The CAPM and the security market line

What does the CAPM say?

The capital asset pricing model (CAPM) prices an asset using only its systematic risk. The expected return is the risk-free rate plus compensation for beta, and the compensation per unit of beta is the market risk premium , the market’s expected return over the risk-free rate.

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

The result is also the required return on the asset: the return investors must expect to hold it, given its systematic risk.

What does the CAPM assume?

Like any model, the CAPM simplifies. The CAPM assumptions are:

1. Investors are risk-averse, utility-maximizing and rational.
2. Markets are frictionless: no transaction costs, no taxes, no limits on short selling, and borrowing and lending at the risk-free rate.
3. Everyone plans for the same single holding period.
4. Investors have homogeneous expectations.
5. All investments are infinitely divisible.
6. Investors are price takers.

Not all assumptions matter equally. Costs, taxes and the borrowing rate change the conclusions only a little. Limits on short selling can bias prices, and non-homogeneous expectations matter if they produce very different optimal portfolios.

What is the security market line?

The security market line (SML) is the CAPM drawn on a chart: beta on the horizontal axis, expected return on the vertical axis. The intercept is the risk-free rate and the slope is the market risk premium. Every asset and every portfolio, efficient or not, should plot on it if it is correctly priced. The table compares it with the capital market line (CML).

	CML	SML
Risk measure	σ (total risk)	β (systematic risk)
Which assets	efficient portfolios only	every asset and portfolio
Slope	market Sharpe ratio	market risk premium

Move the risk-free rate and the market risk premium and watch the line redraw. Then drag the analyst’s forecast above or below the line: above the line is cheap, below the line is expensive.

How is the CAPM used?

What the CAPM is used forit gives a required return for a given level of systematic risk

• Estimating a required return Use it cost of equity, discount rate for valuation and capital budgeting
• Security selection Use it compare an analyst’s forecast with the CAPM return
  • Forecast above the SML Memorize undervalued, buy
  • Forecast below the SML Memorize overvalued, avoid or sell
• Performance appraisal Use it compare a portfolio’s actual return with its CAPM return (alpha)
• Portfolio construction Use it tilt away from the market toward positive-alpha assets, accepting some nonsystematic risk

Cost of equity and valuation. The CAPM return is the discount rate for equity valuation and capital budgeting. It is normally the first estimate analysts use.

Security selection. Compare an analyst’s forecast with the CAPM required return. The gap sorts undervalued and overvalued securities : a positive alpha means the asset plots above the SML.

$$\alpha_i = E_{forecast}(R_i) - \left[R_f + \beta_i\,(E(R_m) - R_f)\right]$$

Performance appraisal. The regression of an asset’s excess returns on the market’s excess returns is the security characteristic line . Its slope is beta and its intercept is Jensen’s alpha, which the next lesson uses to judge a manager.

Portfolio construction. A passive investor holds the market. An active manager tilts toward positive-alpha assets and away from negative-alpha ones, accepting some nonsystematic risk in exchange for a chance of beating the market.

A portfolio is priced like any asset, using its beta from the weighted average of its holdings.

Where does the CAPM fall short?

Why the CAPM is only a benchmarka useful first estimate, weak in tests

• Theoretical limits Use it built into the model itself
  • Single factor Use it only beta is priced; no other characteristic counts
  • Single period Use it ignores what happens in later periods, so decisions can be short-sighted
• Practical limits Use it arise when the model is applied
  • The market portfolio cannot be observed Use it it holds every asset, including non-investable ones (Roll’s critique)
  • Proxies for the market differ Use it different analysts get different returns for the same asset
  • Beta is estimated from history Use it the model looks forward; betas change with period, interval and index
  • Poor predictor of returns Use it empirical support is weak
  • Needs homogeneous expectations Use it otherwise many optimal portfolios and many SMLs

Because of these limits, models that add factors were developed. The arbitrage pricing theory (APT) is the theoretical one: it also gives a linear relationship, but with any number of factors, each with its own premium λ and sensitivity β.

$$E(R_p) = R_f + \lambda_1\,\beta_{p,1} + \dots + \lambda_K\,\beta_{p,K}$$

Beyond the CAPMmore factors than the market

• Theoretical: arbitrage pricing theory Know the idea many factors, not specified; no-arbitrage argument; hard to use
• Practical: Fama–French and Carhart Know the idea market, size, value, momentum; explains returns better, no equilibrium theory behind it

Go deeper Why the CAPM is still used, and Roll’s critique

Despite weak empirical support, the CAPM is simple, needs only one input beyond the risk-free rate, and gives a defensible benchmark return. APT does not name its factors, which makes it hard to apply, and the Fama–French and Carhart models fit past returns better but have no equilibrium theory behind them and may not keep working.

Richard Roll argued that the CAPM cannot really be tested, because the true market portfolio, containing every asset, cannot be observed.

Exam tip Premium first: subtract Rf from the market return, multiply by beta, then add Rf back. Above the SML means undervalued.