In the paper "A Simple Derivation of the Capital Asset Pricing Model from the Capital Market Line" the authors reason:
Given the CML
$$R_p = R_f +\frac{R_m - R_f}{\sigma_m}\sigma_p$$
where:
- $R_p$ is the return on an efficient portfolio
- $R_f$ is the risk-free rate
- $R_m$ is the return on the market portfolio
- $\sigma_m$ is the standard deviation of returns on the market portfolio
- $\sigma_p$ is the standard deviation of returns on efficient portfolio p.
They claim that:
Efficient portfolios along the CML and are perfectly correlated with the market portfolio.
Based on this statement they can extend the CML-equation by multiplication with $1 = \rho_{pm}$, i.e. the correlation between the efficient portfolio P and the market-portfolio, to define the return on any portfolio as a function of its total risk:
$$ R_p = R_f +\frac{R_m - R_f}{\sigma_m}\sigma_p\rho_{pm} $$
From which the CAPM-formula immediately follows.
Now I have two questions:
- The statement that all efficient portfolios are perfectly correlated seems wrong, as only holding the risk-free asset is an efficient portfolio. The risk-free asset is not correlated to the market-protfolio at all. So this statement cannot be correct? Is there really in error in the paper? Where is my misunderstanding here?
- If the simple approach above does not work, is the idea in general salvagable, and can the CAPM be derived from the CML?