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From Ben Felix

The Arithmetic of Indexing: Why the Passive Approach Wins

By leveraging low fees, broad diversification, and the inherent efficiency of markets, index funds outperform the vast majority of active managers over the long term.

The High Cost of Trying Too Hard

In most areas of life, paying a premium suggests you will receive a superior product. In the world of investing, the opposite is usually true. The primary driver of the index fund’s success is its radical cost efficiency. In Canada, for example, the average fee for an index fund is roughly 0.19%, while actively managed funds often charge 0.85% or more—excluding the additional costs of financial advice. These fees are not merely a nuisance; they are the single best predictor of future performance. As Vanguard founder John Bogle famously noted, in investing, you get what you don’t pay for.

This isn't just an observation; it is a mathematical necessity. Nobel laureate Bill Sharpe formalized this as the 'arithmetic of active management.' Before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar because, collectively, active managers are the market. However, after costs, the active investor must come out behind. When you factor in higher management fees and the 'trading expense ratio'—the hidden costs of buying and selling stocks—active management becomes a negative-sum game for the investor.

Capturing the Outliers

Beyond costs, index funds benefit from a structural reality of the stock market: returns are positively skewed. Most stocks are actually duds. Research spanning nearly a century of U.S. data shows that only about 42% of stocks even outperformed one-month Treasury bills over their lifetimes. More strikingly, only a small fraction of companies—roughly 30%—generate the returns that drive the overall market’s growth. If you miss those few winners, your portfolio is destined to underperform.

Active managers try to find these needles in the haystack by concentrating their portfolios. While this can lead to spectacular gains if they choose correctly, the statistical probability is against them. They are far more likely to pick the losers that make up the majority of the market. An index fund, by contrast, holds everything. It guarantees that you will own the next Amazon or Apple, ensuring that the portfolio captures the massive gains of the few stocks that truly matter.

The Illusion of Skill and Persistence

Many investors are drawn to active funds because they see a track record of past success. They assume that a manager who beat the market for five years possesses a unique skill that will persist. However, the data suggests that outperformance is rarely durable. Studies consistently show that top-performing managers in one period frequently fall to the bottom in the next. This lack of persistence suggests that much of what we perceive as 'alpha' is actually just luck—randomness masquerading as expertise.

Even when a manager is genuinely skilled, they face the hurdle of 'diseconomies of scale.' When a manager performs well, new capital floods into the fund. As the fund grows, the manager must find more places to put that money, often diluting their best ideas or moving prices against themselves as they trade. Eventually, the fund becomes so large that the manager can no longer outperform. In this scenario, the manager still earns massive fees on the large asset base, but the benefits of their skill accrue to the management firm rather than the individual investor.

Investing as a Loser’s Game

The psychological benefit of indexing is often overlooked. In his seminal 1975 paper, Charles Ellis described investing as a 'loser’s game.' In a 'winner’s game'—like professional tennis—the outcome is determined by the superior actions of the winner. In a 'loser’s game'—like amateur tennis—the outcome is determined by the mistakes of the loser. To win an amateur match, you don't need to hit powerful winners; you simply need to keep the ball in play until your opponent hits it into the net.

Investing functions the same way. Most people lose money not because they lack a brilliant strategy, but because they make unforced errors: they trade too much, they chase hot themes, or they panic during market downturns. Indexing removes the burden of constant decision-making. It is a simple, transparent strategy that is easy to stick with during volatile times. By doing less, you often end up with more.

The Theoretical Foundation

The shift toward indexing isn't just a trend; it is the practical application of the most robust theories in finance. Modern Portfolio Theory, developed by Harry Markowitz, suggests that the only way to maximize returns for a given level of risk is through broad diversification. This was furthered by Eugene Fama’s Efficient Market Hypothesis, which argues that market prices already reflect most available information. If markets are even 'mostly' efficient, trying to find mispriced stocks is a futile exercise for the average person.

Even Fama, a Nobel laureate, acknowledges that while markets aren't perfectly efficient, they are efficient enough that investors should treat them as such. When you combine the insights of Markowitz, Sharpe, and Fama, the conclusion is clear: the most sensible portfolio for the vast majority of people is a low-cost, market-capitalization-weighted total market index. It is the only strategy that aligns with both the mathematical reality of costs and the theoretical reality of risk.

A Note of Caution on 'Passive' Labels

It is important to distinguish between total market indexing and the explosion of 'thematic' ETFs. Today, there are more indexes than there are stocks. Many of these funds—focused on niches like AI, crypto, or cannabis—are actually active strategies in disguise. They often launch at the peak of a trend's hype and deliver poor subsequent returns. True indexing means owning the whole market, not betting on a specific sector or a single country's large-cap stocks like the S&P 500.

For most investors, the goal should be global diversification. Modern asset allocation ETFs now allow investors to own thousands of stocks across dozens of countries in a single, low-cost vehicle. This approach ignores the noise of the daily market and the marketing of fund managers, focusing instead on the only things an investor can truly control: their costs, their diversification, and their own behavior.

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