Estimating Portfolio CVaR from Simulated Risk-Factor Scenarios
Summary
The document describes a scenario-based approach to estimating Conditional Value at Risk for a portfolio. Rather than simulate each security in isolation, define scenarios for the risk factors that drive asset prices, reprice the entire portfolio under each scenario, and collect the resulting portfolio values. Sorting those values identifies the adverse tail; CVaR is estimated by averaging outcomes beyond the chosen loss percentile. The example question proposes Monte Carlo simulation and explicitly does not require a normal distribution.
The answer confirms that the broad approach is sound and notes that scenario construction depends on the assets, factor models, confidence level, and computational constraints. It also states that CVaR is a coherent risk measure. The result depends on the quality of the factor model and scenario set, and the brief explanation does not resolve implementation details such as how to handle threshold ties or report CVaR as a positive loss versus a portfolio value.
Key ideas
- Portfolio scenarios should specify the risk factors that drive the assets being valued.
- Reprice the whole portfolio under each scenario to obtain its scenario value or loss.
- Estimate CVaR from the average of outcomes in the adverse tail beyond the selected percentile.
- Monte Carlo scenarios need not assume normally distributed returns.
- The answer identifies CVaR as a coherent risk measure, while scenario quality depends on the model and sampling choices.
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Full text
# Calculate CVaR for a portfolio
# Calculate CVaR for a portfolio
I would like to calculate the Conditional Value at Risk for a portfolio. To be honest, I'm trying for a few days to find an example to calculate for an entire portfolio, not just for one security and I really have a hard time understanding. All the examples are for a single security. I need to add that I'm at the beginning of learning econometrics/statistics.
Let's say that I have a portfolio composed from 3 investments. If I want to calculate CVaR using Monte Carlo prices from the 3 investments, here is what I'm thinking: 1. create a simulated portfolio of 3 investments and take into the account the nominal value of every security and the direction (long/short). 2. run the above portfolio through Monte Carlo for n times and generate a distribution of P/L by calculating the difference between start and end of NAV for every MC iteration. 3. let's say I want to calculate at 99% confidence ratio. Then I get the mean of 1% of the worst losses resulted from the Monte Carlo distribution.
I would like to emphasize that I don't want to use a normal distribution.
Are the steps above correct for finding the CVaR of a portfolio? Also, does respect the coherent risk measure? Thank you.
## Answer by jaamor (score 3, accepted)
https://quant.stackexchange.com/a/17541
This sounds correct, however step 2 is a little vague, so I will try to restate the steps here for you.
- The assets in your portfolio must be priced with respect to a set of risk factors (e.g. interest rate curve).
- Each scenario consists of a value for each of your risk factors. Given the value of your risk factors you can price your portfolio.
- You want to generate a number of scenarios ($S_i$). Your choice on the number of scenarios chosen depends on the number of your assets, the way you choose to model your risk-factors, what your confidence interval is and time/computational constraints. The way you generate these scenarios is important. For example take a look at short-rate models.
- You price your portfolio for each $S_i$.
- Sort the portfolio values $V_i$ for each $S_i$.
- For CVaR, as you say, you can average the $V-i$'s that correspond to a loss higher than the $a^{th}$ percentile. For more information. This is the most helpful introductory paper I have found on the topic: paper by Rockafellar and Uryasev. It has details on how to calculate CVaR.
And, yes, CVaR is a coherent risk measure.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.