Sensitivity and Historical Scenarios for VaR Stress Testing
Summary
The discussion considers how to stress a portfolio whose VaR is estimated with a variance-covariance method. It distinguishes sensitivity analysis, which applies specified shocks to risk factors, from historical scenario analysis, which applies movements observed during past crises. The proposed sensitivity factors include yield curve moves, equity index changes, currency moves, and volatility changes.
For an equity index shock, one answer suggests applying the percentage move to each constituent in a price-weighted index such as the Dow Jones Industrial Average. For a historical crisis, the replies recommend applying the period’s risk-factor returns to today’s holdings, using proxy instruments when current assets did not exist then. They also suggest considering broader crisis periods and covariance-based or exponentially weighted scaling. The discussion is informal and does not provide a complete implementation or validate the specific shocks. It notes that older rate data may be difficult to obtain or less reliable, and that scenario choice and proxy selection require judgment.
Key ideas
- Sensitivity stress tests revalue a portfolio after applying shocks to selected risk factors.
- Historical scenario tests can apply past risk-factor returns to current holdings.
- Proxy instruments can represent assets that did not exist during the historical crisis.
- Equity shock implementation depends on how the index is constructed.
- Older interest-rate histories may be difficult to source and can be erratic.
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Full text
# Stress Testing for VaR # Stress Testing for VaR I am trying to perform stress testing for VaR and have taken into consideration two methods:- 1. Sensitivity analysis 2. Historical scenario analysis. According to the Derivatives Policy group we need to take into consideration 5 factors which are:- o Parallel yield curve in ±100 basis points. o Yield curve shifts of ±25 basis points. o Stock index changes of ±10%. o Currency changes of ±6%. o Volatility changes of ±20%. - I am trying to perform the stress testing through sensitivity analysis in excel for which I am not able to figure out how to mould the prices for equities,bonds and derivatives by taking into account above factors through the excel function data table. For instance, if I take into account the 3rd factor mentioned above as STOCK INDEX CHANGES OF +- 10% and one of my stock in my portfolio is listed in Dow Jones, so how can I adjust the prices for a particular time period (say 6 months).? 2.Secondly if I take historical scenario analysis in which I am taking the scenario for instance 1997 Asian crisis, how do I adjust the prices in this scenario also. In this case, for instance, my portfolio contains all the asset class which are issued in the last 10 years and therefore I dont have any data (prices etc.) for them related to the 1997 asian crisis. SO how do I adjust the prices in this case also?. P.S :-I am using variance covariance method for calculating VaR. Eagerly waiting for valuable suggestions on this. ## Answer by user68819 (score 1) https://quant.stackexchange.com/a/79422 Question to your question, why are you stress testing var ? Vars definition is clear. Apply a stress test on top. The derivatives policy you mention seems to be quite basic. I'd either pick a stress such as covid etc. And EWMA scale or use a historic covariance matrix to derive stresses. ## Answer by Dark (score 0) https://quant.stackexchange.com/a/25662 - To replicate a STOCK INDEX CHANGES OF +- 10%, you just have to move the price of each stock by +- 10% (in case of the Dow Jones Index anyway because this index is a simple average of the prices of its components) - You can use the 1997 scenario and apply it to your current portfolio by proxying your instruments to the instruments from 1997. ## Answer by swordfish81 (score 0) https://quant.stackexchange.com/a/63181 For historical scenario analysis you could replicate the returns from the 1997 crisis or even the 2008 crisis for that matter. You would be looking at the daily change or returns, so what you need is the time series for the risk factors from those periods. Bloomberg, Reuters and even some free websites like investing.com or Yahoo.com provide you with free historical timeseries for these periods (atleast for equities). For rates I suppose you will have to use Bloomberg or Reuters, but bear in mind that the further you go back in the timeseries the more erratic the timeseries becomes.
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