You've already defined beta as co-movement priced by a diversified investor, and computed one from a return table. Every finance portal does the same thing on an industrial scale. It regresses the stock's returns on an index and reports the slope. Before you paste that number into a valuation, look at what it's made of.
Why is a regression beta so noisy?
There are four degrees of freedom in that slope, and nobody discloses them. (1) Period. Is it 2 years or 5? Five years of monthly data includes a company that may no longer exist in any economic sense. A firm that de-levered, divested, or pivoted drags its ghost through the regression. (2) Return interval. Daily returns behave differently from weekly or monthly ones. Daily betas on thinly traded stocks are biased down by non-synchronous trading. Your stock "didn't move today" because it didn't trade, and that says nothing about how risky it is. This bias is endemic in Indian small- and mid-caps. (3) Index. Nifty 50, Sensex, Nifty 500, MSCI India, S&P 500? Each gives a different slope for the same stock. (4) Adjustments. Bloomberg's default "adjusted beta" is (2/3) × raw + (1/3) × 1.0. That's a crude mean-reversion patch, and betas do drift toward 1 as firms diversify and mature, but a patch isn't a measurement.
Then there's the standard error, and it's the worst part. A typical single-stock regression beta carries a standard error of ±0.2 or worse, and on Indian mid-caps ±0.3 is routine. So your "β = 1.10" really means "β ∈ [0.7, 1.5] at 95% confidence." Run that through CAPM with India's ERP of 7.1%. The band runs from 4.5 + 0.7×7.1 = 9.5% to 4.5 + 1.5×7.1 = 15.2%, a cost of equity that's uncertain by ~6 points. At a Gordon terminal value, that's the difference between a business worth 20× next year's cash flow and one worth 9×. That's a lot of value riding on one noisy slope. On its own, a regression beta is a rumor.
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What is beta actually made of?
So what is beta actually made of? Step back to economics. A business's sensitivity to the market's tides comes from three layers:
- Cyclicality of demand. Discretionary purchases (cars, hotels, capital goods) swing with incomes. Staples (soap, salt, medicines) don't. Cement gets poured when the economy builds, and toothpaste gets bought regardless.
- Operating leverage. High fixed costs amplify revenue swings into profit swings, the margin mechanics from your ratio toolkit. An airline and a staffing firm can share demand cyclicality, but the airline's fixed fleet makes its profits far more violent.
- Financial leverage. Debt is a fixed claim ahead of equity, so every rupee of it makes the equity slice riskier. This layer is mechanical, and that's good news, because mechanical means adjustable by formula.
What is a bottom-up beta?
Layers 1 and 2 belong to the business. Layer 3 belongs to the balance sheet. So you measure the business risk from an average of many firms in the same business, where the noise cancels, and then bolt on the specific company's own balance-sheet arithmetic. That's the bottom-up beta.