A “leave” vote in the British EU referendum will not leave any market unshaken and could have a profound impact on many multi-asset class portfolios. While there are many unknowns, there are some things we can be sure of: trading will be rapid and volatility will rise. With this in mind, the risks in multi-asset class portfolios need to be very well understood in order to prevent large unexpected losses.
This post, which I authored along with my BISAM colleague, Velislav Bodurov, illustrates the design flexibility of BISAM’s Cognity stress-testing module and how Fat-Tailed Monte-Carlo engines can produce scenarios close to our current understanding of what a Brexit event may look like, and do so with a non-negligible probability.
Our Monte Carlo analysis on Brexit follows below, but first a quick glimpse on the specific Cognity capabilities that our customers can leverage to run their own scenarios.
Brexit Stress-Testing in Cognity
BISAM supports Cognity customers exploring vastly different scenarios. Brexit stress-tests include predictions on UK market losses primarily in the 10-20% range, but there are also scenarios with some gain projections, albeit in longer-term stress-tests. Views on yield dynamics also vary across the stress-test scenarios. The majority assumes depreciating yields in both EU and UK, but predictions on the reverse are also being considered with just the U.S. yields being further lowered, and precious metals gaining. With such varying scenarios, the ability to design and run flexible tests in the current market is indeed crucial.
Cognity helps our users to design stress-tests quickly and efficiently, and with a great deal of flexibility:
- Scenarios can be defined by factor group, by set of curves, set of indices or even greater detail down to an individual risk driver. Shocks can be defined in absolute or relative terms, or based on a historical time-period.
- Users can choose “transmission” rules – in the most extreme scenarios, transmissions allow all key stressed factors to affect all markets; in less extreme scenarios, users can define flexible transmission groups by asset-class or by region, or by using any user-defined criteria.
- The correlation matrix for the dependence structure that is being used to estimate predictive stress-tests, as well as the factor model fit can also be user-defined or even stress-tested on its own – users can choose different historical periods, varying data frequency or dependence models.
Users are then equipped with tools to study the transmission effects on the rest of the factors during the stress-test design process.
- In addition, the upcoming Cognity 5.1 release allows for multi-period stress-tests and pilot customers are already exploring this new functionality.
Now that we've shown you how Cognity users are armed with the tools required to quickly and confidently evaluate their portfolios under varying stress-test conditions, let's move on to the Brexit Stress-Testing Study...
Stress-Testing with Smart Monte-Carlo Engines
The fact that so vastly different scenarios are being considered across the industry, exposes the reality that no-one actually knows what the reaction of the financial markets would be in a Brexit event. And this is a situation in which it is now, more than ever, desirable to also complement the user-defined scenarios with Monte-Carlo (MC) experiments. The latter can present an unbiased set of possible scenarios, and help us uncover whether there are further possible risky outcomes not considered in the first place.
The critique of such statistical approaches and the reluctance to use them stems from the fact that models relying on historical data can only mimic the past. Indeed MC engines based on either Normal assumptions or on modifications of the Historical approach can hardly assign a meaningful probability to such a profound market event. The Normal approach would assign a virtually zero probability on any scenario close to what our clients design as Brexit stress-tests unless we put the horizon of the scenario 10-20 years in the future to scale the variance. The Historical approach would not consider such a scenario at all, since there is no precedent.
However, Cognity offers more than the typical Normal or Historical approaches. The Fat-Tailed Monte-Carlo engines can produce scenarios close to our current understanding of what a Brexit event may look like, and do so with a non-negligible probability.
To demonstrate this we designed a straightforward example:
We selected an intriguing and quite extreme stress-test from a client of ours and asked the question “How close can the scenarios produced by the Cognity engine be to this one?” This “Target Scenario” includes a total of64 risk variables – two currencies (EUR and USD), seven market indices, 20 yield points (10 mid- and 10 long-term) and 35 credit spread points (a variation of that scenario is depicted on the Cognity screens above).
We then estimate the “distance” between the Target Scenario and the simulated scenarios as weighted Euclidean distance. The weight for each risk variable is constructed so that each type of risk variables (i.e. index versus yield versus spread versus exchange rate) has an equal weight, with the risk variables within each group having equal weight as well. We then take the difference between our Target Scenario and a particular simulation for a given risk variable and square it, weight it and then we do a sum across all risk variables, taking the square root of that sum[1].
We then compare the thus measured distance for the main Cognity Monte-Carlo models – the Normal model and the Cognity Fat-tailed model (based on Stable Distributions). In both cases we use two years of daily data to fit the model and a three-month simulations horizon. Ten thousand scenarios are run from each model and 10,000 distances between each of the scenarios and our Target Scenario are estimated. We are interested to see how many of those 10,000 scenarios are close enough to our target scenario, i.e. what is the model probability of something similar to our Target Scenario (Brexit) to happen?
The magnitude of the distance is not particularly telling as it might be altered by varying the horizon of the MC experiment. Thus the numbers presented below are scaled by the first quantile of the distance distribution of the Fat-tailed (Stable) model.
Scaled distance (epsilon) |
1.0628 |
Fat-tailed scenarios within Epsilon |
10.00% |
Normal scenarios within Epsilon |
1.20% |
Table 1 (above) - Percentage scenarios falling within the 10^{th} percentile of the Fat-tailed (Stable) distances. The table illustrates our finding: if the Threshold is selected so that to have 10% of the Fat-tailed Scenarios to be close to our Target Stress-test Scenario, we only see 1.2% of the Normal Scenarios to be equally close.
Of course the threshold of ”closeness” is arbitrary, but the tighter we chose it to be, the more pronounced the differences between the models becomes.
Threshold as percentile of Fat-tailed distances |
20% |
10% |
5% |
1% |
% fat-tailed distances within Epsilon |
20% |
10% |
5% |
1% |
% normal distances within Epsilon |
2.67% |
1.20% |
0.58% |
0.07% |
Ration Normal/Fat-tailed scenarios within Epsilon |
13.35% |
12.00% |
11.60% |
7.00% |
Table 2 (above) - Comparison of Fat-tailed and Normal scenarios within Epsilon from Target Scenarios for different thresholds for “closeness”.
So what do those closest scenarios look like? Are they indeed close enough? We continue our research based on the 10^{th} percentile threshold as described above.
Chart 1 (above) - Target Scenario, Max/Min Scenario and the first five Smallest Distance Scenarios (SDR) from the Fat-tailed model. Max/Min Scenario represents an artificial scenario constructed from the largest scenarios obtained for each risk variable during the simulation experiment for all positive target scenario shocks and the smallest (largest in negative value) scenarios obtained for each risk variable during the simulation experiment for all negative target scenario shocks. All shocks are standardized.
We observe that the Fat-tailed model is capable of producing scenarios that are quite close to the Target Scenario, except for the spreads, for which the fat-tailed scale parameter seems small in magnitude. Nevertheless the extreme scenarios produced are of the same order of magnitude and we can claim that the model produces scenarios close to possible human-designed subjective stress-values.
Chart 2 (above) - Target Scenario, Max/Min Scenario and the first five Smallest Distance Scenarios (SDR) from Normal model. Max/Min Scenario represents an artificial scenario constructed from the largest scenarios obtained for each risk variable during the simulation experiment for all positive target scenario shocks and the smallest (largest in negative value) scenarios obtained for each risk variable during the simulation experiment for all negative target scenario shocks. All shocks are standardized.
For the Normal model, even the extreme scenario is far away from the values of the risk variable in the Target Scenario. The Normal MC approach is not capable of generating simulations representative of market extremes.
Conclusions
Our experiment aimed to demonstrate how Cognity is equipped with adaptive models that have in their DNA structure the genes of a possible black-swan event.
Note: Cognity customers can choose to use a model that assumes higher or milder probability of “black-swan event” mutation to occur, based on advanced settings not covered here. In any event those options are included in the realm of possible model outcomes.
Our example validates that well-designed Monte-Carlo engines can provide meaningful stress-test scenarios even for very extreme market conditions. Such "smart" Monte-Carlo machines can help risk managers to explore huge set of scenarios and thus make sure limits would not be breached, or at least know what market movements could trigger a breach. Cognity customers use reverse stress-tests based on Value-at-Risk and Expected Tail Loss to gain that information.
Such scenarios can also be used as a coverage check on the set of stress-tests being run. Furthermore, some Cognity clients utilize an approach whereby selecting the most severe scenarios produced in a Monte-Carlo experiment[2] augments their subjective stress-tests sets.
The Cognity Stress-Test module equips our users with fast and efficient tools to confidently design complex user-defined stress-tests. Additionally, the flexibility and adaptive modeling capabilities of the system equip even the most demanding Quant shops with all the right tools to confidently measure their risk.
Footnotes:
[1] We defined “distance between scenarios” as the squared root of the weighted sum across all risk variables of the square of the deviation of a Cognity MC scenario and our target scenario, after standardization. This defines the well know Euclidean distance.
[2] Selection can be done via importance sampling algorithms
FinAnalytica's Cognity® platform, now part of BISAM’s suite of market-leading portfolio analytics, is a unique, comprehensive, multi-asset class solution for market risk, portfolio construction and investment decision analytics – designed specifically for the buy-side. Visit www.bisam.com/risk to request a demo.