Risk and the cost of capital

01diversification and the capm

Cost of equity, CAPM

rE = rf + β × ERPr_f the risk-free rate, ERP the equity risk premium.

Beta as a regression slope

β = Cov(ri, rm) / Var(rm)r_i the share's returns, r_m the market's; this is the slope of the least-squares line.

• Two dimensions: return and variance¹

  Harry Markowitz showed that, under given conditions, choosing a portfolio can be reduced to balancing two things: its expected return and its variance. Risk becomes a property of the portfolio, not of each asset alone - which is why diversification is worth something.

• The CAPM: return in proportion to beta^1,2

  William Sharpe's capital asset pricing model says that in an efficient market an asset's risk premium, and so its expected return, varies in direct proportion to its beta - its sensitivity to the market as a whole. In practice the cost of equity is the risk-free rate plus beta times the equity risk premium.

• Beta is a regression slope, and an unlisted company has to borrow one³

  Beta is estimated by regressing a stock's returns on the market's: the slope of the line. That needs a traded price. For a private company, a project or a division there is no return series to regress, so beta is taken from listed companies that are similar enough to stand in for it.

• The cost of debt comes from the market, not the CAPM³

  Nothing in theory stops the CAPM being applied to debt, but in practice banks price it by benchmarking: the credit spreads on comparable debt issues, added to the risk-free rate. That is DCM's daily work, and the debt capital markets page covers it.

next: the weighted average cost of capital →

02the weighted average cost of capital

WACC

WACC = (E/V)·rE + (D/V)·rD·(1 − t)E and D at market value, V = E + D, t the tax rate.

• The formula²

  WACC equals the equity share of the firm's market value times the cost of equity, plus the debt share times the cost of debt times one minus the tax rate. It is the discount rate for cash flow available to all capital providers, and the hurdle rate a new project has to clear.

• Why debt is taxed down²

  Interest is deductible from taxable income, so the after-tax cost of debt is lower than its coupon. That single line is where the tax advantage of borrowing enters a valuation - and it is one of the assumptions the capital structure page shows the theory setting aside.

• Frankfurt against Milan, worked (illustrative)^2,4

  Take a company with a beta of 1.2, an illustrative 3% risk-free rate, debt at 5% making up 30% of its value and a 30% tax rate. With Germany's 4.23% premium from the section below, r_E = 3% + 1.2 × 4.23% = 8.08% and WACC = 0.7 × 8.08% + 0.3 × 5% × 0.7 = 6.70%. With Italy's 6.69%, r_E = 11.03% and WACC = 8.77%. Valued as 100 a year growing at 2% for ever, the business is worth 100 / (6.70% − 2%) = 2,126 in the first case and 100 / (8.77% − 2%) = 1,477 in the second: the same cash flows, about 31% less value. Scaling the whole premium by beta is one simple convention among several.

next: the equity risk premium, as of january 2026 →

03the equity risk premium, as of january 2026

• What investors are pricing in⁵

  The implied equity risk premium is an internal rate of return for stocks: the rate that equates the index level to its expected cash flows from dividends and buybacks, less the risk-free rate. For the S&P 500 at the start of 2026 Damodaran puts it at 4.23%, on an expected return of 8.41%.

• The same company, a different premium by country⁴

  A country risk premium is added to the mature-market figure where a sovereign carries default risk. At the start of 2026 that left Germany, Switzerland and the Netherlands at the 4.23% base, the UK and France at 5.01%, Spain at 5.78% and Italy at 6.69%. A Milan deal and a Frankfurt deal start from different discount rates.

• Quote it with its source and its date^4,5

  Estimates differ by what they measure, even from one author: 4.23% implied for the S&P 500, 4.46% as the total US premium once a country premium is added. Both move with the market, as do the risk-free rates under them on the market-awareness page.

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