# Capital Asset Pricing Model and Arbitrage Pricing Theory — Which one? When?

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# What is CAPM:

**“The excess return on any stock”**

CAPM, allows predicting the relationship between the risk of an asset and its expected return. This provides a benchmark rate of return for evaluating asset returns. Additionally, the CAPM model can be used to derive an expected return on yet to be traded publicly, e.g. IPOs and major projects. (Bodie, et al., 2014)

The model by Harry Markowitz published by William Sharpe, John Lintner, and Jan Mossin predicts equilibrium expected returns on risky assets.

# Capital Allocation Line (CAL) and Capital Market Line (CML)

If an investor was to choose the *market *portfolio, i.e. the value-weighted portfolio of all assets in the investment universe, the capital allocation line will also become the capital *market *line, as depicted above. (Bodie, et al., 2014)

# Expected returns:

The CAPM is developed on the premise that a fair appropriate risk premium on an asset will be determined by its contribution to the risk a portfolio. This assumes investors will demand a risk premium based on portfolio risk contribution by each individual asset.

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# Risk premium:

The reward-to-risk ratio for investment in the market portfolio is:

**Market risk premium / Market variance = E(RM)** (Bodie, et al., 2014)

The above ratio indicates the market price of risk** **as it quantifies the excess return that investors demand to bear portfolio risk.

# Beta:

If the reward-to-risk ratio was better for one investment than another, investors would implement higher weightings for the better trade-off, adding pressure on prices until the ratios reach equilibrium. Therefore, it can be concluded that the reward-to-risk ratios of a single asset (A) and the market portfolio should be equal.

E(RA) = Cov(RA,RM) / σM2 xE(RM)

The ratio Cov(*R*GA, *RM*)/σ*M*2 measures the contribution of A to the variance of the market portfolio as a fraction of the…