Calculating beta when holding market portfolio

Question

Suppose that CAPM holds and that you hold a portfolio of the market portfolio and the risk-free asset with weights equal to 0.74 and 0.26 respectively. What is the beta of your portfolio?

My questions are;

1. What does it mean that "CAPM holds"? I've googled this but can't seem to find any answer.

2. When I tried calculating beta, this is what I did;

$$ r_i=r_f+\beta(r_m-r_f)$$ $$ r_i-r_f=\beta(r_m-r_f) $$ but since the portfolio is the market portfolio, I thought that I could use $r_i=r_m$, so I get

$$\beta=\frac{r_i-r_f}{r_m-r_f}=\frac{r_m-r_f}{r_m-r_f}=1 $$.

When looking at the answer, they say that the beta of my portfolio is 0.74, but I don't understand why. Any help would be greatly appreciated.

Answer 1

The phrase "The CAPM holds" refers to the assumption, that any asset return $r_i$ fulfills the pricing relation $r_i=r_f+\beta_i(r_m-r_f)$, where $r_m$ denotes the market return, $r_f$ the risk-free rate and $\beta_i$ the beta-factor of the asset. The CAPM is an economic theory, but be aware that plenty of empirical research does not support the CAPM, it is long ago "shot dead" by academics.

Your calculation is right, that the beta-factor of the market portfolio equals 1. But further, your portfolio is a linear combination of 74% market portfolio and the remaining investment in the riskless asset. As the latter one has a beta of zero, your portfolio beta is $0.74\cdot 1 + 0.26 \cdot 0 = 0.74$.