Seth Klarman is one of the market’s most highly regarded investors. For many, he resides in the same zip code that Warren Buffett called the home of superstar investors: “Graham and Doddsville.”

A billionaire, Klarman founded and is CEO of the Baupost Group, a Boston-based private investment partnership, with almost $30 billion in assets under management. He is also the author of a book on value investing, titled Margin of Safety: Risk-Averse Value Investing Strategies for the Thoughtful Investor.

One of my firm’s clients recently asked if I would read the book and provide my thoughts on it. Given Klarman’s reputation, I was surprised to come across the following from its introduction: “Hundreds of billions of dollars are invested in virtual or complete ignorance of underlying business fundamentals, often using indexing strategies designed to avoid significant underperformance at the cost of assured mediocrity.”

The idea that indexing guarantees only mediocre returns is one of the biggest lies (and most persistent myths) perpetrated by Wall Street on the investing public. Indeed, the campaign against indexing began nearly immediately after John Bogle and Vanguard launched the first publicly available index fund, the First Index Investment Trust, on December 31, 1975. The fund was later renamed the Vanguard 500 Index Fund.

When it was formed, the fund was heavily derided by the mutual fund industry. It was even described as “un-American,” and inspired a widely circulated poster showing Uncle Sam calling on the world to “Help Stamp out Index Funds.” The fund was also lampooned as “Bogle’s Folly.”

Fidelity’s chairman, Edward Johnson, assured the world that Fidelity had no intention of following suit when he said: “I can’t believe that the great mass of investors are going to be satisfied with receiving just average returns. The name of the game is to be the best.” Ironically, today Fidelity is one of the market’s largest providers of index funds. At the time, another fund manager, National Securities and Research Corporation, categorically rejected the idea of settling for “average.” In a flier the firm stated: “Who wants to be operated on by an average surgeon.” And that refrain became one of the big lies that Wall Street tells: indexing (and passive investment in general) gets you average (or mediocre) returns. Yet, nothing could be further from the truth.

The truth is that indexing doesn’t get you average returns. It gets you the market return. And because it does so with lower costs and greater tax efficiency, by definition you earn above average returns, at least as long as investors have the discipline to stay the course. This is about the only guarantee there is in investing. All it takes is a bit of simple arithmetic to demonstrate the truth.

Before going through the mathematics, we can take a look at the actual evidence to see if indexing, and more generally passive investing, in “virtual or complete ignorance of underlying business fundamentals” has truly provided average or mediocre returns.

The table below presents Morningstar percentile rankings for funds from two leading providers of passively managed funds, Dimensional Fund Advisors (DFA) and Vanguard. The rankings are for the ten- and 15-year periods that ended September 18, 2015.

Vanguard is a leading provider of index funds. While DFA’s funds are passively managed, they’re not index funds. (Full disclosure: My firm, Buckingham, recommends DFA funds in constructing client portfolios.)

When reviewing the rankings, keep in mind that they contain survivorship bias. Funds that have done poorly often disappear, either because investors fled and the fund was closed or the fund family decided to merge a poorly performing fund into a better performing one. About 7% of funds close every year.

Because poorly performing funds tend to disappear from the rankings, the actual performance ranking of surviving funds is significantly understated. And the longer the period, the worse the survivorship bias becomes (due to more funds having gone to the mutual fund graveyard).

All above data as of Sept. 18, 2015.

For the seven Vanguard index funds, the average ten- and 15-year rankings were the 31st and 46th percentile, respectively. Keep in mind our caution about the impact of survivorship bias on long-term rankings. If survivorship bias were accounted for, the ten- and 15-year rankings for Vanguard’s funds would be much higher. Turning to the DFA funds, the ten- and 15-year rankings for the firm’s 13 passively managed funds were the 26th and 22nd percentile, respectively. Outperforming 74% and 78% of the surviving funds is hardly an average or mediocre performance. Again, if Morningstar accounted for survivorship bias, the rankings would be considerably higher.

It’s interesting as well that DFA’s highest rankings were in the very asset classes active management proponents say are the most inefficient: emerging-markets small-cap stocks and international small-cap stocks. Even with all the survivorship bias in the data, in both of these asset classes the DFA funds managed to post a first-percentile ranking.

It’s also important to note that the rankings are based on pre-tax returns. In most cases, index and other passively managed funds will be more tax efficient, due to their typically lower turnover. ETF versions can further enhance the tax efficiency of index funds.

Furthermore, each time Standard & Poor’s releases its twice yearly Indices Versus Active (SPIVA) performance scorecards, you see additional evidence regarding just how big a lie it is that indexing gets you average or mediocre returns.

Having presented the evidence, we’ll now turn to the irrefutable logic of the laws of mathematics.

In 1991, William Sharpe wrote a paper, “The Arithmetic of Active Management.” Using simple math, he demonstrated that active management, in aggregate, must be a loser’s game. On average, active managers must underperform proper benchmarks.

Sharpe’s “proof” demonstrated that this holds true not only for the broad market, but also for when the market is in a bull or bear period as well as for market subsectors (for example, both small stocks and emerging-market stocks). The reason is simple: all stocks must be owned by someone.

A simple example will demonstrate conclusively that active investing, despite claims to the contrary, must, in aggregate, be a loser’s game. The market can be made up of only two types of investors: active and passive. For the purpose of this example, let’s assume that 70% of investors are active and 30% are passive (it doesn’t matter what percentages are used, the outcome will be the same).

Let’s further assume that the market returns 15% per year for the period in question. We know that on a pre-expense basis, a passive strategy (owning Vanguard’s total stock market fund, for instance) must earn 15%. What rate of return, before expenses, must active managers have earned? The answer must also be 15%.

The following equations show the math:

• A = Total Stock Market; B = Active Investors; C = Passive Investors
• A = B + C
• X = Rate of Return Earned by Active Investors
• 15% (100%) = X% (70%) + 15% (30%)
• X must equal 15%

If one active investor outperforms because he overweighted the top-performing stocks, another active investor must have underperformed by underweighting those very same equities. The investors that outperformed had to buy those winning securities from someone. Since passive investors simply buy and hold, the stock must have been sold by another active investor. In aggregate, on a pre-expense basis, active investors earn the same market rate of return as passive investors.

Note that if we substituted the S&P 500 Index—or small-value stocks, real estate investment trusts (REITs) or emerging-market stocks—for the total stock market, we would come to an identical conclusion. It doesn’t matter which asset class we are discussing, the math is exactly the same.

The same thing is true for bull and bear markets. The math doesn’t change if the bull is rampaging or the bear comes out of hibernation. Active management must earn the same pre-expense gross return as passive management, regardless of asset class or market condition.

However, because active managers also bear the burden of greater costs incurred in the pursuit of outperformance (operating expenses, transactions costs, market impact costs, the drag of low returns on cash holdings and, for taxable accounts, taxes) their net returns—the only kind you get to spend—must, in aggregate, be lower.

Given the evidence and the logic, it’s truly amazing that investors are still regularly bombarded with big lies. These lies include statements such as: indexing earns average returns, indexing is fine in bull markets but does poorly in bear markets at which times active managers protect you, and active management wins in inefficient markets.

While it’s possible to win the game of active management, the odds are so poor that it simply isn’t prudent to try. Which is why Charles Ellis called active management the loser’s game. Making matters worse, the evidence demonstrates clearly that active management is a game that has become increasingly difficult to win. In fact, the percentage of active managers generating alpha has fallen about 90% in relative terms (from about 20% to about 2%) over the past 20 years.

Wall Street needs you to believe in the myth that active management is the winning strategy because, while it’s the loser’s game for investors, it’s the winner’s game for them.