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I am trying to figure out the method for calculating the portfolio volatility using matrices. I have read online the following definition for calculating the portfolio volatility using matrix algebra

The variance of a portfolio of correlated assets can be written as WTvW, where W is a column vector (ie a matrix with a single column) containing the weights of different assets in the portfolio. V is the covariance matrix, and WT is the transpose of the matrix W.

I have tried to calculate this on a spreadsheet, but am not sure if i have done it correctly. More specifically, im not sure if i am multiplying the vectors with the covariance matrix correctly.

Can someone please confirm my calculation I have used commas below to separate the different values in the vector and matrix

assuming my weights vector is 0.89, 0.11 my covariance matrix is a 2x2 matrix = 1 , 0.674571 0.674571, 1

to calculate the result i first multiply my weights vector with the covariance matrix

i.e 0.89*1 + 0.11*0.674571
and 0.89*0.674571 + 0.11*1

which gives the following vector A 0.964202851 0.710368523

I then multiply vector A with the weights vector, i.e

0.964202851 * 0.89 0.710368523 0.11 = 0.964202851*0.89+0.710368523 *0.11 = 0.936281075

Is this correct, or do i have an error in my calculation

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Your calculation is correct. By the way, there are free software packages available that make it easier to do these kinds of calculations. For example, using Octave, you simply type

V=[1, .674571; .674571, 1]
W=[.89;.11]
W'*V*W

and it will give you the answer:

ans =  0.93628
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Let $R \in \mathbb{R}^d$ and $w \in \mathbb{R}^d$ denote the asset returns and portfolio allocation, respectively. Assuming that $w$ is deterministic, then the portfolio return is given by $r_p = R^\prime w$, such that \begin{equation} Var(r_p) = Var(R^\prime w) = w^\prime Var(R)w = w^\prime \Sigma w \end{equation} where $\Sigma = Var(R)$ is the covariance matrix of asset returns.

You can calculate the same without matrix notation, which is less tractable, nonetheless: \begin{equation} r_p = \sum_{i=1}^d w_i \times R_i \end{equation} such that \begin{equation} Var(r_p) = Var(\sum_{i=1}^d w_i \times R_i) = \sum_{i=1}^d w_i^2 Var(r_i) + \sum_{i \neq j}^d w_i w_j Cov(r_i,r_j) \end{equation}

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