The question
My fund beat its benchmark by almost 5 points a year. Is that skill or luck?
The idea
- Three scorecard numbers answer it together.Beta: how far the fund moves for each 1% its benchmark moves. A beta of 1.2 means it tends to rise 1.2% when the benchmark rises 1%, and fall 1.2% when it falls.Alpha: the yearly return beyond what beta predicts. Some of a lead is just extra market risk. Alpha is what remains.R²: the share of the fund's weekly moves the benchmark explains, 0 to 1. Near 1, it is a good yardstick.
- Alpha is an estimate with a margin of error, its standard error. The t-stat is alpha divided by that margin. Below 2, the alpha could be chance. The scorecard also prints a 95% range for alpha. If it includes zero, zero alpha cannot be ruled out.
- All three use excess return: the return above Treasury bills, the near-riskless rate (Intermediate lesson 2). Only that part pays for risk.
Worked example
The 5 steps beside the drawing at the top work this through on ETFIQ data. Point at a step to light the part of the drawing it describes.
AVUV is an actively managed Avantis fund of cheap-looking small US companies. Its benchmark is the Russell 2000 Value Index, measured through IWN, a fund that tracks it. Window: Oct 4, 2019 to Nov 6, 2026, 370 weekly returns. (Not a pick.)
| AVUV | IWN | |
|---|---|---|
| Return a year | 15.28% | 10.61% |
| Above Treasury bills | 15.11 points | 10.49 points |
What that means: over this window the data cannot tell skill from luck yet. Another year or so of the same lead would push the t-stat past 2.
The common mistake
"A big, significant alpha proves skill." Check R² first. SMH, a semiconductor fund, is measured against world stocks (ACWI). From Dec 30, 2011 to Nov 5, 2026, its alpha was +11.7% a year with a t-stat of 2.71: significant. But its R² was 0.63. World stocks explain under two thirds of a chip fund's moves.
So that "alpha" is mostly a one-industry bet. Real return, but not proof of skill.
A second mistake: ignoring the window. A short one makes the range wide.
Check your understanding
Pick an answer to see why. Two of three right passes the lesson.
1. A fund's beta to its benchmark is 1.2. The benchmark earned 8 points above bills; the fund earned 11. Roughly what is its alpha?Answer: C. 1.4 points. beta predicts 1.2 × 8 = 9.6; 11 − 9.6 = 1.4. Not A: 3 ignores the extra risk.2. A fund shows alpha of +3% a year with a t-stat of 2.4, but R² against its benchmark is 0.40. What is the fair reading?Answer: D. The alpha passes the chance test, but the benchmark may be the wrong yardstick. 2.4 passes the test, but R² of 0.40 means the benchmark explains little. Not A: a poor fit mostly measures the bet itself.3. An alpha's 95% range is −1% to +5%. What can you say?Answer: A. An alpha of zero cannot be ruled out. the range crosses zero. Not B: the middle is positive, but zero is allowed.
Takeaways
- Alpha is the return left after beta, not the whole lead.
- Check R² first: alpha means little against a poor-fit benchmark.
- A t-stat under 2, or a range crossing zero, means the edge is unproven.