A crisis feeds on itself

TO BE NOTED: From Vox:

Modelling financial turmoil through endogenous risk

Jon Danielsson Hyun Song Shin Jean-Pierre Zigrand 11 March 2009

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By incorporating endogenous risk into a standard asset-pricing model, this column shows how banks’ capacity to bear risk seemingly evaporates in the face of market turmoil, pushing the financial system further into a tailspin. It suggests that risk-sensitive prudential regulation, in the spirit of Basel II, makes systemic financial crises sharper, larger, and more costly.

Financial crises are often accompanied by large price changes, but large price changes by themselves do not constitute a crisis. Public announcements of important macroeconomic statistics, such as the US employment report, are sometimes marked by large, discrete price changes at the time of announcement. However, such price changes are arguably the signs of a smoothly functioning market that is able to incorporate new information quickly. The market typically finds composure quite rapidly after such discrete price changes.

A crisis feeds on itself

In contrast, the distinguishing feature of crisis episodes is that they seem to gather momentum from the endogenous responses of the market participants themselves. Rather like a tropical storm over a warm sea, they gather more energy as they develop. As financial conditions worsen, the willingness of market participants to bear risk seemingly evaporates. They curtail their exposures and generally attempt to take on a more prudent, conservative stance.

However, the shedding of exposures results in negative spillovers on other market participants from the sale of assets or withdrawal of credit. As prices fall, measured risks rise, or previous correlations break down, market participants respond by further cutting exposures. The global financial crisis of 2007-9 has served as a live laboratory for many such distress episodes.

Modelling endogenous risk

In a new paper (Danielsson, Shin and Zigrand, 2009), we explicitly model the endogeneity of risk. The risks impacting financial markets are attributable (at least in part) to the actions of market participants. In turn, market participants' actions depend on perceived risk.

In equilibrium, risk should be understood as the fixed point of the mapping from perceived risk to actual risk. When banks believe trouble is ahead, they take actions that bring about realised volatility. So, market turmoil results because banks anticipate such turmoil. This is so even if the underlying fundamental risks are constant. Such a fixed point is the “endogenous risk” in our title.

Risk appetite and trading constraints

A model of endogenous risk enables the study of the endogenous propagation of financial booms and distress. Among other things, we can make precise the notion that market participants appear to become “more risk-averse” in response to deteriorating market outcomes. For economists, preferences and beliefs would normally be considered independent of one another.

However, we can distinguish “risk appetite” which motivates traders' actions, from “risk aversion”, which is a preference parameter hard-wired into agents' characteristics. A trader's risk appetite may change even if his preferences are unchanged. The reason is that risk taking may be curtailed by the constraints that traders operate under, such as those based on Value-at-Risk (VaR).

In our framework, all active traders are risk-neutral, but they operate under VaR constraints, which are widespread among financial firms and encouraged by the Basel regulations. The Lagrange multiplier associated with the VaR constraint is the key quantity in our model. It plays two important roles. First, it affects the portfolio choice of the traders. Second, we show that the Lagrange multiplier is related to a generalised Sharpe ratio for the set of risky assets traded in the market as a whole and hence depends on the forecast probability density over future outcomes.

Beliefs and risk appetite are thus linked through the Lagrange multiplier. To an outside observer, it would appear that market participants' preferences change with minute-by-minute changes in market outcomes. Crucially, shocks may be amplified through the feedback effects that operate from volatile outcomes to reduced capacity to bear risk. In this sense, the distinction between “risk appetite” and “risk aversion” is more than a semantic quibble. This distinction helps us understand how booms and crises play out in the financial system.

Endogenous volatility clustering and non-linear dependence

The model solution reveals several suggestive features that are consistent with empirical properties of asset returns found in practice.
The volatility of returns on financial assets generally changes over time, even though the fundamental shocks are constant. This is a well-known phenomenon known as volatility clustering. In the jargon, the model endogenously generates stochastic volatility.

Empirical evidence also suggests that option implied volatilities, and volatilities of volatilities, are shown to be high during market downturns, a result also predicted by our model.
Correlation also emerges where none exists at the fundamental level. During times of financial turmoil, correlations of returns are observed to increase with upward shifts in volatility. This phenomenon is known as non-linear dependence. We show that such features arise naturally in our model. Decrease in risk appetite and higher volatilities coincide with increased correlations, even though the underlying shocks are constant and independent across the risky assets.

Applying the model to financial crises

A common feature of asset price bubbles followed by a financial crisis is that the markets go through long periods of high return amid low volatility, implying high Sharpe ratios. The bubble expands under tranquil conditions. Then suddenly, at the first hint of turbulence, the willingness of market participants to bear risk seemingly evaporates. The price path associated with a bubble exhibits the pattern traders describe as “going up by the escalator but down by the elevator”.

However, the resulting shedding of exposures results in negative spillovers on other market participants from the sale of assets or withdrawal of credit. As prices fall, measured risks rise, previous correlations break down, or some combination of these occurs, market participants respond by further cutting their exposures. The global financial crisis of 2007-9 is strewn with examples of such distress episodes.

Since our model explicitly captures such phenomena, it provides a useful framework for analysing outcomes in asset markets during financial crisis and could be a starting point for better analysis of financial stability.

Prudential banking regulations can be destabilising

By pointing to the endogenous nature of risk, we highlight the role played by risk management rules used by active market participants, which serve to amplify aggregate fluctuations. Although it is a truism that ensuring the soundness of each individual institution ensures the soundness of the financial system, this proposition is vulnerable to the fallacy of composition.

Actions that an individual institution takes to enhance its soundness may undermine the soundness of others. If the purpose of financial regulation is to shield the financial system from collapse, it is a deeply flawed practice to base financial regulation on the “best practice” of individually optimal risk management policies, as is done under the current Basel II capital regulations. Risk is endogenous, and individually optimal risk management makes systemic financial crises sharper, larger, and more costly.

References

Danielsson, Jon, Hyun Song Shin and Jean-Pierre Zigrand (2009) “Risk Appetite and Endogenous Risk”

"Much of today’s financial regulation assumes that risk can be accurately measured"

A view about regulation on Vox from Jon Danielsson:

"The myth of the riskometer

Much of today’s financial regulation assumes( MECHANISTIC EXPLANATION ) that risk can be accurately measured – that financial engineers, like civil engineers, can design safe products with sophisticated maths informed by historical estimates. But, as the crisis has shown, the laws of finance react to financial engineers’ creations, rendering risk calculations invalid. Regulators should rely on simpler methods.(HUMAN AGENCY EXPLANATIONS )

There is a widely held belief that financial risk is easily measured – that we can stick some sort of riskometer( CAN'T BE DONE ) deep into the bowels of the financial system and get an accurate measurement of the risk of complex financial instruments. Such misguided belief in this riskometer played a key role in getting the financial system into the mess it is in.

Unfortunately, the lessons have not been learned. Risk sensitivity is expected to play a key role both in the future regulatory system and new areas such as executive compensation.

Origins of the myth

Where does this belief come from? Perhaps the riskometer is incredibly clever – after all, it is designed by some of the smartest people around, using incredibly sophisticated mathematics.

Perhaps this belief also comes from what we know about physics. By understanding the laws of nature, engineers are able to create the most amazing things. If we can leverage the laws of nature into an Airbus 380, we surely must be able to leverage the laws of finance into a CDO.

This is false. The laws of finance are not the same as the laws of nature. The engineer, by understanding physics, can create structures that are safe regardless of what natures throws at them because the engineer reacts to nature but nature does not generally react to the engineer.( NOT IN THE SAME WAY )

The problem is endogenous risk

In physics, complexity is a virtue( NO. SIMPLICITY IS A VIRTUE. ). It enables us to create supercomputers and iPods. In finance, complexity used to be a virtue. The more complex the instruments are, the more opaque they are, and the more money you make. So long as the underlying risk assumptions are correct( USEFUL ), the complex product is sound. In finance, complexity has become a vice( JUSTIFICATION FOR UNSOUND INVESTMENTS ).

We can create the most sophisticated financial models, but immediately when they are put to use, the financial system changes. Outcomes in the financial system aggregate intelligent human behaviour( TRUE. BUT THAT'S TRUE OF ALL OF THE HUMAN SCIENCES. ). Therefore attempting to forecast prices or risk using past observations is generally impossible( THAT'S FALSE. PREDICTING THE FUTURE PERFECTLY ISN'T POSSIBLE. ). This is what Hyun Song Shin and I called endogenous risk (Danielsson and Shin 2003).( IT'S NOT THAT PROFOUND )

Because of endogenous risk, financial risk forecasting is one of the hardest things we do( SO WHAT? ). In Danielsson (2008), I tried what is perhaps the easiest risk modelling exercise there is – forecasting value-at-risk for IBM stock. The resulting number was about +/- 30% accurate, depending on the model and assumptions. And this is the best case scenario. Trying to model the risk in more complicated assets is much more inaccurate. +/- 30% accurate is the best we can do( THE BEST YOU CAN DO ).

Applying the riskometer

The inaccuracy of risk modelling does not prevent us from trying to measure risk, and when we have such a measurement, we can create the most amazing structures – CDOs, SIVs, CDSs, and the entire alphabet soup of instruments limited only by our mathematical ability and imagination. Unfortunately, if the underlying foundation is based on sand, the whole structure becomes unstable. What the quants missed was that the underlying assumptions were false.( ABOUT MODELS AND REALITY, YES. )

We don’t seem to be learning the lesson, as argued by Taleb and Triana (2008), that “risk methods that failed dramatically in the real world continue to be taught to students”, adding “a method heavily grounded( HERE'S THE PROBLEM ) on those same quantitative and theoretical principles, called Value at Risk, continued to be widely used. It was this that was to blame for the crisis( I DON'T AGREE ).”

When complicated models are used to create financial products, the designer looks at historical prices for guidance. If in history prices are generally increasing and risk is apparently low, that will become the prediction for the future( IF YOU'RE A ROBOT ). Thus a bubble is created( THAT'S NOT THE CAUSE OF A BUBBLE. SORRY. ). Increasing prices feed into the models, inflating valuations, inflating prices more. This is how most models work( BUT NOT PEOPLE ), and this is why models are often so wrong. We cannot stick a riskometer( THERE ISN'T ONE ) into a CDO and get an accurate reading.

Risk sensitivity and financial regulations

One of the biggest problems leading up to the crisis was the twin belief that risk could be modelled( IT'S JUST A MODEL ) and that complexity was good( NOT GOOD ). Certainly the regulators who made risk sensitivity the centrepiece of the Basel 2 Accord believed this.

Under Basel 2, bank capital is risk-sensitive. What that means is that a financial institution is required to measure the riskiness of its assets, and the riskier the assets the more capital it has to hold. At a first glance, this is a sensible idea, after all why should we not want capital to reflect riskiness? But there are at least three main problems:( 1 ) the measurement of risk, ( 2 )procyclicality (see Danielsson et. al 2001), and the( 3 ) determination of capital.

To have risk-sensitive capital we need to measure risk, i.e. apply the riskometer. In the absence of accurate( TRUE ) risk measurements, risk-sensitive bank capital is at best meaningless and at worst dangerous.

Risk-sensitive capital can( MAYBE ) be dangerous because it gives a false sense of security. In the same way it is so hard to measure risk, it is also easy to manipulate risk measurements( THIS IS TRUE ). It is a straightforward exercise to manipulate risk measurements to give vastly different outcomes in an entirely plausible and justifiable manner, without affecting the real underlying risk. A financial institution can easily report low risk levels whilst deliberately or otherwise assuming much higher risk. This of course means that risk calculations used for the calculation of capital are inevitably suspect.( HERE I AGREE )

The financial engineering premium

Related to this is the problem of determining what exactly is capital. The standards for determining capital are not set in stone; they vary between countries and even between institutions. Indeed, a vast industry of capital structure experts exists explicitly to manipulate capital, making capital appear as high as possible while making it in reality as low as possible( TRUE. LEVERAGING. ).

The unreliability of capital calculations becomes especially visible when we compare standard capital calculations under international standards with the American leverage ratio. The leverage ratio limits the capital to assets ratio of banks and is therefore a much more conservative measure of capital than the risk-based capital of Basel 2. Because it is more conservative, it is much harder to manipulate.( IT'S ALSO MORE CONSERVATIVE, AND INHERENTLY LESS RISKY. I DON'T FOLLOW THE HARDER ARGUMENT. )

One thing we have learned in the crisis is that banks that were thought to have adequate capital have been found lacking( AND? ). A number of recent studies have looked at the various calculations of bank capital and found that some of the most highly capitalised banks under Basel 2 are the lowest capitalised under the leverage ratio, an effect we could call the financial engineering premium.( NO. COMPLETELY WRONG. THE BANKS AND INVESTORS WERE LOOKING FOR WAYS TO CUT CAPITAL RESTRICTIONS. THAT'S WHY THEY CHOSE CDSs, CDOs, AND THE MATH MODELS THAT JUSTIFY THEM. THEY COULD HAVE CHOSEN OTHER LESS MATHEMATICAL WAYS OF DOING THIS. )

As Philipp Hildebrand (2008) of the Swiss National Bank recently observed “Looking at risk-based capital measures, the two large Swiss banks were among the best-capitalised large international banks in the world. Looking at simple leverage( THAT'S ALWAYS WHAT YOU NEED TO LOOK AT ), however, these institutions were among the worst-capitalised banks”

The riskometer and bonuses

We are now seeing risk sensitivity applied to new areas such as executive compensation. A recent example is a report from UBS (2008) on their future model for compensation, where it is stated that “variable compensation will be based on clear performance criteria which are linked to risk-adjusted value creation.” The idea seems laudable – of course we want the compensation of UBS executives to be increasingly risk sensitive.

The problem is that whilst such risk sensitivity may be intuitively and theoretically attractive, it is difficult or impossible to achieve in practice. One thing we have learned in the crisis is that executives have been able to assume much more risk than desired by the bank( TRUE ). A key reason why they were able to do so was that they understood the models and the risk in their own positions much better than other parts of the bank( TRUE ). It is hard to see why more risk-sensitive compensation would solve that problem. After all, the individual who has the deepest understanding of positions and the models is in the best place to manipulate the risk models. Increasing the risk sensitivity of executive compensation seems to be the lazy way out.( THERE ARE BETTER WAYS )

This problem might not be too bad because UBS will not pay out all the bonuses in one go, instead, “Even if an executive leaves the company, the balance (i.e. remaining bonuses) will be kept at-risk for a period of three years in order to capture any tail risk events.” Unfortunately, the fact that a tail event is realised does not by itself imply that tail risk was high, and conversely, the absence of such an event does not imply risk was low. If UBS denies bonus payments when losses occur in the future and pays them out when no losses occur, all it has accomplished is rewarding the lucky and inviting lawsuits from the unlucky. The underlying problem is not really solved.( NOT REALLY, NO )

Conclusion

The myth of the riskometer is alive and kicking. In spite of a large body of empirical evidence identifying the difficulties in measuring financial risk, policymakers and financial institutions alike continue to promote risk sensitivity.

The reasons may have to do with the fact that risk sensitivity is intuitively attractive, and the counter arguments complex. The crisis, however, shows us the folly of the riskometer. Let us hope that decision makers will rely on other methods.

References

Danielsson, Jon and Hyun Song Shin, 2003, “Endogenous Risk”, chapter in Modern Risk Management: A History.
Danielsson, Jon, Paul Embrechts, Charles Goodhart, Con Keating, Felix Muennich, Olivier Renault and Hyun Song Shin (2001) “An Academic Response to Basel II”, 2001.
Danielsson, Jon (2008) “Blame the models”, VoxEU.org, 8 May 2008
Hildebrand, Philipp M. (2008) “Is Basel II Enough? The Benefits of a Leverage Ratio”, Financial Markets Group Lecture, London School of Economics .
Taleb, Nassim Nicholas and Pablo Triana (2008) “Bystanders to this financial crime were many” Financial Times December 7.
UBS (2008) “Compensation report: UBS’s new compensation model”

This is a strange argument. There is no riskometer. There are math models that are more or less useful. I don't see any argument that they can't be useful. Blaming the crisis on math models is itself a mechanistic explanation, based upon an incorrect understanding of how and why theories are useful. A theory or model can have very limited scope and be useful.

A warning about how models relate to the world is important, but it is possible to measure( although I don't like the word "measure" ) risk. If it weren't, no one would do anything.