As (re)insurance companies accumulate more and more risks, the data contained in these portfolios continues to grow. Understanding how to make sense of it all is critical, and there is no shortage of metrics one can employ. Sure, there are the basic CAT model output metrics such as Average Annual Loss, Exceedance Probability (EP), and Return Periods discussed in our recent blog post—but what other portfolio metrics can provide additional insights?
In this post, we’ll demystify several other real-time metrics that can be computed with Analyze Re to shed more light on your portfolio. Some of those metrics (all of which are derived from the outputs of catastrophe models) require a little bit of math using metrics you can get from Analyze Re to compute. (Coefficient of Variation, for example, isn’t supported directly, but we can give you standard deviation and mean and you can do the division from there.) If you’re looking to build your own internal risk transfer pricing or portfolio management systems, or you’re just trying to evaluate your risks from a different perspective, read on!
1) Window Value at Risk (WinVAR)
WinVAR, Censored Tail Value at Risk (CENTVAR), and Risk Managed Layer (RML) are all slight variations within the Tail Value at Risk (TVaR) family of metrics, where TVaR is the average of all simulated losses at and beyond a specified threshold. Thus, if you’re looking to calculate your 1% TVaR, then it is the average of all event losses at and beyond the 1% exceedance probability.
WinVAR is the average of losses between two exceedance probabilities (e.g., 1.0% ≤ X ≤ 0.1%). The great thing about WinVAR is that it throws out the most extreme event losses, which may have an outsized effect on TVaR.
WinVAR provides you with a sense for the steepness of the EP curve between two points. For example, in analyzing average losses between the 1% EP and the 0.4% EP, as opposed to just analyzing individual events, you get a sense for how much all of these years affect the full EP curve. If the WinVAR average skews close to your 0.4% EP event point, then you know that there are likely some large events around 0.4% that may be worth investigating.
WinVAR is also a practical metric to analyze since most companies typically do not try to protect themselves against losses at the most extreme return periods. Thus, if you only choose to manage your portfolio down to say 0.4% (the 250-year return period), you can do this by analyzing the WinVAR from 1% down to 0.4%.
2) Censored Tail Value at Risk (CENTVAR)
Instead of ignoring your most extreme event losses above a certain EP, with CENTVAR, you take whatever your losses are above a certain EP (e.g., above 0.4%) and set those losses equal to the loss at your 0.4% EP. For example, let’s say that your company’s financial and strategic planning call for only managing up to USD 700 million in losses in a given year, which corresponds to your 0.4% EP. So, for all event losses beyond 0.4% EP, you censor any losses above USD 700 million and essentially round those losses down to USD 700, reflecting the fact that it is not financially feasible for your company to protect for losses beyond that amount.
Table 1. With CENTVAR you “censor” any losses above a certain amount by setting them equal to the EP that you can financially insure against. (Source: AIR)
In Table 1, the TVaR at 0.4% EP is approximately USD 663 (the average of the Value at Risk column), while the CENTVAR at 0.4% EP is USD 621 (the average of the Censored Value column). Note that the above example has been overly simplified, as a 10,000 year catalog would of course have other events listed in the EP table.
If you’re looking for a more technical discussion on the calculations behind CENTVAR and WinVAR, check out this in-depth AIR Currents article on the topic.
3) Risk Managed Layer (RML)
Risk Managed Layer, as some in the re/insurance industry refer to it, is the average yearly metric around a targeted EP point. For example, while you may be interested in the 1% EP, with the RML you would select all of the points from the 0.67% to 1.25% EP and take their average. This sounds similar to the WinVAR, but the purpose of the RML is to better understand the characteristics of the years that create loss results that are close to your 1% EP point. WinVAR, on the other hand, is designed specifically to ignore the extremes of your tail risk. To run an RML calculation in Analyze Re, just set up a WinVAR function for the range you are interested in calculating.
A common use case of RML is during reinsurance purchase decisions—by analyzing the events around a certain EP point, you now have a better understanding of the how these losses break out across perils, regions, and lines of business. Having greater visibility into your risk can allow you to determine what additional cover to purchase, or provide you with insight when it comes to negotiating reinstatement terms.
4) Coefficient of Variation
While more a general statistic rather than an insurance industry metric, Coefficient of Variation (CV) describes the spread in a series of data points relative to the mean. It is a unitless metric that allows you to compare data sets to each other; the lower the CV the lower the variability.
By applying simple division of CAT model output Standard Deviation (SD) and Average Annual Loss you get:
Coefficient of Variation = SD / AALFigure 1.
Because SDs and AALs can vary widely depending on the peril you’re looking at, Coefficient of Variation makes it easier to compare the amount of variation between perils.
Determining what real-time metrics to report on and analyze comes down to what your larger goals are. While there are many others to look at, hopefully this post gave you a few ideas for how CAT modeling output can be manipulated into additional metrics that can provide the insight you need to make better decisions about your whole portfolio, all the way down to you individual contracts.