FINM7008 Chap.9 The Capital Asset Pricing Model, Beta and Alpha
The Capital Asset Pricing Model, Beta and Alpha
From the market portfolio to beta
If every investor holds the same optimal risky portfolio, it must be the market portfolio.
The capital asset pricing model then prices each security by its beta, its covariance with the market over the market's variance.
Using the SML
The chapter derives the security market line, computes portfolio betas, uses alpha to flag underpriced and overpriced assets, compares the SML with the capital market line, and covers how beta is estimated in practice and which assumptions the model needs.
Using it in answers
Most CAPM questions follow one path: write the security market line, compute the fair return from beta, compare it with the forecast or average return, and state the alpha with its sign.
Fund rankings use the same path, which is why a fund with a lower raw return can still have the higher alpha.
What this chapter covers
- 01
Homogeneous expectations and the market portfolio
- 02
The CAPM equation
- 03
Beta as systematic risk
- 04
Portfolio beta
- 05
The equilibrium argument
- 06
Alpha and mispricing
- 07
SML versus CML
- 08
Estimating beta by regression
- 09
The CAPM assumptions
Worked example · free
Reading two stocks against the security market line
- 1Q's fair return: 4% + 1.3 × 7% = 13.1%.
- 1R's fair return: 4% + 0.8 × 7% = 9.6%.
- 1Alphas: Q is 15 − 13.1 = +1.9 points; R is 8 − 9.6 = −1.6 points.
- 1Q plots above the line and looks underpriced, so buy it; R plots below and looks overpriced, so sell it.
Key terms
- Market Portfolio
- The portfolio of all risky assets, each weighted by its share of total market value.
- Beta
- A security's covariance with the market divided by the market's variance.
- Capital Market Line
- The capital allocation line through the market portfolio, holding for efficient portfolios.
- Homogeneous Expectations
- The assumption that all investors use the same inputs for returns, variances and covariances.
- Market Proxy
- An index, such as the S&P 500, used in place of the unobservable market portfolio.
- Alpha
- The difference between an asset's expected return and the return the SML assigns to its beta.
The Capital Asset Pricing Model, Beta and Alpha FAQ
Why is beta, not standard deviation, the risk that is priced?
Inside a diversified portfolio, a security's firm-specific risk washes out, and what it adds to portfolio risk is its covariance with the market. Only that systematic part cannot be avoided, so only beta earns a premium in equilibrium.
What is the difference between the SML and the CML?
The capital market line plots expected return against standard deviation and holds only for efficient portfolios. The security market line plots expected return against beta and holds for every asset and portfolio in equilibrium.
How is beta estimated in practice?
By regressing the asset's excess returns on the market's excess returns, with a market proxy such as the CRSP index, the S&P 500 or a local index, and a weekly or monthly return interval. Many professionals buy betas from vendors.
What does a negative alpha tell you?
That the asset's expected or average return is below what its beta requires on the security market line. Under the CAPM it looks overpriced: selling it would push its price down and its expected return up until it lies on the line.
What is the beta of a mix of bills and an index fund?
Portfolio beta is the weighted average of the components' betas. Bills have a beta of zero and a broad index fund a beta close to one, so a 30% bills and 70% index portfolio has a beta of about 0.7, as the lecture's example shows.
Which assumptions does the CAPM need?
Rational, risk-averse investors with homogeneous expectations and a single holding period, and frictionless markets with no taxes or transaction costs, price-taking investors, the freedom to borrow or lend any amount at the risk-free rate, and infinitely divisible assets.
Exam move
Write the five-step equilibrium argument from memory, then compute a portfolio beta, a required return and two alphas. Finish by listing the CAPM assumptions grouped into investors and markets. Practise saying which line applies, CML or SML, before you draw or use either one. For the estimation material, be ready to justify a market proxy and a return interval for a named market in two sentences.
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