CAPM: how beta turns the market risk premium into a discount rate

CAPM answers one practical question: what return a shareholder is entitled to demand if they agree to bear only the risk that diversification cannot remove. The answer is the sum of the risk-free rate and the market risk premium multiplied by the company's beta. In corporate finance this is no academic exercise: the resulting figure becomes the cost of equity, feeds into WACC, from there into the rate used to discount cash flows, and into the test of whether a project creates value or eats it away. A condensed definition of the model is in the glossary: the entry on CAPM, CAPM.

Which risk the model actually prices

The logic of the model rests on a distinction that usually gets lost when people talk about stocks. The risk of an individual security splits into a part that is unique to the issuer — a fire at the plant, a lawsuit, the departure of the management team — and a part that is common to the whole market: interest rates, the cycle, investors' attitude to risk in general. The first part is cancelled out by the portfolio itself, through a spread of different names; the market will not pay for bearing it, because avoiding it costs nothing. The second cannot be cancelled out by any set of stocks, and it is precisely for this part that the investor earns a premium.

This leads to the key property of CAPM: all uncertainty in it is reduced to the market factor. The model, proposed by Sharpe in 1964, deliberately simplifies the world so that the output is a number that can be plugged into a valuation. That is both its strength and the source of its errors.

Where each component comes from

The risk-free rate. In Russian practice it is taken from the yield on government bonds with a maturity comparable to the horizon of the cash flows being valued. The yield curve and the list of issues are on the OFZ page; the general section on the debt market is bonds. A typical mistake is to take a short rate for a long project: the maturity of the instrument must match the timing of the cash flow.

The market risk premium. This is the excess return that equities deliver on average over the risk-free rate. It is either estimated from the historical difference or derived from current prices and expected dividends — the second route is related to the Gordon model and the dividend discount model, where the premium is obtained as the residual after the growth rate is subtracted. Different methods give different values, and an honest valuation always states which method was chosen and why.

Beta. The sensitivity of a security's return to the return of the market. It is calculated by regressing the stock's returns on the index's returns; the result depends on the observation window, the frequency of the data and the choice of index. For thinly traded securities the estimate is biased downwards — there are few trades, the security "does not have time" to react, and the model reports a deceptively low risk. Check liquidity and price history on the instrument's page: the equity market, {{instrument:SBER}}.

Beta is not volatility

These concepts are confused all the time. Volatility measures the range of a security's fluctuations in its own right; beta measures how far those fluctuations coincide with the market. A security can jump around more than the index and still have a low beta if it moves for reasons of its own and out of step with the market. For CAPM only the correlated part of the movement matters — the part that a portfolio will not smooth out.

This has a consequence for corporate finance: a company's beta depends on both its business and its debt. Debt amplifies the sensitivity of equity to market swings, which is why the betas of comparable companies are converted to their unlevered form and then relevered with the capital structure of the firm being valued. Without this step a comparison with a "peer" is meaningless: you are comparing different levels of financial leverage.

The steps for calculating the cost of equity

Step 1 — choose the valuation horizon and select a risk-free rate to match it. Step 2 — estimate the market risk premium and record the method. Step 3 — obtain beta: from the security itself if there is enough history, or from a group of peers with an adjustment for leverage. Step 4 — assemble the cost of equity and combine it with the cost of debt in WACC, using the weights of the market capital structure rather than the book capital structure. Step 5 — sanity-check the result: compare the implied valuation with market multiples, for example 3,77, and with the reported figures in the issuer financial statements section.

Where the model stops working

CAPM is more sensitive to its inputs than it looks: a small shift in the risk premium or in beta noticeably changes the present value of long-dated cash flows. This is classic model risk — on model risk — and the cure is not to refine the decimal places but to run a sensitivity analysis: show a range, not a point.

Some limitations are worth keeping in mind. Historical beta describes the past and says nothing about a change of business model. For small-cap companies and for securities with a thin order book the model systematically understates the required return. The dividend forecasts that are sometimes used to calibrate the premium have a life of their own — see the payment calendar in the dividends section. Finally, the corporate discount rate is calculated before the investor's taxes: the shareholder's actual return is reduced by tax, the base for which is determined separately — 13%.

Assessing credit quality, as opposed to the cost of capital, calls for a different tool — scoring models such as the Altman model, the Altman model article. CAPM and the Z-score answer different questions, and you cannot substitute one for the other.