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Post Closed as "Not suitable for this site" by Quantuple, LocalVolatility, amdopt, msitt, Helin
Removed irrelevant tags, improved formatting and title
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edit approved May 16, 2017 at 16:24
Richard Hardy
edit approved May 16, 2017 at 16:24
Richard Hardy
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Portfolio volatility with Volatility of a multiple assets-asset portfolio

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma_{port, t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^2_{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$$\sigma^2_{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 \text{Cov}_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical standard deviation. This is not what I am after since the individual volatilites are estimated using their individual model.

Portfolio volatility with multiple assets

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma_{port, t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^2_{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical standard deviation. This is not what I am after since the individual volatilites are estimated using their individual model.

Volatility of a multiple-asset portfolio

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma_{port, t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^2_{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 \text{Cov}_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical standard deviation. This is not what I am after since the individual volatilites are estimated using their individual model.

Changed mathematical notation to avoid confusions between volatility/variance
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edit approved May 16, 2017 at 16:16
JejeBelfort
edit approved May 16, 2017 at 16:16
JejeBelfort
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I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma^{port}_{t}$$\sigma_{port, t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$$\sigma^2_{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical std.standard deviation. This is not what I am after since the individual volatilites are estimated using their individual model.

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma^{port}_{t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical std. deviation. This is not what I am after since the individual volatilites are estimated using their individual model.

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma_{port, t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^2_{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical standard deviation. This is not what I am after since the individual volatilites are estimated using their individual model.

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WJA
WJA
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Portfolio volatility with multiple assets

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant.

Now I want to determine the portfolio volatility $\sigma^{port}_{t}$ by combining the individual volatilities, using the weights and correlations.

I know that for two assets you can do:

$\sigma^{port} = w^{2}_1 \sigma^{2}_1 + w^{2}_2 \sigma^{2}_2 + w_1 w_1 Cov_{1,2}$

But what do you do when you have N assets?

Important: I know that you can calculate the portfolio volatility using the portfolio returns and then simply taking the historical std. deviation. This is not what I am after since the individual volatilites are estimated using their individual model.