0
$\begingroup$

The expected return of a portfolio can be formulated as a weighted average of the constituent assets' returns:

$$r_p = w_1 r_1 + w_2 r_2 + \dots + w_N r_N + \epsilon$$

Does it also follow that the empirical distribution, or density, of a portfolio's return series (a vector with observations $x_{t=1}, x_{t=2},$ etc, whose expected value is $r_p$ above) is just a weighted average of the constituent assets' return distributions?

$$f(r_p) = Pr(x_t) f(x_t|r_1) + Pr(x_t) f(x_t|r_2) + \dots + Pr(x_t) f(x_t|r_N)$$

where $f(r_p)$ is the portfolio's return density function such as a Gaussian, and $Pr(x_t) f(x_t|r_N)$ is the probability or likelihood that a datapoint came from asset $n$'s distribution.

If not, how should the probability formula be corrected?

Improve this question
$\endgroup$
  • 2
    $\begingroup$ No, this is the domain of copulas $\endgroup$ – Chris Jul 15 '20 at 3:57
  • $\begingroup$ what is the corresponding copula analogue of the firat linear equation shown above? $\endgroup$ – develarist Jul 15 '20 at 15:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.