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Capital Asset Pricing Model

A clear, simple guide to the Capital Asset Pricing Model. Learn the CAPM formula, what beta means, how to compute expected return, assumptions, limits, and a worked example.

Quick summary

The Capital Asset Pricing Model, or CAPM, is a way to estimate the return an investor should expect for taking on risk. It links the expected return of an asset to how much that asset moves with the market. You use CAPM to find a fair required return. That helps with valuing stocks, setting discount rates, and judging portfolio performance.

The CAPM formula

Expected return = Risk-free rate + Beta × (Market return − Risk-free rate)

Written another way:

E[R_i] = R_f + β_i × (E[R_m] − R_f)

Where:

  • E[R_i] is the expected return of the asset.
  • R_f is the risk-free rate.
  • β_i (beta) measures how much the asset moves with the market.
  • E[R_m] − R_f is the market risk premium.

What each piece means

  • Risk-free rate. This is a rate you can earn with no risk. In practice people use short-term government bills for short projects or long-term government bonds for long projects. Pick the one that matches your time horizon.

  • Market return. This is the return of the broad market, like the S&P 500. The market risk premium is the extra return the market gives over the risk-free rate.

  • Beta. Beta shows sensitivity to market moves. If beta = 1, the asset shows the same risk as the market. If beta = 1.5, the asset tends to move 1.5 times as much as the market. If beta = 0.5, it moves half as much. Beta can be negative for assets that move opposite the market.

Why CAPM matters

  • Cost of equity. Companies use CAPM to set the required return for equity. That feeds into weighted average cost of capital and valuation.

  • Portfolio choice. CAPM helps decide how much return you need for added risk.

  • Performance check. If a stock returns more than CAPM predicts after risk, it may have positive alpha. If it returns less, alpha is negative.

Example

Assume:

  • Risk-free rate R_f = 3%
  • Expected market return E[R_m] = 9%
  • Stock beta β = 1.2

Market risk premium = 9% − 3% = 6%

Expected stock return = 3% + 1.2 × 6% = 3% + 7.2% = 10.2%

So the stock should earn about 10.2% given its market risk.

How to estimate inputs

  • Beta. Use regression of the stock returns against market returns. Many financial sites list beta estimates. Look at betas over different windows to see stability.

  • Risk-free rate. For short-term analysis pick a short government bill. For long-term projects pick a long government bond.

  • Market return. Use a long-term historical average or survey-based forward estimates. Common historical market premium values range from 4% to 7% depending on the country and period.

Assumptions behind CAPM

  • Investors are rational and care only about mean and variance of returns.
  • Markets are efficient. Prices reflect all information.
  • Everyone can borrow and lend at the risk-free rate.
  • One period model and no taxes or transaction costs.
  • Investors hold diversified portfolios that look like the market portfolio.

These assumptions are strong. They make the model simple. They also limit how accurate CAPM is in practice.

Strengths

  • Simple and intuitive.
  • Easy to compute and use in practice.
  • Gives a clear benchmark for required return.
  • Widely used in finance, corporate valuation, and regulation.

Limitations and common issues

  • Beta is not always stable. It can change over time.
  • The market portfolio is not directly observable. We use a proxy like the S&P 500.
  • CAPM is a single factor model. Real returns may depend on other factors like company size or value.
  • Empirical tests show anomalies. Low beta stocks sometimes outperform what CAPM predicts. Small stocks and value stocks also show patterns CAPM does not explain.
  • Assumes same borrowing rate for all investors. In reality investors face different borrowing costs.

Practical tips

  • Use CAPM as a starting point, not the final answer.
  • Check different betas and time windows. See how sensitive your result is.
  • Combine CAPM with other models like Fama-French when you want more precision.
  • If you need a discount rate for valuation, match the risk-free rate to the project horizon.

Final thought

CAPM gives a clear link between market risk and expected return. It is simple and useful. It also leaves out many real world details. Use it to get a solid baseline. Then adjust based on judgment and other evidence.

Keywords: Capital Asset Pricing Model, CAPM formula, beta, market risk premium, cost of equity, expected return, Security Market Line, alpha.

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