If you've been following our series on statistical significance in active fund performance, you'll know how easy it is to confuse genuine skill with random chance. In this third and final installment, we introduce a valuable tool that's often overlooked in the industry.

We tracked more than 2,000 funds over 20 years and discovered that even the average winner would need 153 years of data to prove their outperformance isn't just luck.

Here's the simple three-input calculator that lets you test any manager's track record yourself — and evaluate decades of performancce claims in less than a minute.

What if the average winning fund manager — someone who survived 20 years and beat their benchmark — would need 153 years of data to prove they're not just lucky? Not 20 years. Not 40. One hundred and fifty-three years. That's not a typo. It's mathematics.

The first two parts of this series showed that star managers are usually lucky, and proving otherwise requires decades of data. But we're not asking you to take our word for it. By the end of this article, you'll be able to test any manager's track record yourself within a few moments.

You'll learn to use a simple online calculator with three inputs that reveals whether a fund's performance is likely skill or randomness. The tool is free. The implications are profound.

First we'll show you the evidence: what happened when we analyzed more than 2,000 funds over 20 years. Then we'll explain why your brain will resist it. Finally, we'll give you the tool to verify it yourself on any fund you choose. By the end, you'll never look at a "star manager" the same way again.

The Landscape: 2,000 Funds, 20 Years, One Devastating Result

IFA tracked 2,116 US mutual funds in large-cap growth from January 1, 2005 to December 31, 2024. Each fund was measured against its Morningstar-assigned benchmark. This isn't cherry-picked — it's every fund with at least 90% US equity and enough data to analyze.

73% of these funds no longer exist. Nearly 2,000 closed or merged, typically to bury poor performance. Survivorship bias affects perception: results often reflect only surviving funds. Losers vanish quietly, taking investors' capital with them.

Of 2,116 funds, only 237 (8.83%) delivered positive alpha over 20 years. Already a tiny minority. Among these survivors who outperformed, the average annual edge was 1.04%.

That 1.04% came with a standard deviation of 6.44%. Translation: year-to-year performance swung wildly. One great year, then mediocrity. Or worse.

Look at the chart below. Each blue dot is a fund. The diagonal dotted line is the t-statistic threshold of two — the statistical bar for proving skill (we'll explain shortly what a t-statistic is). Above the line (i.e. the green zone) equals skill. Below it (the red zone) equals indistinguishable from luck. The vast majority of funds — including most with positive alpha — sit in the red zone.

Now let's test the average winner. Average alpha: 1.04%. Standard deviation: 6.44%. Time period: 20 years. Input those numbers into IFA's t-stat calculator.

153 years.

That's how long you'd need to be 95% confident the 1.04% alpha isn't luck. Most managers don't work for 40 years, let alone 153. By the time you'd have proof, the manager is gone.

Even among the rare funds that survive two decades and outperform, the typical edge is so small and noisy that proving it's real is effectively impossible. And this is the average winner. Of the funds that survived the 20-year period, half did worse.

Why Your Brain Wants to Reject This

If you're thinking "153 years can't be right" or "but I know a manager who's different," that's normal. What you've just seen contradicts decades of marketing and probably your own experience. Before you dismiss it, understand why.

Humans see patterns in noise. We credit managers for outcomes driven by chance. We mistake streaks for skill. As Nassim Taleb wrote in his famous book, Fooled by Randomness, our brains are wired for storytelling, not statistics.

Flip a coin 12 times. You can easily get ten heads and two tails — pure chance. But if that "coin" is a fund manager, we write headlines about genius.

Three good years feel convincing. But Jacob Bernoulli proved centuries ago that the more trials you run, the closer you get to true probability. In fund management, we don't have enough trials within a career to confirm skill. That's the structural problem. As Michael Jensen's foundational 1968 study demonstrated, even 20 years of data often fails to separate luck from genuine alpha once you account for risk.

The t-statistic separates signal from noise. It asks: "Is this result meaningfully different from zero, or could it be randomness?" That's what this article shows you how to use.

The Tool: Understanding the T-Statistic

What Statistical Significance Means

When a fund outperforms its benchmark, is that result reliably different from zero, or could it be luck? Statistical significance answers that question.

A t-statistic of two means there's only about a 5% chance the outperformance is due to random variation — a 95% confidence level. Below that? Could easily be noise.

Eugene Fama — Nobel laureate and godfather of efficient markets — argues that in markets this noisy, even t-stats of two aren't enough. Some academics demand t-stats of three. We'll use two as our baseline, but keep that higher bar in mind. As Fama and French demonstrated in their 2010 paper, Luck versus skill in the cross-section of mutual fund returns, proving genuine skill above luck requires vast amounts of data and large, stable alpha — assumptions that almost never hold .

The Formula: Plain-English Breakdown

Here's the formula that powers the test:

t-stat = (√T × average alpha) / standard deviation of alpha

Don't worry — the calculator does this for you. But understanding the components shows why proving skill is so hard. 

The numerator contains two elements that push the t-stat up. Average alpha: bigger outperformance equals higher t-stat. A fund that beats its benchmark by 5% per year has a better shot at proving skill than one that beats it by 0.5%. √T (square root of time period): more years equals more reliability. That's why 20 years beats three.

The denominator drags the t-stat down. Standard deviation of alpha measures how much the outperformance bounces around year-to-year. High volatility kills credibility. Even if the average alpha is positive, wild swings mean it could easily be luck. As Mark Carhart showed in his comprehensive 1997 analysis of 31 years of mutual fund performance data, once you control for known risk factors, apparent persistence largely vanishes — the volatility swamps the signal.

The intuition: to clear the bar, you need large alpha, delivered consistently, over decades. If any of those three is weak, the t-stat collapses. That's why so few managers prove skill.

How to Use the Calculator

IFA's t-stat calculator requires just three inputs: average excess return (alpha), standard deviation of alpha, and time period in years. Click "Calculate" and you'll see how many years of data you'd need for a t-stat of two.

Most fund rating services — Morningstar, Lipper, Bloomberg — hide the standard deviation of alpha. Why? Because it exposes how unreliable most track records are.

IFA's 20-year fund performance chart shows everything you need: average alpha, standard deviation, and year-by-year breakdown. Click "Sort by Fund Company," select a fund, and the data appears. This transparency is the exception, not the rule.

A Note on Benchmarks

The examples ahead use Morningstar benchmarks — the consumer-grade standard. Later, we'll show you what happens when academics apply a stricter test using Fama-French factors. Spoiler: funds that look like winners often vanish under scrutiny. But first, let's see what the standard method reveals.

Testing the Claims: Real Funds, Real Numbers

Theory is one thing. Let's run the test on real funds. We'll start with a dramatic example, escalate to the absurd, and finish with Warren Buffett.

Baron Partners Retail (BPTRX): The One-Year Wonder

Some funds look brilliant — until you examine when the outperformance happened. Baron Partners Retail (BPTRX) is the perfect cautionary tale.

Over 20 years (2005-2024), Baron Partners delivered 110% cumulative excess return versus the Russell 1000 Growth benchmark — roughly 6% annual alpha. Sounds impressive.

The chart below tells a different story. That towering green bar in 2020 accounts for 110.03% — nearly the entire 20-year outperformance. One year. Strip out 2020, and the fund hugged or lagged the benchmark for 19 years.

(excerpt from the Statistical Significance of Alpha Among 2116 U.S. Mutual Funds Chart)

Of the 6% average annual alpha, 5.5% came from a single year. The calculator confirms: Baron Partners needs 73 years to prove skill because the standard deviation is massive (25.76%). That volatility — the wild swings year to year — kills the statistical case.

This chart, then, is the perfect illustration of luck in action. No doubt many investors looked at that 2020 performance and assumed the manager was skillful. But anyone who piled in after that extraordinary one-year result experienced less favorable performance. 

One strong year may reflect chance, not skill. 

The Extreme Outliers: When Luck Screams

If 73 years sounds ridiculous, brace yourself. When alpha is tiny and volatility is wild, the numbers get comical. These are real funds with real investors.

MassMutual Equity Opportunities R5 (MFVSX): 6,882 Years

Average alpha: 0.27%. Standard deviation: 11.36%. T-statistic: 0.11. Time needed to prove skill: 6,882 years.

What happened? One word: 2009. In the post-crisis recovery, MassMutual spiked 35% above its benchmark in a single year. Lucky sector bets at precisely the right moment. Then the alpha vanished. Look at the chart below: one massive peak, surrounded by mediocrity and red bars.

(excerpt from the Statistical Significance of Alpha Among 2116 U.S. Mutual Funds Chart)

This performance may reflect randomness rather than skill. The standard deviation (11.36%) is so high that even 20 years of data can't distinguish this from noise.

Pin Oak Equity (POGSX): 14,718 Years

Average alpha: 0.23%. Standard deviation: 13.68%. T-statistic: 0.07. Time needed to prove skill: 14,718 years.

Same story, bigger magnitude. Pin Oak delivered 51% outperformance in 2009 — in the depths of the crisis. Spectacular. Unrepeatable. Every other year? Tiny gains or losses. The chart is chaos.

(excerpt from the Statistical Significance of Alpha Among 2116 U.S. Mutual Funds Chart)

Again, this is what luck looks like. One massive spike, no consistency, a t-stat indistinguishable from zero.

Imagine you're an investor. You see that 2009 performance. You read the headlines. You think: this manager has the golden touch. You invest heavily in 2010. What happens? The alpha disappears. You get mediocrity for a decade. That's the danger of chasing recent performance — you're buying after randomness has already struck, mistaking the echo for the signal.

Warren Buffett: Even the GOAT Regressed

If anyone could prove skill, it's Warren Buffett. Greatest investor of the modern era. Decades of outperformance studied in business schools worldwide. Let's run the test.

Period One: 1981-2002 (The Golden Years)

(excerpt from the The Decline of Warren Buffett's Alpha chart)

For the first 22 years of our data, Berkshire Hathaway delivered extraordinary results against the Russell 1000 Value benchmark:

• Average alpha: 16.77% per year
• Standard deviation: 25.15%
• T-statistic: 3.13
• Years needed to prove skill: 22 years

This is genuinely exceptional. A t-stat of 3.13 exceeds even Fama's stricter threshold. By statistical standards, this is skill.

But even here, there's a caveat. Benjamin Graham — Buffett's mentor — famously said he made more money on the insurance company GEICO than all my other investments combined. Buffett's single GEICO investment generated more profit than the rest of his portfolio. Was that skill, or one extraordinarily lucky bet early in his career? Even Buffett might call it luck. The concentrated nature of that one bet — documented thoroughly in IFA's analysis — suggests that even the greatest track records often hinge on singular events indistinguishable from fortune.

Period Two: 2003-2023 (The Collapse)

(excerpt from the The Decline of Warren Buffett's Alpha chart)

Now look at the next 21 years. The numbers collapse:

• Average alpha: 0.15% (down from 16.77%)
• Standard deviation: 11.81%
• T-statistic: 0.06
• Years needed to prove skill: 23,988 years

Nearly 24,000 years. For Warren Buffett. In his second act.

What happened? Regression to the mean. As Berkshire grew too large to exploit market inefficiencies, the edge eroded. Buffett himself has acknowledged this: it's harder to move the needle with $500 billion than with $5 million. Even the greatest investor alive couldn't sustain outperformance once scale became a constraint.

If Buffett — with a t-stat of three in his prime — regressed to luck in his second act, what hope does a mid-tier manager have? And here's the brutal truth: by the time you know a manager has skill (after 20 to 50 years of data), that skill has often already faded.

The identification problem is fundamental. If you'd invested with Buffett in 1981, you'd have done spectacularly — but you'd have been betting on someone without a proven track record. If you waited until his record "proved" skill in the early 2000s and invested in 2003, you caught the regression. You got mediocrity for two decades. Timing is everything and unknowable in advance.

The Benchmark Trap: Why Even Winners Don't Always Win

By now you're thinking: "OK, most funds can't prove skill. But what about the tiny number of funds that are in the green zone? Didn't Fidelity Small Cap Growth, for example, pass the test?" Fair question. The answer reveals how benchmarks can flatter mediocrity.

Three Methods, Three Results

Not all benchmarks are equal. The standard investors see — Morningstar's style-box categories — is simplified for consumers. Academics use far stricter methods. Results differ dramatically.

Morningstar benchmarks use broad style categories: large growth, small value, mid-cap blend. Easy to understand, but imprecise. Funds can drift between styles and claim credit for capturing factor premiums that anyone could access via index funds.

Fama-French factors use a three-factor regression model that adjusts for exposure to size, value, and momentum. This is the academic gold standard. If a fund's alpha survives Fama-French adjustment, it's genuinely rare. As Barras, Scaillet, and Wermers demonstrated in their 2010 paper, False discoveries in mutual fund performance, once you account for multiple testing and factor exposures, only about 1% of mutual fund managers display genuine skill and roughly the same proportion show significant anti-skill.

Index funds represent the investor's true goal: zero alpha, zero volatility around that alpha. Just reliable beta — market returns — at minimal cost.

Why does this matter? A fund can look like a winner against Morningstar's benchmark but vanish against Fama-French. The fund wasn't beating the market — it was capturing known factor premiums (like small-cap or value) that academics identified decades ago. That's not manager skill; that's factor exposure anyone can access cheaply.

In other words, Morningstar uses a consumer-simplified methodology that lets managers get away with style drift. The academic three-factor regression model doesn't. It catches them.

The Fidelity Reveal

Fidelity Small Cap Growth (FCPGX) looked impressive against the Morningstar benchmark: 2.99% annual alpha, 4.70% standard deviation. It sat in the green "skill" zone.

Now re-test using Fama-French factors. Watch what happens.

Against Fama-French factors: alpha drops to 0.84%, standard deviation rises slightly to 5.7%, and the fund falls below the t-stat threshold into the red zone. The "skill" evaporated.

What happened? The fund wasn't beating the market through manager skill — it captured size and value premiums academics have known about since the 1990s. "Small growth" funds aren't locked into small growth stocks. Prospectuses allow broad mandates. When value stocks were outperforming, Fidelity tilted toward small value territory. When momentum stocks surged, they chased that factor. They captured factor premiums that anyone could access via low-cost index funds and charged active management fees for it.

If a fund only clears the skill threshold against a consumer-grade benchmark, be skeptical. Demand Fama-French-adjusted results. If it can't survive that test, you're paying active fees to capture passive factor exposure.

The Index Fund Cluster

Go back to the master chart showing all 2,116 funds. See that tight cluster in the bottom-left corner — near zero alpha, near zero standard deviation? Those are index funds.

Index funds don't try to beat the market. They are the market. Zero alpha by design. Zero volatility around that alpha. They sit exactly where investors should aim: reliable, low-cost, low-volatility exposure to market returns — what academics call beta.

Active funds scatter across the red zone — high volatility, insufficient t-stats. The handful in the green zone are rare and vulnerable to benchmark gaming, as the Fidelity example demonstrates. The index fund cluster is where discipline lives.

What This Means for You

The Impossibility Problem

Fund managers don't work for 50, 100, or 150 years. Most have 20 to 30-year careers if they're lucky. By the time you'd have enough data to verify skill statistically, the manager is gone. Retired. Managing a different fund with a different strategy.

Even if a fund has a 20-year track record, it's rarely the same person running it. Teams change, star analysts leave for hedge funds, strategies drift with market conditions. A 20-year fund record is often three to four different managers under the same name. You're not investing in a person — you're investing in a brand. And brands don't have skill; people do. When the person leaves, so does any edge they possessed.

The Costs Are Real, The Alpha Is Not

Active funds charge 0.5% to 1.5% annually — a massive hurdle. If the average winner delivers 1.04% alpha (most of it noise), fees consume the entire "edge" before it reaches your account.

Add taxes. Active funds trade frequently, generating short-term capital gains taxed at ordinary income rates. Index funds are tax-efficient by design; active funds are tax nightmares. After accounting for fees, taxes, and the overwhelming evidence that most alpha is illusory, the case for active management collapses.

William Sharpe's 1991 paper, The Arithmetic of Active Management, proved this mathematically decades ago: before costs, the average actively managed dollar must equal the market return. After costs, the average active investor must underperform. It's not cynicism — it's subtraction.

The Alternative

The logical strategy isn't hunting for the next Warren Buffett. It's capturing beta — the market's return — as cheaply and reliably as possible. Broad diversification across asset classes and geographies. Minimal costs through index funds or evidence-based factor strategies. Factor exposure to size and value if appropriate, captured systematically rather than through active bets. No drama.

Aim for that bottom-left cluster on the scatter plot: zero alpha, zero volatility. That's not boring — it's rational.

Why does this work? Over decades, market returns compound beautifully. The S&P 500 has delivered approximately 10% annualized over the long term. You don't need to beat that — just capture it. Minimize fees, defer taxes through buy-and-hold discipline, and let time work.

Use the Calculator Going Forward

Any time you're pitched a "star" fund — by a broker, an advisor, or a glossy brochure — demand the data. What's the average annual alpha? What's the standard deviation? How many years of data?

Then open the t-stat calculator and run the test. If the result says "100 years," walk away.

Don't accept stories. Don't accept three-year track records. Don't accept "our team is special" or "this time is different." Demand statistical proof that clears the t-stat threshold of two. If they can't provide it — and they almost never can — you have your answer.

The Power Is In Your Hands

You now have a tool that cuts through marketing and hype. Three inputs, one calculator, a definitive answer. You can test whether any track record is skill or luck in 30 seconds.

Once you see that the average winner needs 153 years of data, that spectacular one-year returns typically vanish, and that even Warren Buffett regressed in his second act, you stop chasing mirages.

Here's what to do next:

●     Bookmark the calculator: https://www.ifa.com/t-stat-calculator#tcalc2

●     Test any fund you're considering before investing

●     If the result says "100 years," walk away

●     Focus on capturing market returns with the lowest cost, broadest diversification, and longest time horizon you can manage

Investing isn't about finding heroes. It's about accepting what markets actually reward: patience, diversification, low costs, and discipline. The fund management industry has been selling you a story for decades — the myth of the star manager, the promise of market-beating returns, the allure of superior insight. Now you have the evidence to see through it.

The question was never whether skill exists. A tiny fraction of managers may possess genuine talent. The questions that matter are: Can you identify them in advance? Will they stay at the same fund long enough? Will their edge persist as assets grow? And will the fees leave enough alpha to justify the risk?

For nearly all investors, the answer to all four is no.

Markets are ruthlessly efficient at separating luck from skill — far more efficient than our pattern-seeking brains. Most managers fail. The average winner barely wins and can't prove it. Even the greatest investor alive regressed when scale became a constraint.

As Mark Hebner says in Step 3 of his award-winning book, Index Funds: The 12-Step Recovery Program for Active Investors, you're much better off avoiding active funds together and trusting in the wisdom of millions of stock market investors around the world: "Trust the collective brain, buy the haystack, and maintain risk-appropriate exposures in low-cost globally diversified index portfolios."

Resources

Barras, L., Scaillet, O., & Wermers, R. (2010). False discoveries in mutual fund performance: Measuring luck in estimated alphas. Journal of Finance, 65(1), 179–216.

Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57–82.

Fama, E. F., & French, K. R. (2010). Luck versus skill in the cross-section of mutual fund returns. Journal of Finance, 65(5), 1915–1947.

Jensen, M. C. (1968). The performance of mutual funds in the period 1945–1964. Journal of Finance, 23(2), 389–416.

Sharpe, W. F. (1991). The arithmetic of active management. Financial Analysts Journal, 47(1), 7–9.

Taleb, N. N. (2001). Fooled by randomness: The hidden role of chance in life and in the markets. Random House.

ROBIN POWELL is the Creative Director at Index Fund Advisors (IFA). He is also a financial journalist and the Editor of The Evidence-Based Investor. This article reflects IFA's investment philosophy and is intended for informational purposes only.

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