Monte Carlo VaR for Portfolios with Different Trade Gearings
Summary
The document outlines a Monte Carlo framework for estimating portfolio value at risk when positions have different gearing. Rather than treating broker margin as the risk measure, it starts with a model that generates future returns for each underlying asset. Simulated innovations are transformed by that return model into return scenarios, and the desired VaR is obtained as the selected quantile of the portfolio outcomes.
For multi-period horizons, the process can be repeated over successive periods and returns compounded. The answer suggests several ways to draw innovations, including normal or Student-t distributions and filtered historical simulation. It does not provide the requested spreadsheet layout or show the explicit mapping from each product’s gearing to portfolio P&L. Thus, implementation still requires a return model and a clear position-level transformation from underlying moves to the leveraged product’s gains and losses.
Key ideas
- Generate scenarios from a model of future returns for each underlying asset.
- Transform simulated innovations into return outcomes, then calculate the desired VaR as a quantile.
- For longer horizons, simulate successive periods and compound their returns.
- Normal, Student-t, and filtered historical simulation are possible approaches to sampling innovations.
- The framework requires an explicit mapping from each position’s gearing to portfolio P&L.
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# Calculating portfolio VaR for (custom) leveraged products
# Calculating portfolio VaR for (custom) leveraged products
I have been searching online for a few days regarding how to calculate portfolio VaR for a portfolio consisting of leveraged products - but so far, I have not been able to come up with anything remotely useful and practical (i.e. so that I can implement it in a spreadsheet for example).
I am trading custom leveraged products, and my PnL movements are based on the following two criteria:
- The gearing with respective to a point movement in the market (At the point at which the transaction is created, I get to choose the gearing - for example, I can choose to risk 100 cents for every point move in the underlying market).
- The margin gearing which relates to how much margin the broker requires in order to establish a position (actually this may be irrelevant in risk calculation, as margining appears to be ignored in futures VaR calculation).
My questions are:
- How can I build a VaR model that takes into account the fact that each trade (i.e. transaction) may have a different gearing?
- What would be the steps required to build a simple Excel model to help me calculate a VaR for my portfolio?
## Answer by Bob Jansen (score 3, accepted)
https://quant.stackexchange.com/a/4588
First of all you need a model to generate future returns, I assume you already have this.
Since its just a model, there will be an unexplained component in the predictions made for every period $t$ and for every asset $i$. Let $\varepsilon_{t, i}$ denote this random innovation and $\mathrm{E}[r_{t, i}] = f(\varepsilon_{t, i})$ the expected asset return as a function of the innovation. In a Monte Carlo you pseudo-randomly generate the innovations, apply $f$ to obtain a random sample from your return distribution, in pseudo code, for one period:
```
r = zeros(1, N)
for i=1:N
eps = draw_from_distribution()
r(i) = f(eps)
end
```
with `N` the number of simulations. This is all there is to it, to find the 5% VaR just take the 5% quantile from `r`.
An advantage of Monte Carlo simulation is that it is easy to take an asset return model of a high frequency and apply it to a VaR of a lower frequency. In that case you repeat the code above for every period and calculate the cumulative return from the one period returns.
There are a number of ways to do a `draw_from_distribution`. You can simply use a distribution like the normal or the student-t or perform Filtered Historical Simulation.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.