Class 3 Market risk. Beyond VaR

1. Class 3Market risk. Beyond VaR

2. How VaR concept may be applied elsewhere: Cash flow at risk (CaR) • The worst-case cash flows over a certain period with a given confidence level (95% or 99%): Prob(E[CF] - CF < CaR) = 1-α • Example: a company expects annual CashFlowof $80m, the volatility is $50m. • Assuming normal distribution,CaR5% = 1.65*$50m = $82.5m. • If the critical sustainable level of cash flows for the company is $20m, than it has chosen a too risky strategy. • Which companies prefer CaR (or VaR)? • VaR measures risk for the company’s value, usually applied for financial companies • CaR is relevant for companies that cannot readily trade their assets and rely on their cash flows to finance their investment projects

3. In-class discussion: What are the main drawbacks of VaR? • It does not show the actual magnitude of the worst losses • Due to model risk, the measurement error may be large • Esp. for a high confidence level • Implicit assumptions may be wrong • No intraday trading • Risks are described by exposures to several risk factors • It may be manipulated by choosing… • Strategies neutral to given risk factors • Portfolios with very unlikely extreme losses • It is not subadditive • The ptfVaR may exceed the sum of VaRs of individual positions

4. VaR is measued for a static portfolio. How to do a sensitivity analysis for VaR? • Incremental VaR: ΔVaRdue to a change in the position • Precise measurement requires re-estimation • VaRdelta: partial derivative wrt factor or position • Marginal (component) VaR: Delta*Position • Additive: ptfVaR is a sum of all component VaRs • VaRbeta: % contribution of a given position to the overall ptf risk

5. Example of VaR decomposition Sum of individualVaRs Portfolio VaR

6. Marginal VaR vs. Incremental VaR VaR Incremental VaR VaR delta Marginal VaR New Position Current Position Position Size

7. Should regulators tie capital requirements to VaR (validated by exceptions)? • Basel penalizes the bank if there are too many exceptions • 2006 Risk survey: banks report far fewer exceptions thanexpected • It seemed that banks wereoverly conservative in capital calculations • However, this did not help them go through the crisis in 2008 • Only two banks recorded 0-4 exceptions (out of 250) in 2008: Goldman Sachs and… Lehman Brothers • A responsive VaR model reflecting changes in position and market behavior produces volatile risk estimates • “it is inconsistent with the idea that capital levels should be stable” • “Setting capital requirements is the job of regulators, not the job of the people who calculate VAR”

8. Model risk: VaR estimate depends on the modeling approach • Some banks may be too conservative, and the others may be too aggressive. As a consequence, their capital will be excessive or insufficient relative to the true level of risk. • “If you had two different institutions measurethe VAR of the same portfolio, they wouldproduce different values and different changesin VAR over time.” • Is it possible to solve this problem?

9. In-class discussion: pros and cons of 2011 suggestion by VikramPandit (Citi CEO) • “Regulators should create a “benchmark” portfolio and require all financial institutions, not just banks, to measure risk against that. • The benchmark portfolio would not actually exist on the balance sheet of any one institution. Rather, it would be a collection of real investments that stand in for the kinds of assets that most financial institutions actually hold at the time. What is more, its contents would be 100% public. • Institutions would be required to produce, on a quarterly basis for that benchmark portfolio, a hypothetical loan/loss reserve level, value at risk, stress-test results and risk-weighted assets. • Right now these measures are run only against an institution’s actual portfolio and only a limited number of the results are disclosed. • How a given company’s risk measurements perform against the benchmark portfolio tells the world how its management thinks about risk, and so just how conservative or risky its own portfolio probably is.”

10. The actual losses may be much larger than VaR due to fat tails • The CIO of a large U.S. public-sector fund • “We use correlations and noticed that, during recent crises, correlations were not static but moved. But we did not think that tails were so dismally fat. In the space of six years, we had the equivalent of Pearl Harbor (i.e., 11 September 2001) and 1929 (i.e., events from mid-2007 to the first quarter of 2009). That makes two black swan events, but we need a better concept than black swans.” • VaR could be gamed. • “VaR ignored the slim likelihood of giant losses, which could only come about in the event of a true catastrophe(e.g., CDS)”

11. Which modeling approaches can predict actual losses? • Conditional VaR/ Expected shortfall: E[Loss | Loss > VaR] • It is a coherent measure • Monte Carlo simulations • Ability to model fat tails under different assumptions • Stress testing • Performance under different market conditions • Extreme value theory • Compute the distribution of the maximum value of losses • “CVaR can be explained reasonably well to clients.” • “Even CVaR does not tell us what the maximum loss might be. We need to look at the system as a whole, the macro links. A macro view is very useful. We ask our macroeconomists not only to give their views on inflation, GDP, and so on, but for more of a strategic, operative view as all volatilities and correlations are going up.”

12. Extreme Value Theory: e.g. using generalized Pareto distribution for the tail

13. What if assumptions do not work? Rising correlations and failure of diversification • Diversification seems to fail when it is needed most. • “In 2007, the world saw the most profound bubble in risk assets ever seen, [and as a consequence], there was no way that portfolio construction techniques could have reduced the size of the overall losses.” • “It was considered that diversification would work. People forgot that markets are not exogenous; there is interconnectivity of markets and of economies.” • A popular way of describing the recent crash is to say that “all correlations went to 1.”

14. VaR may neglect important risks • It was not only market risk that had not been properly considered prior to the 2008 crash but also liquidity risk, counterparty risk, systemic risk, and leverage • “What people missed was liquidity. The management of liquidity risk was the big failure. Counterparty risk, credit risk was also missed, and to some degree, market risk in the portfolios was missed.” • “In the absence of liquidity, pricing becomes academic because there is no market.”

15. How to modify VaR modeling approach to account for market liquidity risk? • Stressed VaRbased on more severe assumptions • VaR adjusted for the effective spread depending on the transaction size and timing • Harder to measure for the OTC market • Increases during the crisis • Monte Carlo analysis: adjust VaR accounting for • Direction and size of positions • Ideally, should know elasticity of price to volume • Correlation between market dynamics and liquidity • Asymmetry between bullish and bearish markets • Stress testing, accounting for • Margin requirements • The likelihood of systemic crisis

16. VaR can only measure quantifiable risks • NassimTaleb: • “The greatest risks are never the ones you can see and measure, but the ones you can’t see and therefore can never measure.” • Black swan: “an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight” • “A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives.”

17. In-class discussion: How to deal with black swans or “unknown unknowns”? • Identifying black swans at an early stage • Inside: stress testing, risk mapping, open communications • External experts with fresh view • External sources of information (news, customer surveys) to identify key trends and strange events • Dealing with the risks that remain unknown • Maintaining financial strength: low leverage, strategic reserves • Making the procedures simpler: e.g. size limits • Making the business more robust in case a black swan happens: e.g. via diversification • Making personnel ready to crisis management: preparing a plan of actions, training key managers

18. Was the crisis an example of the futility or utility of risk modeling? • “…a computer does not do risk modeling. People do it. And people stopped being careful. They took on too much leverage. This was much more a failure of management than of risk management. Blaming models for this would be very unfortunate. You can’t blame math.” • “People like to have one number they can believe in.” • Investors, regulators, boards,… • At the height of the bubble, there was so much money to be made that any firm that pulled back because it was nervous about risk would forsake huge short-term gains and lose out to less cautious rivals. The fact that VaR didn’t measure the possibility of an extreme event was a blessing to the executives. It made black swans all the easier to ignore. All the incentives — profits, compensation, glory, even job security — went in the direction of taking on more and more risk, even if you half suspected it would end badly. After all, it would end badly for everyone else too. • “As long as the music is playing, you’ve got to get up and dance.”

19. How did Goldman Sachs manage to sidestep the subprime crisis? • In December 2006, Goldman’s various indicators, including VaR and other risk models, began suggesting that something was wrong. • “We have lots of models here that are important, but none are more important than the P&L, and we check every day to make sure our P&L is consistent with where our risk models say it should be. In December our mortgage business lost money for 10 days in a row. It wasn’t a lot of money, but by the 10th day we thought that we should sit down and talk about it.” • Goldman called a meeting of about 15 people, including several risk managers and the senior people on the various trading desks. The mortgage-backed securities market “felt like it was going to get worse before it got better. So we made a decision: let’s get closer to home.”

20. How do companies use VaR post-crisis? • CIO of a fund in Europe • “We use classical VaR and always keep in mind that all figures from models are information for decision making, not a prediction for the future. We take a strategic view; the future cannot be predicted. But model results allow us to look at the past and reason on the future.” • Another source: • “We use VaR as part of the asset/liability management [ALM] study to determine strategic asset allocation. We have not found anything much better. VaR is only so useful. It gives a 95% confidence level, but as in 2008, people forget to look at the remaining 5%. If one wants to cover the 5% or even 1%, the black swan events, you might as well become an insurance firm that gets by with 2 or 3% returns.”

21. How do companies use VaR post-crisis? • CIO of a Dutch pension fund • “In the past, the policy was you can only control risk. What mattered most were returns, and then next, we looked at the risk. We need to turn this upside down, to look at the risk first and ask, Can we live with this risk and accept the returns?” • Another CIO: • “Risk models are not as robust as they could be. Only in the last five years has the investment management industry put considerable investment into risk management, and we still do not have the tools to manage risk on the private side.” • “We tracked VaR throughout the crisis but did not use it as our main measure. Rather, we used correlations. Our risk management is driven by factors.”

22. Measuring market risk (VaR): the implementation process • Measurement • Specifying assumptions explicitly • Controlling for portfolio effects and instruments with non-linear payoff • Using different methods for robustness • Using complementary measures • Back testing • Verifying the precision of the risk estimates • Stress testing • Analyze a worst-case scenario

23. What is the purpose of stress testing? • Analyzingthefirm’svalueunderarare, butpossiblescenario • Showthemagnitudeoflosses, whichexceedVaR • Helptoidentifythecompany’sweaknesses • Be prepared to any possible crisis, even though we don’t know its probability of occurring

24. How to implement stress testing? • Historicalscenarios • August 1998: Russiangvtdefault, rubledevaluation, creditspreadsrising, developedcountries’ bondsratesfalling, gradualliquiditycrisis • Shockforacertainassetclass: BlackMondayforthe US stockmarketin 1987, warinIraqandoilprice, etc. • Shockforacertainregion: Asiancrisisin 1997 (foremergingmarkets), weakeningofthedollar • 9/11 terrorattack, Enronreportingscandal, Yukoscase, etc. • Hypotheticalscenarios: e.g. imposed by Fed on the US banks • Peak unemployment rate: 12.1% • Drop in equity prices: more than 50% • Decline in housing prices: more than 20% • Sharp market shock for the largest trading firms

25. New methods of stress testing • Reverse stress testing • Identifying the scenarios that could threaten the survival of the firm • Liquidation plan in case of bankruptcy • Making sure that the large bank may be dissolved swiftly and without significant damage to the others