Module 5 · Risk, return and the cost of equity Core

Investors demand a higher expected return for bearing more risk. The question is which risk counts.

Two kinds of risk

Company-specific (unsystematic) risk comes from events affecting one firm: a product recall, a lawsuit, a strike. It can be diversified away by holding many stocks. Market (systematic) risk comes from economy-wide events: recessions, interest rates, inflation. It cannot be diversified away. Because diversification is nearly free, the market pays a premium only for systematic risk.

Beta

Beta measures how much a stock moves with the market. A beta of 1.0 moves with the market; 1.5 moves 50% more; 0.5 moves half as much. Beta is estimated by regressing the stock's returns on the market's returns, typically over two to five years.

The capital asset pricing model

• Risk-free rate: the yield on a long-term government bond in the same currency as the cash flows.
• Equity risk premium (ERP): the extra return investors expect from stocks over government bonds. Historical estimates for developed markets cluster around 4% to 6%.
• Example: risk-free 3.5%, beta 1.2, ERP 5%: cost of equity = 3.5% + 1.2 x 5% = 9.5%.

Leverage and beta

Debt makes equity riskier, so observed (levered) betas reflect each company's capital structure. To compare companies or to value a private firm, remove the effect of debt, then add back the target's own leverage.

• Unlevered beta = levered beta / [1 + (1 minus tax rate) x debt/equity]
• Relevered beta = unlevered beta x [1 + (1 minus tax rate) x debt/equity]

Example: a peer has a levered beta of 1.2, debt/equity of 0.5 and a 25% tax rate. Unlevered beta = 1.2 / 1.375 = 0.873. For a target with debt/equity of 1.0, relevered beta = 0.873 x 1.75 = 1.53.

Alternative: the dividend growth model

Cost of equity = next year's dividend / price + growth rate. A stock at $40 paying $2 next year and growing 4% implies 5% + 4% = 9%.

Adjustments used in practice

Some analysts add a size premium for small companies, a country risk premium for emerging markets, or a company-specific premium for private firms. Each is a judgment; state it and keep it modest.

Limits of the CAPM

Beta is unstable over time, the ERP cannot be observed directly, and research shows other factors (size, value, profitability, momentum) also explain returns. RS 302 covers this. The CAPM remains the standard starting point because it is simple and its inputs are available.

The equity risk premium in practice

There are three ways to estimate it. Historical: the average excess return of stocks over government bonds, which depends heavily on the period and on whether arithmetic or geometric averages are used. Surveys: what CFOs and analysts say they expect. Implied: the rate that equates today's index level with forecast dividends, buybacks and growth. Implied estimates for the US have mostly ranged between about 4% and 6% over recent decades. Most practitioners use a figure in that range and state it.

Estimating beta well

Choices change the answer: the index (S&P/TSX Composite or a world index), the frequency (weekly or monthly), the period (two or five years) and whether the company's business has changed. Raw betas are noisy and drift toward 1, so services publish adjusted betas, commonly 2/3 x raw beta + 1/3. A raw beta of 1.6 becomes 1.40. An industry average of unlevered betas, relevered to the target's debt, is usually more reliable than one company's own regression.

Country risk

A company with operations in a riskier country may add a country risk premium, often estimated from the spread of that country's US-dollar government bonds over US Treasuries, scaled up for the higher volatility of equities. Apply it in proportion to the company's exposure, not to every company headquartered there.

What the cost of equity is not

It is not the dividend yield, and it is not the return the company 'pays' its shareholders. It is the return investors expect for bearing the risk, and the company must beat it to create value.

Put it into practice