D.1 CAPM SML

Write down the CAPM relationship for a project's expected discount rate (all equity financed)

$E[r_A] = r_f + \beta \space \cdot (E[r_M] - r_f)$

$\implies E[r_A] :=$ The discount rate or rather the expected return of an

$\beta$ $:=$ The CAPM Beta (Definition in D.2)

$E[r_M] :=$ The expected return of the market

D.2 CAPM Beta

How is the beta of a firm defined? What does it capture?

The beta is defined as a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole.

It can be denoted as: $\beta = \frac{Cov(r_A,r_M)}{Var(r_M)}$

D.3 CAPM and Markowitz

State the CAPM implied expected return-risk relationship for the market portfolio and explain how it relates to the mean-variance portfolio theory

The CAPM has the following assumptions:

• all investors are identical Mean-Variance portfolio optimizers
• all investors share the same homogeneous expectations about the risk-free rate $r_f$, the expected holding period return of all assets, $\mu$ , and the covariance matrix $\Sigma$.

The consequences from these assumptions are:

• All investors will come p with the same tangency portfolio, which as a result can be called the market portfolio.

As the market portfolio is a Markowitz efficient portfolio that invests 100% of the wealth in the TP portfolio it holds

$E[r_M]-r_f=\gamma_M*Var(r_M)$

→ $E[r_M]-r_f$: expected market risk premium

→ $\gamma_M$: market´s aggreagte risk aversion