Was that skill, or just a rising market?

A portfolio returned +14% in a year when the market returned +10%. Four points ahead. Before calling that skill, one question has to be answered: how much market was in the portfolio in the first place?

Beta: how much market exposure was carried

Beta measures sensitivity to the market's moves. Formally it is the slope of a regression of the portfolio's returns on the market's returns:

β = covariance(portfolio, market) ÷ variance(market)

A beta of 1.0 means the portfolio has historically moved roughly one-for-one with the market. A beta of 1.4 means about 1.4% of movement for each 1% of market movement — in both directions. A beta of 0.6 means it has historically absorbed only part of the market's swing.

Beta is not a virtue or a vice. It is a description of how much of the market's ride the portfolio has taken on.

Alpha: what is left after paying for the exposure

Given the exposure, there is a return you would expect purely from carrying it:

Expected return = risk-free rate + β × (market return − risk-free rate)

and the remainder is alpha:

Alpha = actual return − [ risk-free rate + β × (market return − risk-free rate) ]

Worked example, using the numbers above with a risk-free rate of 3% and a portfolio beta of 1.4:

• Market excess return: 10% − 3% = 7%
• Expected from exposure: 3% + 1.4 × 7% = 3% + 9.8% = 12.8%
• Alpha: 14% − 12.8% = +1.2 points

The four-point "outperformance" was mostly the portfolio carrying 40% more market exposure than the market itself. Roughly one point of it was unexplained by that exposure.

Now the reverse. A portfolio returned +8% with a beta of 0.6:

• Expected: 3% + 0.6 × 7% = 7.2%
• Alpha: 8% − 7.2% = +0.8 points

It "lagged the market" by two points and still produced positive alpha, because it was never carrying full market exposure. Headline ranking and exposure-adjusted ranking disagree completely.

Two caveats that decide whether any of it means anything

R² — does the market explain this portfolio at all? The regression also produces R², the share of the portfolio's variation the market accounts for. A diversified equity fund might show 0.90; a single gold miner or a market-neutral strategy might show 0.10. When R² is low, the estimated beta is unstable and the alpha computed from it is largely noise wearing a Greek letter.

Yesterday's alpha is today's beta. A great deal of what earlier decades measured as alpha was later identified as exposure to systematic factors — smaller companies, cheaper valuations, momentum, quality, low volatility. Once a pattern is identified and cheaply investable, the return attributable to it stops being anyone's skill and becomes another beta. Each generation of research converts some alpha into exposure.

None of this identifies a manager worth hiring or an asset worth buying. It converts a headline gap into two components — exposure and residual — which is a better question, not an answer.

In the data

A beta is always a beta against something. Apple over the same 120 sessions, measured against the S&P 500 index and then against the Nasdaq-100 fund, each at the first and the latest date of the series:

Same stock, same window, different betas. The yardstick is the whole argument: the residual left over as alpha is a property of the pair you chose, not of the asset.

Try it now

1. Three years of monthly bars for one stock, Apple, and one broad index, the S&P 500. Both series are below; switch each chart to Monthly, Measure every month from January 2023 to December 2025, and write the two columns of monthly returns down.

2. Subtract a cash rate from both series. Use the 3% a year from the example above, 0.25% a month, as a flat stand-in; a real test would use each month's bill rate. Then regress the stock's excess returns on the index's excess returns (any spreadsheet will do it). The slope is beta; the intercept is the monthly alpha — multiply it by 12 for an annual figure. Regressing raw returns instead gives an intercept of alpha + risk-free × (1 − beta), which at the 3% rate and 1.4 beta used above is off by −1.2 points a year, which in this example cancels the alpha exactly: regress raw returns and the +1.2 you were looking for reads as zero. To check your work: the same regression on month-end adjusted closes, computed on 28 September 2026 over the 36 months of 2023 to 2025, gives a slope of 0.92, a monthly intercept of 0.73% (about 8.8% a year) and an R² of 0.27. Readings taken off a chart land near those, not on them.
3. Read the R². Then compare your regression slope with the 120-session betas against the S&P 500 in the section above; they cover different windows and different bar lengths, so expect them to differ. State, in one neutral sentence, how much confidence that R² and that spread of betas justify in the alpha you just computed.