The CAPM

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Project 5: A Simple Model in Asset Pricing

Jonathan K. Ramani

Overview

This project introduces and explains the Capital Asset Pricing Model (CAPM) — a fundamental framework in financial economics used to understand the relationship between risk and expected return. CAPM provides a simple but powerful formula to price risky securities and is widely used by investors and financial analysts.

What is CAPM?

The Capital Asset Pricing Model states that the expected return of a security is equal to the risk-free rate plus a risk premium. The formula is given by:

[ E(R_i) = R_f + \beta_i (E(R_m) - R_f) ]

Where:

  • ( E(R_i) ): Expected return of asset i
  • ( R_f ): Risk-free rate
  • ( \beta_i ): Beta of the asset (a measure of systematic risk)
  • ( E(R_m) ): Expected return of the market portfolio

Key Concepts

  • Risk-Free Rate: The return on an investment with zero risk, typically government bonds.
  • Market Risk Premium: ( E(R_m) - R_f ), the excess return expected from the market over the risk-free rate.
  • Beta (( \beta )): A measure of an asset’s sensitivity to market movements.
    • ( \beta = 1 ): asset moves with the market.
    • ( \beta > 1 ): asset is more volatile than the market.
    • ( \beta < 1 ): asset is less volatile.

Assumptions of CAPM

  1. Investors are rational and risk-averse.
  2. Markets are efficient.
  3. Investors can borrow and lend at the risk-free rate.
  4. Homogeneous expectations about returns and risks.
  5. Single-period investment horizon.

Applications

  • Portfolio Management: Identifying undervalued or overvalued assets.
  • Cost of Equity Calculation: In corporate finance, CAPM helps compute the cost of equity for discounting cash flows.
  • Performance Evaluation: Comparing actual returns to those predicted by CAPM.

Limitations

  • Relies on assumptions that may not hold in the real world (e.g., perfect markets).
  • Beta is based on historical data and may not predict future risk accurately.
  • Fails to account for unsystematic risk.

Conclusion

Despite its limitations, CAPM remains a foundational model in finance. Its simplicity and intuitive appeal make it a cornerstone in understanding how risk affects return. This project outlines the logic behind CAPM and serves as a stepping stone to more advanced asset pricing theories.

This project draws upon foundational work in financial theory, notably:

  • Sharpe, William F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.”
  • Lintner, John (1965), “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.”

Last updated: June 2025

References