Expected risk and return
Expected return
The expected monthly return of a portfolio is given by the following formula:
\mathbb{E}(r) = \mathbb{E}(r)_1 \times w_1 + \mathbb{E}(r)_2 \times w_2 + \dots + \mathbb{E}(r)_n \times w_n
where
\begin{align*}
E(r)_i & : \text{expected monthly return of instrument in the portfolio}, \\
w_i & : \text{weight of instrument in the portfolio}, \\
n & : \text{total number of instruments in the portfolio},
\end{align*}
and
w_1 + \dots + w_n = 1.
The expected annual return of the portfolio is calculated by
return_{annual} = (1+E(r))^{12}-1.
Expected return for the instruments in the portfolio will vary based on the configuration. It can be one out of the three below:
- Historical return of the category where instrument is connected
- Houseview of the category
- Houseview for instrument
If method one is applied, the expected monthly return of an instrument is calculated by
E(r)_i = E\{log(\frac{pf}{po})\}
where po and pf are the instrument values at the beginning and the end of month, respectively.
Expected risk
The calculation of the expected volatility of a portfolio is done through the following two steps. First we calculate the monthly variance of the portfolio by using the following formula:
\sigma^2 = w^T \Sigma w
where:
\begin{align*}
\sigma^2 & : \text{variance}, \\
w & : \text{(column) vector of weights for each instrument in the portfolio}, \\
\Sigma & : \text{covariance matrix of the expected monthly returns of the instruments in the portfolio}, \\
T & : \text{transpose operator of vector/matrix}.
\end{align*}
Here,
w = [w_1, \dots, w_n]^T.
Second, we calculate the expected annual risk (in %) by using this formula:
risk_{annual} = \sigma \times \sqrt{12} \times 100.
Expected risk for the instruments in the portfolio will vary based on the configuration. It can be one out of the three below:
- Historical risk measured on a monthly data
- Houseview risk of the category
- Houseview risk for the instrument