CAPM Equation – Beta, Risk-Free Rate & Market Return

The mathematical heart of modern finance. This single equation dictates the cost of capital for almost every public company in the world.

The Formula

E(R_i) = R_f + beta_i * (R_m - R_f)

Where:

• E(Ri): Expected Return of asset i (Cost of Equity).
• Rf: Risk-Free Rate (e.g., 10-year Govt Bond Yield).
• Beta_i: Beta of asset i (Systematic Risk).
• Rm: Expected Return of the Market (e.g., Nifty 50 return).
• (Rm - Rf): Market Risk Premium (The extra return demanded for holding stocks over bonds).

Breaking Down the Components

1. Risk-Free Rate (Rf)

The theoretical return of an investment with zero risk.

• Proxy: Typically the yield on the 10-Year Government Bond of the country.
• India: ~7.0%
• USA: ~4.0%

2. Beta (Beta)

Calculated by regressing the stock's returns against the market's returns.

• Formula: Beta = Cov(Ri, Rm) / Var(Rm)
• It is the slope of the regression line.

3. Market Risk Premium (Rm - Rf)

The historical difference between stock market returns and government bond returns.

• Typical range: 4% to 6%.

Calculation Example

Calculate the Expected Return for Tata Motors if:

• Risk-Free Rate (Rf) = 7%
• Beta = 1.2 (More volatile than market)
• Market Return (Rm) = 12%

Solution: Solution:

E(R) = 7% + 1.2 * (12% - 7%)

E(R) = 7% + 1.2 * (5%)

E(R) = 7% + 6% = 13%

Interpretation: Investors demand a 13% annual return to hold Tata Motors. If the company cannot generate 13%, the stock price will fall.

Security Market Line (SML)

If you plot Beta (x-axis) vs Expected Return (y-axis), the CAPM equation forms a straight line called the Security Market Line.

• Undervalued Stocks: Lie above the SML (Offer higher return than CAPM predicts).
• Overvalued Stocks: Lie below the SML.

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