CVaR Portfolio Optimization without copulas

Hi,

I'm trying to do the CVaR Portfolio Optimization using the instructions on Mathworks (link to example). However, the CVaR model in this example uses an empirical distribution with copulas. How could i calculate CVaR, which replaces the variance (risk) from mean-variance model with the quantiles of the return distribution. In other words, the CVaR average-conditional quantile method.

Help is much appreciated

Answer 1

[Shantanu Dixit]

Hi Agne,

To calculate 'CVaR' using the average-conditional quantile method and replace the variance (risk) from the mean-variance model, you can follow the below steps:

1. Simulate portfolio returns from your asset scenarios.
2. Calculate the 'VaR' by finding the (1-alpha) quantile of the portfolio returns. (alpha: confidence level)
3. Calculate 'CVaR' as the average of the returns below the 'VaR' threshold.

Below is a small snippet which replaces the variance with 'CVaR' based on quantiles of the return distribution

portfolioWeights = w1(:, portNum); % Weights of selected portfolio
portfolioReturns = AssetScenarios * portfolioWeights; % Portfolio returns

% Calculate VaR (quantile at alpha level)
VaR_alpha = quantile(portfolioReturns, 1 - alpha);

% Calculate CVaR (average of returns below VaR)
CVaR_alpha = mean(portfolioReturns(portfolioReturns <= VaR_alpha));

Additionally you can refer to the following MathWorks documentation for more information:

quantile: https://www.mathworks.com/help/matlab/ref/quantile.html

Hope this helps!

[Agne]

Thank you for a clear explanation

Answer 2

[Alejandra Pena-Ordieres]

Hi Agne,

The PortfolioCVaR object uses a sample of returns to compute the condiitonal value-at-risk of the portfolio. In other words, PortfolioCVaR internally computes the average losses of a portfolio that are above sepecific quantile from the scenarios that you provide to the object. You can define the quantile of interest using the ProbabilityLevel input.

To substitue the t-copula distribution with the returns distribution, you'd need to simulate several returns scenarios from your returns distribution and then feed those scenarios into the AssetScenarios input. In the AssetScenarios input, each row represents one scenario from the returns distribution and each column represents the returns of each asset for different scenarios.

Hope this helps,

Alejandra