What it means
Most of an equity portfolio's return comes from the market. If the market rises 10% and a fund rises 12%, the extra 2% might be skill, might be luck, or might be the result of taking more risk than the market: holding volatile stocks that rise more when the market rises and fall more when it falls.
Alpha corrects for that last possibility. Using the Capital Asset Pricing Model, the expected return of the fund is the risk-free rate plus the fund's beta multiplied by the market's excess return over the risk-free rate.
Alpha is the actual return minus that expected return. A fund with a beta of 1.5 that returns 12% when the market returns 10% has not produced alpha; it has produced roughly what its extra risk would predict.
Alpha is what active managers are paid to deliver and what index funds do not attempt. The evidence is that alpha is scarce: after fees, most active funds have negative alpha over long periods, and the managers who produce positive alpha in one period do not reliably repeat it.
This is the foundation of the case for low-cost index investing, and also the reason genuine alpha commands high fees when it can be identified. The measure depends on the model.
Single-factor alpha against a market index can be inflated by exposures to other rewarded factors such as small size, value or momentum; multi-factor models strip those out and often reduce the apparent alpha of managers whose "skill" was a consistent tilt. Alpha also needs enough time to be distinguished from noise: a year or two of outperformance is consistent with luck, and statistical tests typically need many years of data to conclude that alpha is real.
For a company rather than a fund, the same idea underlies economic value added: the return earned on capital above the return investors require for the risk. In both settings alpha is the answer to the question "did this earn more than it should have, given what it was?"
In practice
Real-world examples.
Example
An equity fund reports a three-year alpha of 2.4% against its benchmark and highlights it in marketing; a consultant notes that against a multi-factor model including value and size, the alpha is 0.3%.
Example
A pension scheme replaces an active manager with an index fund after twelve years in which the manager's alpha averaged minus 0.8% after fees.
Example
A hedge fund charges a performance fee only on returns above a market-linked hurdle, so that investors pay for alpha rather than for beta.
Think of it
“Alpha is like a student's grade relative to their predicted score based on study time. If they score higher than expected, that extra is alpha.
Formula
Calculation
Alpha = Actual Portfolio Return minus [ Risk-free Rate + Beta x (Market Return minus Risk-free Rate) ]
The bracketed term is the expected return from the Capital Asset Pricing Model.
Worked example. Over a year, a fund returned 14.5%. The market index returned 11%, the risk-free rate was 3%, and the fund's beta, measured from its historical relationship with the market, is 1.2.
- Expected return = 3% + 1.2 x (11% minus 3%) = 3% + 9.6% = 12.6%
- Alpha = 14.5% minus 12.6% = 1.9%
The fund beat the market by 3.5 points, but 1.6 points of that was compensation for its higher beta. The manager's skill, on this model, is worth 1.9 points. After a 1% management fee the investor's net alpha is about 0.9%.
Comparison with a second fund that returned 13% with a beta of 0.8:
- Expected return = 3% + 0.8 x 8% = 9.4%
- Alpha = 13% minus 9.4% = 3.6%
The second fund returned less than the first but produced more alpha, because it did so with less market risk. Over ten years, an investor would be more confident that the second manager's outperformance was skill, though even a decade may not be conclusive.
Statistical caution: if the fund's alpha varies by plus or minus 6% from year to year, a single year's 1.9% is well within the range of luck. Roughly speaking, the manager would need to sustain that average alpha for around ten years for a standard test to reject luck with confidence.Case study
Seen in the real world.
A family office had employed an equity manager for eight years who had beaten the index in six of them, by an average of 2.5% a year, and was regarded as a star. A new chief investment officer commissioned a factor analysis. The manager's portfolio had a beta of 1.25 and a persistent tilt towards smaller companies and towards stocks with strong recent price momentum.
Against the plain index, alpha was 2.5%. Adjusted for beta, it fell to 0.9%. Adjusted for the size and momentum factors, which could be bought through cheap index products, it fell to minus 0.4%, and the manager's 1.2% fee made the net figure minus 1.6% a year.
The family office replaced the mandate with a low-cost portfolio of factor index funds built to replicate the manager's exposures, and saved about $2 million a year on a $150 million portfolio for the same expected return. The chief investment officer's summary was that the office had been paying alpha fees for beta.
Watch out
Common mistakes.
- Reading outperformance as alpha without adjusting for risk. Higher returns from higher beta are not skill.
- Judging alpha over short periods. A few years of outperformance are consistent with luck.
- Comparing alpha before fees. Investors receive alpha net of what the manager charges.
Questions
People also ask.
What is the difference between alpha and beta?
Beta measures how much a portfolio moves with the market, and the return that comes from that exposure. Alpha is the return above what beta predicts.
Is positive alpha common?
No. After fees, most active managers show zero or negative alpha over long periods, and persistence among the minority who show positive alpha is weak.
Can a company have alpha?
In the sense of earning returns on capital above those its risk would justify, yes. Economic value added and similar measures capture that idea.
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