One of the typical tasks when constructing stress-test scenario is risk factor selection. Obviously, each portfolio has trade-specific factors which directly influence present value (PV) and potential future exposure (PFE) of positions and, thus, overall risk exposure and performance of the portfolio. For example, credit default spreads are needed to price Credit Default Swaps.
In most cases, however, there are global macroeconomic factors (GDP, interest rates, oil price etc.) and market-specific time series (such as market indices and key market drivers), which have indirect influence on trade-specific factors and, thus, portfolio value. This relationship can be measured ether by correlation, if relationship has no lag, or by autocorrelation, in case of lagged effect.
Effective stress-test scenario, however, cannot include all the numerous factors having acceptable level of correlation.
So, this post describes how to select risk factors for a stress test, using the ranking based on delta equivalents.
Each risk factor (either trade-specific or market one) is assigned a rank. The higher rank is, the higher influence the factor has on the portfolio price. This algorithm also takes into account the consideration that a low-correlated market factor accompanied by high volatility may have more intense effect than highly correlated factors.
Notations:
– trade-specific factor
– market-specific factor
– delta equivalent of i-th risk factor
– standard deviation of i-th risk factor
– correlation between risk factors i and j
– last price/level of factor i
– weight of all trades n , which are subject to trade-specific factor i , in total amount of portfolio target metrics (total PV, total PFE or total UPV).
Algorithm
-
1. Select Portfolio.
2. Rank trade-specific factors , where n=1,..,N are all deals which have trade-specific factor
.
3. Rank market factors , over each
.
4. Construct the list of ALL factors ( and
) and sort them by rank.
5. Select TOP 15 market factors.
6. Compute shock statistics, based on statistics from database.
7. Compute shocks (for predictive stress-test) :