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Beta Refresher

“What is beta?” sounds like a warm-up question and is where a lot of candidates quietly come apart — usually by describing volatility. Beta is the slope of a regression, and a share can be enormously volatile with a beta near zero. Generate a series with a beta you choose, regress it back, and watch how far the estimate lands from the truth you already know.

Then the three adjustments that actually come up: raw to adjusted, levered to unlevered, and bottom-up from a peer set.

Beta is a slope, not a speed. It is what you get when you regress a stock’s returns on the market’s: how much of its movement travels with the market. A share can be wildly volatile and still have a low beta, if almost none of that volatility is shared with anything else. That distinction is the whole reason CAPM uses beta rather than standard deviation — diversification removes the rest, so investors are not compensated for it.

Build a return series

These returns are generated, so unlike real data we know the beta that produced them. The gap between that number and the one the regression recovers is the estimation error — visible rather than described.

Same true beta, different luck. Watch the estimate move while nothing about the company has changed. That is sampling error, and it is why one regression beta is a weak number.

Market return, weeklyStock return, weekly
fitted, β = 1.33 true, β = 1.30
Estimated beta
1.33
true 1.30 · off by 0.03
95% interval
1.09–1.56
±0.24 on the slope
0.54
54% market-driven
Stock volatility
27%
market 15% · annualised

Read this before the number. The stock is running at 27% annualised volatility against a market at 15%, and only 54% of its variance is explained by the market. The other 46% is company-specific, and a diversified investor holds it away to nothing — which is exactly why beta prices only the first part. Raise the noise slider and watch total volatility climb while beta does not move: volatility and beta are different questions.

1 · Raw to adjusted

Betas drift toward 1.0 over time, so the regression estimate is shrunk two-thirds of the way from itself toward the market. It is a shrinkage estimator, not a theory about the company.

Raw regression beta1.326
× 0.670.888
+ 0.33 × 1.000.330
Adjusted (Blume)1.218

The trap: Bloomberg’s BETA screen and most FactSet pulls report the adjusted figure in the headline slot without labelling it. Apply Blume to a number you took off a screen and you have shrunk it twice.

2 · Levered to unlevered

An observed beta contains both the risk of the business and the risk the borrowing adds. Strip the financing out and what remains is the asset beta — comparable across companies with different debt loads.

βU = βL / (1 + (1 − t) × D/E)
Levered beta (adjusted)1.218
At D/E0.35
Unlevered0.965

Leverage raises the equity beta because debt holders are paid first: the same swing in operating profit lands on a thinner slice of equity. More debt, more amplification.

3 · Bottom-up

Unlever every comparable at its own structure, take the median, relever at yours. It beats one regression on precision, and it is the only route when there is no share price — a private company, a pre-IPO business, a new division.

Peer A1.28 @ 0.45 0.957
Peer B0.94 @ 0.12 0.862
Peer C1.51 @ 0.80 0.944
Peer D1.10 @ 0.30 0.898
Peer E1.67 @ 1.10 0.915
Median unlevered0.915
Bottom-up beta1.155

Four things people get wrong

✗ “Beta measures how risky a stock is.

Beta measures only the part of risk that moves with the market. Total risk is volatility. A biotech awaiting a trial readout can be enormously risky and have a beta near zero, because its risk has nothing to do with the index.

✗ “A beta is a property of the company.

It is a property of the company and the index and the window and the return frequency. The same business prints different betas against the S&P and against STOXX. Quote a beta without those four and it cannot be checked.

✗ “A high R² means a reliable beta.

R² tells you how much the market explains, not whether the slope is precise. What you want is the standard error. A low-R² name can still have a tight slope estimate if the market moved enough over the window.

✗ “Negative beta means the stock always falls when the market rises.

It means that on average, over the window, it leaned the other way. With a low R² that lean may be noise. Genuine negative-beta assets are rare, which is what makes them expensive when they exist.

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