Tag Archives: economic modelling

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.

The imperfect art of climate change modelling

The completed Group I report from the 5th Intergovernmental Panel on Climate Change (IPCC) assessment was published in January (see previous post on summary report in September). One of the few definite statements made in the report was that “global mean temperatures will continue to rise over the 21st century if greenhouse gas (GHG) emissions continue unabat­ed”. How we measure the impact of such changes is therefore incredibly important. A recent article in the FT by Robin Harding on the topic which highlighted the shortcomings of models used to assess the impact of climate change therefore caught my attention.

The article referred to two academic papers, one by Robert Pindyck and another by Nicholas Stern, which contained damning criticism of models that integrate climate and economic models, so called integrated assessment models (IAM).

Pindyck states that “IAM based analyses of climate policy create a perception of knowledge and precision, but that perception is illusory and misleading”. Stern also criticizes IAMs stating that “assumptions built into the economic modelling on growth, damages and risks, come close to assuming directly that the impacts and costs will be modest and close to excluding the possibility of catastrophic outcomes”.

These comments remind me of Paul Wilmott, the influential English quant, who included in his Modeller’s Hippocratic Oath the following: “I will remember that I didn’t make the world, and it doesn’t satisfy my equations” (see Quotes section of this website for more quotes on models).

In his paper, Pindyck characterised the IAMs currently used into 6 core components as the graphic below illustrates.

click to enlargeIntegrated Assessment Models

Pindyck highlights a number of the main elements of IAMs which involve a considerable amount of arbitrary choice, including climate sensitivity, the damage and social welfare (utility) functions. He cites important feedback loops in climates as difficult, if not impossible, to determine. Although there has been some good work in specific areas like agriculture, Pindyck is particularly critical on the damage functions, saying many are essentially made up. The final piece on social utility and the rate of time preference are essentially policy parameter which are open to political forces and therefore subject to considerable variability (& that’s a polite way of putting it).

The point about damage functions is an interesting one as these are also key determinants in the catastrophe vendor models widely used in the insurance sector. As a previous post on Florida highlighted, even these specific and commercially developed models result in varying outputs.

One example of IAMs directly influencing current policymakers is those used by the Interagency Working Group (IWG) which under the Obama administration is the entity that determines the social cost of carbon (SCC), defined as the net present damage done by emitting a marginal ton of CO2 equivalent (CO2e), used in regulating industries such as the petrochemical sector. Many IAMs are available (the sector even has its own journal – The Integrated Assessment Journal!) and the IWG relies on three of the oldest and most well know; the Dynamic Integrated Climate and Economy (DICE) model, the Policy Analysis of the Greenhouse Effect (PAGE) model, and the fun sounding Climate Framework for Uncertainty, Negotiation, and Distribution (FUND) model.

The first IWG paper in 2010 included an exhibit, reproduced below, summarizing the economic impact of raising temperatures based upon the 3 models.

click to enlargeClimate Change & Impact on GDP IWG SCC 2010

To be fair to the IWG, they do highlight that “underlying the three IAMs selected for this exercise are a number of simplifying assumptions and judgments reflecting the various modelers’ best attempts to synthesize the available scientific and economic research characterizing these relationships”.

The IWG released an updated paper in 2013 whereby revised SCC estimates were presented based upon a number of amendments to the underlying models. Included in these changes are revisions to damage functions and to climate sensitivity assumptions. The results of the changes on average and 95th percentile SCC estimates, at varying discount rates (which are obviously key determinants to the SCC given the long term nature of the impacts), can be clearly seen in the graph below.

click to enlargeSocial Cost of Carbon IWG 2010 vrs 2013

Given the magnitude of the SCC changes, it is not surprising that critics of the charges, including vested interests such as petrochemical lobbyists, are highlighting the uncertainty in IAMs as a counter against the charges. The climate change deniers love any opportunity to discredit the science as they demonstrated so ably with the 4th IPCC assessment. The goal has to be to improve modelling as a risk management tool that results in sensible preventative measures. Pindyck emphasises that his criticisms should not be an excuse for inaction. He believes we should follow a risk management approach focused on the risk of catastrophe with models updated as more information emerges and uses the threat of nuclear oblivion during the Cold War as a parallel. He argues that “one can think of a GHG abatement policy as a form of insurance: society would be paying for a guarantee that a low-probability catastrophe will not occur (or is less likely)”. Stern too advises that our focus should be on potential extreme damage and that the economic community need to refocus and combine current insights where “an examination and modelling of ways in which disruption and decline can occur”.

Whilst I was looking into this subject, I took the time to look over the completed 5th assessment report from the IPCC. First, it is important to stress that the IPCC acknowledge the array of uncertainties in predicting climate change. They state the obvious in that “the nonlinear and chaotic nature of the climate system imposes natu­ral limits on the extent to which skilful predictions of climate statistics may be made”. They assert that the use of multiple scenarios and models is the best way we have for determining “a wide range of possible future evolutions of the Earth’s climate”. They also accept that “predicting socioeconomic development is arguably even more difficult than predicting the evolution of a physical system”.

The report uses a variety of terms in its findings which I summarised in a previous post and reproduce below.

click to enlargeIPCC uncertainty

Under the medium term prediction section (Chapter 11) which covers the period 2016 to 2035 relative to the reference period 1986 to 2005, a number of the notable predictions include:

  • The projected change in global mean surface air temperature will likely be in the range 0.3 to 0.7°C (medium confidence).
  • It is more likely than not that the mean global mean surface air temperature for the period 2016–2035 will be more than 1°C above the mean for 1850–1900, and very unlikely that it will be more than 1.5°C above the 1850–1900 mean (medium confidence).
  • Zonal mean precipitation will very likely increase in high and some of the mid-latitudes, and will more likely than not decrease in the subtropics. The frequency and intensity of heavy precipitation events over land will likely increase on average in the near term (this trend will not be apparent in all regions).
  • It is very likely that globally averaged surface and vertically averaged ocean temperatures will increase in the near term. It is likely that there will be increases in salinity in the tropical and (especially) subtropical Atlantic, and decreases in the western tropical Pacific over the next few decades.
  • In most land regions the frequency of warm days and warm nights will likely increase in the next decades, while that of cold days and cold nights will decrease.
  • There is low confidence in basin-scale projections of changes in the intensity and frequency of tropical cyclones (TCs) in all basins to the mid-21st century and there is low confidence in near-term projections for increased TC intensity in the North Atlantic.

The last bullet point is especially interesting for the insurance sector involved in providing property catastrophe protection. Graphically I have reproduced two interesting projections below (Note: no volcano activity is assumed).

click to enlargeIPCC temperature near term projections

Under the longer term projections in Chapter 12, the IPCC makes the definite statement that opened this post. It also states that it is virtually certain that, in most places, there will be more hot and fewer cold temperature extremes as global mean temper­atures increase and that, in the long term, global precipitation will increase with increased global mean surface temperature.

I don’t know about you but it seems to me a sensible course of action that we should be taking scenarios that the IPCC is predicting with virtual certainty and applying a risk management approach to how we can prepare for or counteract extremes as recommended by experts such as Pindyck and Stern.

The quote “it’s better to do something imperfectly than to do nothing perfectly” comes to mind. In this regard, for the sake of our children at the very least, we should embrace the imperfect art of climate change modelling and figure out how best to use them in getting things done.