0

I have to prove that $\mu_\pi=r+\beta_\pi(\mu_M-r)$, (where $\mu_\pi$ is the expected return of a portfolio, $r$ is the interest rate, $\beta_\pi$ is the beta factor of the portfolio, and $\mu_M$ is the expected return of the market), using the CAPM formula, which states that $\mu_i=r+\beta_i(\mu_M-r)$ for any asset $i$.

I already proved that $\beta_\pi=\sum_{i=1}^N(\pi_i\beta_i)$ and I think I am supposed to use this in my proof.

I started by substituting in:

$\mu_\pi=r+\beta_\pi(\mu_M-r)$ => $\sum_{i=1}^N(\pi_i\mu_i)=r+\sum_{i=1}^N(\pi_i\beta_i)(\mu_M-r)$ but I am not sure how to proceed or if this is the right approach.

Thank you for your help

Silvia Rossi
  • 800
  • 1
    I think you need to check the conclusion you have proved. It does not look correct to me that $\beta_\pi=\sum_{i=1}^N(\pi_i\mu_i)$. Rather, I think it should be that $\beta_\pi=\sum_{i=1}^N(\pi_i{\color{red}\beta_i})$. – OnoL Feb 19 '18 at 04:04
  • @OnoL Thank you, I edited my question, I got a bit carried away with copy and paste :) – Silvia Rossi Feb 19 '18 at 04:06
  • Then I think you are done, aren't you? – OnoL Feb 19 '18 at 05:20
  • @OnoL Really? So since $\mu_i=r+\beta_i(\mu_M-r)$ holds, we can say that $\sum_{i=1}^N(\pi_i\mu_i)=r+\sum_{i=1}^N(\pi_i\beta_i)(\mu_M-r)$ holds? – Silvia Rossi Feb 19 '18 at 17:07

0 Answers0