Tag Archives: return period

Tails of VaR

In an opinion piece in the FT in 2008, Alan Greenspan stated that any risk model is “an abstraction from the full detail of the real world”. He talked about never being able to anticipate discontinuities in financial markets, unknown unknowns if you like. It is therefore depressing to see articles talk about the “VaR shock” that resulted in the Swissie from the decision of the Swiss National Bank (SNB) to lift the cap on its FX rate on the 15th of January (examples here from the Economist and here in the FTAlphaVille). If traders and banks are parameterising their models from periods of unrepresentative low volatility or from periods when artificial central bank caps are in place, then I worry that they are not even adequately considering known unknowns, let alone unknown unknowns. Have we learned nothing?

Of course, anybody with a brain knows (that excludes traders and bankers then!) of the weaknesses in the value-at-risk measure so beloved in modern risk management (see Nassim Taleb and Barry Schachter quotes from the mid 1990s on Quotes page). I tend to agree with David Einhorn when, in 2008, he compared the metric as being like “an airbag that works all the time, except when you have a car accident“.  A piece in the New York Times by Joe Nocera from 2009 is worth a read to remind oneself of the sad topic.

This brings me to the insurance sector. European insurance regulation is moving rapidly towards risk based capital with VaR and T-VaR at its heart. Solvency II calibrates capital at 99.5% VaR whilst the Swiss Solvency Test is at 99% T-VaR (which is approximately equal to 99.5%VaR). The specialty insurance and reinsurance sector is currently going through a frenzy of deals due to pricing and over-capitalisation pressures. The recently announced Partner/AXIS deal follows hot on the heels of XL/Catlin and RenRe/Platinum merger announcements. Indeed, it’s beginning to look like the closing hours of a swinger’s party with a grab for the bowl of keys! Despite the trend being unattractive to investors, it highlights the need to take out capacity and overhead expenses for the sector.

I have posted previously on the impact of reduced pricing on risk profiles, shifting and fattening distributions. The graphic below is the result of an exercise in trying to reflect where I think the market is going for some businesses in the market today. Taking previously published distributions (as per this post), I estimated a “base” profile (I prefer them with profits and losses left to right) of a phantom specialty re/insurer. To illustrate the impact of the current market conditions, I then fattened the tail to account for the dilution of terms and conditions (effectively reducing risk adjusted premia further without having a visible impact on profits in a low loss environment). I also added risks outside of the 99.5%VaR/99%T-VaR regulatory levels whilst increasing the profit profile to reflect an increase in risk appetite to reflect pressures to maintain target profits. This resulted in a decrease in expected profit of approx. 20% and an increase in the 99.5%VaR and 99.5%T-VaR of 45% and 50% respectively. The impact on ROEs (being expected profit divided by capital at 99.5%VaR or T-VaR) shows that a headline 15% can quickly deteriorate to a 7-8% due to loosening of T&Cs and the addition of some tail risk.

click to enlargeTails of VaR

For what it is worth, T-VaR (despite its shortfalls) is my preferred metric over VaR given its relative superior measurement of tail risk and the 99.5%T-VaR is where I would prefer to analyse firms to take account of accumulating downside risks.

The above exercise reflects where I suspect the market is headed through 2015 and into 2016 (more risky profiles, lower operating ROEs). As Solvency II will come in from 2016, introducing the deeply flawed VaR metric at this stage in the market may prove to be inappropriate timing, especially if too much reliance is placed upon VaR models by investors and regulators. The “full detail of the real world” today and in the future is where the focus of such stakeholders should be, with much less emphasis on what the models, calibrated on what came before, say.

Arthur opens the US Hurricane Season

After Hurricane Arthur briefly made landfall in North Carolina on Thursday night, a weakened storm is now heading north. I thought this would be good time to have a look at the probable maximum losses (PMLs) published as at the Q1 2014 results by a sample of specialist (re)insurers, first presented in a post in June 2013. That post went into some detail on the uncertainties surrounding the published PMLs and should be read as relevant background to the figures presented here.

Despite predictions of an above average 2013 Atlantic hurricane season, the number of named hurricanes was the lowest since 1982. Predictions for the 2014 season are for a below average number of hurricanes primarily due to cooler sea temperatures in the Atlantic due to the transition to El Niño (although that is now thought to be slower than previously anticipated). The graph below includes the 2014 predictions.

click to enlargeHistorical Atlantic Storms & Hurricanes I like to look at PMLs as a percentage of net tangible assets (NTA) on a consistent basis across firms to assess exposures from a common equity viewpoint. Many firms include subordinated debt or other forms of hybrid debt in capital when showing their PMLS. For example, Lancashire has approximately $330 million of sub-debt which they include in their capital figures and I have show the difference with and without the sub-debt in the percentages for Lancashire in the graph below on US wind PMLs to illustrate the comparison.

Whether hybrid debt comes in before equity or alongside equity depends upon the exact terms and conditions. The detail of such instruments will determine whether such debt is classified as tier 1, 2 or 3 capital for regulatory purposes under Solvency II (although there are generous transitional timeframes of up to 10 years for existing instruments). The devil is often in the detail and that is another reason why I prefer to exclude them and use a consistent NTA basis.

As per the June 2013 post, firms often classify their US wind exposures by zone but I have taken the highest exposures for each (which may not necessarily be the same zone for each firm).

click to enlargeUS Wind PMLs Q1 2014 These exposures, although expressed as percentages of NTAs, should be considered net of potential profits made for 2014 to assess the real impact upon equity (provided, of course, that the expected profits don’t all come from property catastrophe lines!). If for example we assume a 10% return on NTA across each firm, then the figures above have to be adjusted.

Another issue, also discussed in the previous post, is the return period for similar events that each firms present. For example, the London market firms present Lloyds’ realistic disaster scenarios (RDS) as their PMLs. One such RDS is a repeat of the 1926 Miami hurricane which is predicted to cost $125 billion for the industry if it happened today. For the graph above, I have assumed a 1 in 200 return period for this scenario. The US & Bermudian firms do not present scenarios but points on their occurrence exceedance probability (OEP) curves.

As it is always earthquake season, I also include the PMLs for a California earthquake as per the graph below.

click to enlargeCalifornia EQ PMLs Q1 2014 In terms of current market conditions, the mid-year broker reports are boringly predictable. John Cavanagh, the CEO of Willis Re, commented in their report that “the tentacles of the softening market are spreading far and wide, with no immediate signs of relief. We’ve seen muted demand throughout 2014 and market dynamics are unlikely to change for some time to come. The current market position is increasingly challenging for reinsurers.” Aon Benfield, in their report, stated that “the lowest reinsurance risk margins in a generation stimulate new growth opportunities for insurers and may allow governments to reduce their participation in catastrophe exposed regions as insurance availability and affordability improves”. When people start talking about low pricing leading to new opportunities to take risk, I can but smile. That’s what they said during the last soft market, and the one before that!

Some commentators are making much of the recent withdrawal of the latest Munich Re bond on pricing concerns as an indicator that property catastrophe prices have reached a floor and that the market is reasserting discipline. That may be so but reaching a floor below the technical loss cost level sounds hollow to me when talking about underwriting discipline.

To finish, I have reproducing the graph on Flagstone Re from the June 2013 post as it speaks a thousand words about the dangers of relying too much on the published PMLs. Published PMLs are, after all, only indicators of losses from single events and, by their nature, reflect current (group) thinking from widely used risk management tools.

click to enlargeFlagstone CAT losses Follow-on: It occurred to me after posting that I could compare the PMLs for the selected firms as at Q1 2014 against those from Q1 2013 and the graph below shows the comparison. It does indicate that many firms have taken advantage of cheap reinsurance/retrocession and reduced their net profiles, as highlighted in this post on arbitrage opportunities. Some firms have gone through mergers or business model changes. Endurance, for example, has been changed radically by John Charman (as well as being an aggressive buyer of coverage). Lancashire is one of the only firms whose risk profile has increased using the NTA metric as a result of the Cathedral acquisition and the increase in goodwill.

click to enlargeUS Wind PMLs Q1 2013 vrs 2014