Capital asset pricing model

The Capital Asset Pricing Model, CAPM, turns the frontier's conclusion into a price. It dates from the early 1960s (Sharpe, Lintner, Mossin), and Sharpe shared Markowitz's Nobel. We'll keep the derivation intuitive and straight:

Step 1: the right question. If every diversified investor holds the market portfolio, then when they consider one more rupee of stock i, the question is never "how volatile is i?" It's "how much risk does i add to my market portfolio?" You already know that added risk in a large portfolio comes from covariance, because the diversification argument settled it. A stock's marginal contribution to the market portfolio's risk is proportional to its covariance with the market. A stock with high σ but low co-movement adds little, while a modest-σ stock that swings with the cycle adds a lot.

What is beta, and how do you calculate it?

Step 2: standardise the measure. Divide each stock's covariance with the market by the market's own variance, so the market itself scores 1 by construction:

β(i) = Cov(Ri, Rm) / Var(Rm)

That's beta: the stock's systematic risk expressed as a multiple of the average. It has a second, equivalent life that makes it concrete. Plot the stock's periodic returns against the market's and fit the straight line through the scatter. Beta is the slope. When the market moves 1%, the stock tends to move β%. Worked Example 2 computes one by hand from a six-quarter table: deviations, products, covariance, variance. Give it twenty minutes and covariance stops being abstract for good.

Calibrate your instincts with typical published values. They drift with the estimation window and the index, so always check the current figure on your screener (illustrative as of mid-2026):

Beta runs high for economic reasons. It isn't a statistical accident. (1) Demand can be cyclical. Cars and cranes are postponable, soap isn't. (2) Operating leverage turns small revenue swings into large profit swings when fixed costs are high. (3) Financial leverage does the same one layer down, for equity holders, through debt. You'll exploit this in the full cost-of-capital build. Instead of trusting one noisy regression, you'll build beta bottom-up from the business's sector and leverage.

What is the CAPM formula?

Step 3: the pricing line. If co-movement is the only priced risk, and the market portfolio carries one unit of it, then expected returns must line up in proportion to beta:

E(Ri) = Rf + βi × (E(Rm) − Rf)          …the CAPM
                └── the equity risk premium (ERP) ──┘

Rf is the risk-free rate, a default-free government bond yield matched to the currency, which gets refined when you build the full WACC. E(Rm) − Rf is the equity risk premium, the extra return the market demands for holding average-risk equity. Beta scales it. Carry twice the average systematic risk and you earn twice the premium. Plotted with β across and E(R) up, this is a straight line from Rf through the market point, the security market line (SML). In CAPM's world every fairly priced asset lies on it.

Read the formula's radical claim once more. A stock's own σ appears nowhere. Two stocks with identical 40% volatility can have required returns of 8% and 16% if one's turbulence is mostly firm-specific and the other's is mostly cyclical. Firm-specific turbulence gets diversified away and goes unpaid. Cyclical turbulence can't be diversified, so it gets paid. CAPM is the diversification argument turned into a price, nothing more.

CAPM example: US and India required returns

Try a worked one-liner each way (inputs illustrative, so check the current values). In the US, with Rf = 4.2% and ERP = 4.3%, a β = 0.55 staples business prices at 4.2 + 0.55×4.3 ≈ 6.6% and a β = 1.7 chipmaker at 4.2 + 1.7×4.3 ≈ 11.5%. In India, with a clean INR Rf = 4.5% and an India ERP of 7.1%, both built on the country risk premium page, a β = 1.0 domestic lender prices at 4.5 + 7.1 = 11.6% in rupees. It's the same machine with a different premium, and the country-risk build explains the difference.