R-squared

• The Bottom Line: R-squared tells you what percentage of a fund's or stock's price movement can be explained by the movements of a market index (its benchmark).
• Key Takeaways:
• What it is: A statistical measure, expressed as a number between 0 and 100, that shows the correlation of a portfolio's returns to a benchmark, like the S&P 500.
• Why it matters: It's the ultimate B.S. detector for fund managers, revealing whether their success comes from genuine skill or just from riding a market wave. alpha.
• How to use it: A high R-squared (over 85) means the fund hugs its benchmark, making metrics like beta reliable. A low R-squared means the fund marches to its own beat, and the benchmark is a poor comparison.

Imagine you have a small boat (your investment fund) in the ocean (the stock market). The tide represents the overall market's movement, often measured by a benchmark index like the S&P 500. When the tide comes in, most boats rise. When it goes out, most boats fall. R-squared (often written as R²) simply tells you how much of your boat's movement is caused by the tide. It's a score from 0 to 100:

• An R-squared of 100 means your boat is perfectly attached to the tide. Every single rise and fall of your boat is explained by the tide's movement. It doesn't mean your boat rose as much as the tide, just that its movements are perfectly in sync. This is what you'd expect from an index_fund designed to track the market.
• An R-squared of 0 means your boat's movement has absolutely nothing to do with the tide. It might be powered by its own engine, affected only by the wind, or even sailing on a completely different body of water. Its ups and downs are independent of the general market tide.
• An R-squared of 85 means that 85% of your boat's up-and-down movement over the past few years can be attributed to the market tide. The other 15% is due to something else—the skill of your boat's captain (the fund manager), the specific design of the boat (the stocks it holds), or random chance.

In short, R-squared is a measure of correlation, not performance. A fund that consistently goes down whenever the market goes down will have a very high R-squared. It's a tool for understanding why an investment performs the way it does.

“The stock market is a device for transferring money from the impatient to the patient.” - Warren Buffett ¹⁾

For a value investor, understanding the “why” behind performance is everything. We aren't speculators chasing hot returns; we are business analysts seeking predictable, long-term value. R-squared is a critical tool in this analytical process.

• Unmasking “Closet Indexers”: The fund industry is filled with so-called “active” managers who claim to have a unique stock-picking genius. They charge high fees for this supposed expertise. R-squared is your lie detector. If you see a U.S. large-cap mutual fund with an R-squared of 98 against the S&P 500, you've likely found a “closet indexer.” This manager is charging you 1% per year to essentially buy you an S&P 500 index fund, which you could get for 0.05%. A true value-oriented stock picker should have a portfolio that looks significantly different from the index, resulting in a lower R-squared.
• Putting Alpha and Beta in Context: You'll often hear about alpha (a manager's value-add) and beta (a fund's volatility relative to the market). These metrics are only meaningful if the fund is actually correlated with the market you're measuring against. R-squared is the gatekeeper. As a rule of thumb, if the R-squared is below 70, the calculated alpha and beta are statistically unreliable. It's like judging a fish by its ability to climb a tree—you're using the wrong test. A high R-squared (above 70-75) gives you permission to take alpha and beta seriously.
• Focusing on True Diversification: A value investor builds a portfolio of businesses, not a collection of tickers. True diversification means owning assets that behave differently under various economic conditions. If you own five funds and they all have an R-squared of 95+ with the S&P 500, you aren't diversified. You've just bought the same market risk five times. A fund with a low R-squared might offer genuine diversification benefits because its success doesn't depend on the broad market going up.
• Maintaining a Margin of Safety: Understanding what drives your returns is part of your margin_of_safety. If you know a fund's performance is 95% linked to the market, you understand the primary risk you're taking. If another fund's performance is a mystery (low R-squared), you must do more homework to understand its unique risks before investing. R-squared forces you to ask the right questions about where your returns—and your risks—are truly coming from.

For 99.9% of investors, the goal is not to calculate R-squared but to find it and interpret it correctly. You can easily find the R-squared for most mutual funds and ETFs on financial data websites like Morningstar or in the fund's official documents.

While the statistical formula is complex, the concept is simple. R-squared is literally the “square” of another value called the correlation coefficient ®.

• The correlation coefficient ® measures how two things move in relation to each other, on a scale of -1 to +1.
• By squaring this number (r * r), you get R-squared. This mathematical step turns the result into a percentage (from 0 to 1, or 0 to 100) that represents the percentage of variance explained. Don't worry about the math; just remember that it's a measure of explained movement.

Think of R-squared in three main buckets. Let's assume we are comparing a U.S. stock fund to the S&P 500 benchmark.

Let's compare two fictional actively-managed funds. An investor is looking to add a U.S. large-cap fund to their portfolio and is using the S&P 500 as the benchmark.

• Fund A: The “Patriot Large-Cap Trust”
• Fund B: The “Maverick All-American Fund”

Here are their 3-year performance numbers:

Analysis:

• The Patriot Trust (Fund A) has an R-squared of 96. This is extremely high. 96% of its returns can be explained by the S&P 500's movement. While it slightly outperformed the index, its tiny alpha of +0.2 is almost entirely wiped out by its 0.90% fee. A value investor would see this and conclude: “This is a closet index fund. I'm paying a high fee for a return I could get from a low-cost ETF.” This is a clear pass.
• The Maverick Fund (Fund B) has an R-squared of 72. This is in the “moderate” range. It tells us that while the fund is definitely a U.S. large-cap fund, the manager is making significantly different bets than the index. Its lower return (11.0% vs 12.0%) might seem disappointing at first, but its alpha is a much healthier +1.5. The R-squared of 72 is high enough to make that alpha number meaningful. A value investor would see this and think: “This manager has a distinct strategy. Even if they've underperformed slightly in this period, their active decisions are the main driver. I need to investigate their philosophy and holdings to see if their approach aligns with my own.” This fund warrants a deeper look.

The R-squared didn't tell us which fund was “better,” but it gave us the crucial context to ask the right questions and avoid the obvious trap (Fund A).

• Simplicity: It provides a single, easy-to-understand number (0-100) to gauge the relationship between an investment and its benchmark.
• Identifies Closet Indexers: It is the most effective tool for spotting expensive funds that are simply mimicking a low-cost index.
• Contextualizes Other Metrics: It acts as a necessary check before you can trust the validity of more complex metrics like alpha and beta.

• Benchmark Is Everything: R-squared is only as good as the chosen benchmark. Comparing a Japanese stock fund to the S&P 500 will yield a uselessly low R-squared. Always ensure the benchmark is appropriate for the fund's strategy.
• Correlation Is Not Performance: A fund can have a perfect R-squared of 100 and still be a terrible investment if it consistently underperforms the benchmark due to high fees or bad execution. High R-squared only means it tracks the benchmark predictably, not successfully.
• It Is Backward-Looking: R-squared is calculated using historical data (typically 36 months of returns). A fund's strategy can change, so past correlation doesn't guarantee future correlation.

• alpha: Measures a manager's outperformance relative to the benchmark, a metric validated by R-squared.
• beta: Measures a fund's volatility relative to the market; also validated by R-squared.
• benchmark: The index or standard against which an investment's performance and correlation are measured.
• active_management: The strategy of trying to beat the market, which R-squared helps to evaluate.
• passive_investing: The strategy of matching the market, where a high R-squared is the goal.
• correlation_coefficient: The statistical input (“r”) that is squared to produce R-squared.
• diversification: The principle of owning assets that don't move in perfect lockstep, which can be identified by analyzing R-squared.