that there is a certain number of securities in the market. Someone has to own all those securities. Buyers and sellers enter the market daily and sell and buy based on their preferences (for example, assumed mispricing and/or financial needs). Some investors want one security, so they buy it and sell another. Others increase or decrease their allocation to particular securities, and so on. For every buyer, there must be a seller since someone always has to own the securities. The point is that each participant will be overweight and underweight in particular securities based on their preference. However, each person’s preferences would not change the total market value. The selections are what we call active investments.

What does that mean as far as returns? It means that some of those securities will outperform and some will underperform, but the active participants’ average performance will equal the market performance. Hence the saying, “Active management is a zero-sum game”. For every outperformer, there must be an equal underperformer. For every seller, there must be a buyer. For someone to have overweighted a security, someone else must be underweight. Each weight different than the market average weight is an active weight. The sum of all the active weights will always equal zero. The active participant performance will always equal the market performance. Yes, there are the participants that will beat the market, but only if other participants underperform by the same amount.

So now, let’s establish a few other definitions:

• An active investor is someone whose security weights deviate from the market weights.
• A passive investor is someone whose security weights match the exact relative weights of the market.

Given the above, on aggregate, active managers cannot beat the market before expenses only match it. We can move forward and establish why passive investors will outperform active investors. The reason for this is the costs and fees. To perform active management, one must hire someone to manage the investments, conduct research, and spend on technology, marketing, sales, etc. Active management is expensive and time-consuming. You can see that in the difference in fees between the passive and active funds.

By default and simple arithmetic, we show that:

• The average performance before any expense of active market participants will equal the market performance. Or put another way, the active participants within a market do not influence the returns of the total market. Instead, they shuffle the returns amongst themselves.

You may think this is an oversimplified example, but this is actually how capital markets work. IPOs, dividends, and so on do not change the mechanics. Instead, someone must always own the assets and decide how to allocate among them based on their preferences.

In summary, active investors cannot outperform passive investors because the market returns will be the same in aggregate. Active investing involves deviating from the market weightings and incurring additional costs and expenses for research, management, technology, and marketing, which reduce the returns. The sum of all active weights will always equal zero, meaning that there will be an equal underperformer for every outperformer. Hence, the average performance of active investors will equal the market performance, but with higher fees, it will be lower than the market. On the other hand, passive investors match the market weightings and have lower costs, which leads to higher returns over the long term.

Passive investing and diversification are the only free lunch available in the financial markets. However, I am not telling you to never buy an individual stock or hire active asset managers. Just ensure that if you do, you better have an information advantage or know the active manager possesses an edge. Also, for a separate topic, investing in an S&P 500 index fund or ETF is not truly passive. Read:

What entails being a passive investor, and why are most not?

Special thanks to Professor William F. Sharpe, who has done countless research on this topic!

Sources:

“The Arithmetic of Active Management” by William F. Sharpe https://web.stanford.edu/~wfsharpe/art/active/active.htm