Method Documentation
Expected risk and return

10min
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

\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
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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*}

\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*}
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and
w_1 + \dots + w_n = 1.

w_1 + \dots + w_n = 1.
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The expected annual return of the portfolio is calculated by   
return_{annual} = (1+E(r))^{12}-1.

return_{annual} = (1+E(r))^{12}-1.
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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})\}

E(r)_i = E\{log(\frac{pf}{po})\}
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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

\sigma^2 = w^T \Sigma w
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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*}

\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.

w = [w_1, \dots, w_n]^T.
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Second, we calculate the expected annual risk (in %) by using this formula: 
risk_{annual} = \sigma \times \sqrt{12} \times 100.

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
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Updated 05 Jun 2023
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