Finance and the Crisis Umberto Cherubini University of Bologna

1. Finance and the Crisis Umberto Cherubini University of Bologna

2. Outline How the crisis started Securitization structures Toxic assets? How the crisis expanded Counterparty risk Liquidity and the accounting standards Where the crisis ended (did it end?) Public debt and banks The Government budget crisis What’s next?

3. Lessons from crises • September-October, 1998: LTCM, the lesson to be learned is liquidity, and the incomplete market problem • November-December 2001: Enron, the theme is lack of transparency of balance sheet data, problem of incomplete information • May 2005: the crisis on securitization following downgrading of GM to junk. The theme is break in correlation. Hedge funds affected.

4. The crisis of 2008, 2009, 2010… • Credit crisis: “subprime” mortgages were the trigger of the crisis. • Liquidity crisis: difficulty to unwind positions has exacerbated the crisis, like in the LTCM case • Accounting transparency crisis: fair-value accounting has been a vehicle of contagion, Enron’s “lite accounting” has become the practice of the banking system. Use of derivative contracts for “window dressing”: councils, Greece, Italy??

5. How the crisis started • Credit crisis: the crisis began with fear of insolvency on asset-backed-securities (ABS), that is bonds guaranteed by pools of assets as collateral. • Question: bonds guaranteed by collateral, whatever it can be, cannot be riskier than bonds guaranteed by no collateral at all. So why the crisis sprang from these assets, and not from the unsecured ones? • Possible answers: unsecured investment are monitored more closely that collateralized ones (moral hazard); securitized investments are marked-to-market (fair value accounting standards)

6. Securitization deals Senior Tranche Originator Junior 1 Tranche Special Purpose Vehicle SPV Sale of Assets Junior 2 Tranche Mezz Tranche Equity Tranche

7. Synthetic CDOs Senior Tranche Originator Junior 1 Tranche Protection Sale Special Purpose Vehicle SPV Junior 2 Tranche CDS Premia Interest Payments Investment Mezz. Tranche Collateral AAA Equity Tranche

8. The economic rationale • Arbitrage (no more available): by partitioning the basket of exposures in a set of tranches the originator used to increase the overall value. • Regulatory Arbitrage: free capital from low-risk/low-return to high return/high risk investments. • Funding: diversification with respect to deposits • Balance sheet cleaning: writing down non performing loans and other assets from the balance sheet. • Providing diversification: allowing mutual funds to diversify investment

9. Structuring securitization deals • Securitization deal structures are based on three decisions • Choice of assets (well diversified) • Choice of number and structure of tranches (tranching) • Definition of the rules by which losses on assets are translated into losses for each tranches (waterfall scheme)

10. Choice of assets • The choice of the pool of assets to be securitized determines the overall scenarios of losses. • Actually, a CDO tranche is a set of derivatives written on an underlying asset which is the overall loss on a portfolio L = L1 + L2 +…Ln • Obviously the choice of the kinds of assets, and their dependence structure, would have a deep impact on the probability distribution of losses.

11. Tranche • A tranche is a bond issued by a SPV, absorbing losses higher than a level La (attachment) and exausting principal when losses reach level Lb (detachment). • The nominal value of a tranche (size) is the difference between Lb and La Size = Lb – La

12. Kinds of tranches • Equity tranche is defined as La = 0. Its value is a put option on tranches. v(t,T)EQ[max(Lb – L,0)] • A seniortranche with attachmentLa absorbs losses beyond La up to the value of the entire pool, 100. Its value is then v(t,T)(100 – La) – v(t,T)EQ[max(L – La,0)]

13. Arbitrage relationships • If tranches are traded and quoted in a liquid market, the following no-arbitrage relationships must hold. • Every intermediate tranche must be worth as the difference of two equity tranches EL(La, Lb) = EL(0, Lb) – EL(0,La) • Buyng an equity tranche with detachmentLa and buyng the corresponding senior tranche (attachmentLa) amounts to buy exposure to the overall pool of losses. v(t,T)EQ[max(La – L,0)] + v(t,T)(100 – La) – v(t,T)EQ[max(L – La,0)] = v(t,T)[100 – EQ (L)]

14. Risk of different “tranches” • Different “tranches” have different risk features. “Equity” tranches are more sensitive to idiosincratic risk, while “senior” tranches are more sensitive to systematic risk factors. • “Equity” tranches used to be held by the “originator” both because it was difficult to place it in the market and to signal a good credit standing of the pool. In the recent past, this job has been done by private equity and hedge funds.

15. Securitization zoology • Cash CDO vs Synthetic CDO: pools of CDS on the asset side, issuance of bonds on the liability side • Funded CDO vs unfunded CDO: CDS both on the asset and the liability side of the SPV • Bespoke CDO vs standard CDO: CDO on a customized pool of assets or exchange traded CDO on standardized terms • CDO2: securitization of pools of assets including tranches • Large CDO (ABS): very large pools of exposures, arising from leasing or mortgage deals (CMO) • Managed vs unmanaged CDO: the asset of the SPV is held with an asset manager who can substitute some of the assets in the pool.

16. Standardized CDOs • Since June 2003 standardized securitization deals were introduced in the market. They are unfunded CDOs referred to standard set of “names”, considered representative of particular markets. • The terms of thess contracts are also standardized, which makes them particularly liquid. They are used both to hedged bespoke contracts and to acquire exposure to credit. • 125 American names (CDX) o European, Asian or Australian (iTraxx), pool changed every 6 months • Standardized maturities (5, 7 e 10 anni) • Standardized detachment • Standardized notional (250 millions)

17. i-Traxx CDX Tranche Bid Ask Tranche Bid Ask 0-3% 23.5* 24.5* 0-3% 44.5* 45* 3-6% 71 73 3-7% 113 117 6-9% 19 22 7-10% 25 30 9-12% 8.5 10.5 10-15% 13 16 12-22% 4.5 5.5 15-30% 4.5 5.5 (*) Amount to be paid “up-front” plus 500 bp on a running basis Source: Lehman Brothers, Correlation Monitor, September 28th 2005. i-Traxx and CDX quotes, 5 year, September 27th 2005

18. Gaussian copula and implied correlation • The standard technique used in the market is based on Gaussian copula C(u1, u2,…, uN) = N(N – 1 (u1 ), N – 1 (u2 ), …, N – 1 (uN ); ) where ui is the probability of event i T and iis the default time of the i-th name. • The correlation used is the same across all the correlation matrix.The value of a tranche can either be quoted in terms of credit spread or in term of the correlation figure corresponding to such spread. This concept is known as implied correlation. • Notice that the Gaussian copula plays the same role as the Black and Scholes formula in option prices. Since equity tranches are options, the concept of implied correlation is only well defined for them. In this case, it is called base correlation. The market also use the term compound correlation for intermediate tranches, even though it does not have mathematical meaning (the function linking the price of the intermediate tranche to correlation is NOT invertible!!!)

20. Base correlation

21. CDO2 Originator Senior Tranche Senior Tranche ABS (AAA) Junior 1 Tranche Special Purpose Vehicle SPV Junior 2 Tranche Tranche i … Tranche Tranche j Equity Tranche Tranche k

22. Gaussian factor model (Basel II) • Assume a model in which there is a single factor driving all losses. The dependence structure is gaussian. In terms of conditional probabilility where M is the common factor and m is a particular scenario of it.

23. Vasicek model • Vasicek proposed a model in which a large number of obligors has similar probability of default and same gaussian dependence with the common factor M (homogeneous portfolio. • Probability of a percentage of losses Ld:

24. Vasicek density function

25. Vasicek model • The mean value of the distribution is p, the value of default probability of each individual • Value of equity tranche with detachment Ld is Equity(Ld) = (Ld – N(N-1(p); N-1 (Ld);sqr(1 – 2)) • Value of the senior tranche with attachment equal to Ld is Senior(Ld) = (p – N(N-1(p); N-1 (Ld);sqr(1 – 2)) where N(N-1(u); N-1 (v); 2) is the gaussian copula.

26. Vampires, zombies, toxic assets… • We are “fairly” confident that vampires and zombies do not exist: what about toxic assets? • A toxic asset is a creature with 30% attachment. Under which conditions can we create a toxic asset? We mean an asset that is worth 70% of its value. • Assume a homogeneous portfolio of exposures and perfect correlation of the losses in the pool. Then, a toxic asset would require a pool with an average delinquency rate of 30%. Can it be serious? Or is it just another horror movie?

27. Fréchet bound • Men get reflected in mirrors (if they are not vampires) and assets cannot exceed super replication bounds (if they are not toxic). According to the Vasicek formula, super-replication bounds are given by the bounds admitted for copulas (unless you define a new class that you may call vampire copulas). • Say two risks A and B have joint probability H(A,B) and marginal probabilities Ha(A) and Hb(B). We have that H(A,B) = C(Ha, Hb), and C is a copula function. • C(u,v) = uv, independence C(u,v) = min(u,v), perfect positive dependence The perfect dependence cases (we overlook negative dependence here) are called Fréchet bounds.

28. Price bounds of a senior tranche

29. Toxic assets: the definition • “Financial assets the value of which has fallen significantly and may fall further, especially as the market for them has frozen. This may be due to hidden risks within the assets becoming visible or due to changes in external market environment” FT lexicon • It seems then to be a problem of • Liquidity (market frozen) • Ambiguity (hidden risk becoming visible)

30. How the crisis expanded • “Default losses on US sub-prime mortgages about 500 billion dollars. • But in a mark-to-market world, deadly losses are valuation losses • Valuation losses as high as 4 trillion • Major banks failed without single penny of default • BIS study of rescue package: EUR 5 trillion in committed resources” Eli Remolona,IV Annual Risk Management Conf., Singapore, July 2010

31. Recipe for contagion • Ambiguity: assets for which you do not know whether they are collateralized or not or the quality of the collateral are traded at discount • Counterparty risk: you do not trust your neighbour, in spite of safety nets (netting, collateral). What went wrong? • Liquidity: funding liquidity (compete for funds from everyone except your neighbor) and market liquidity (try to unwind positions in assets) • Accounting: losses due to whatever (included liquidity) are marked-to-market and impair the balance sheet.

32. Ambiguity • Knightian uncertainty: uncertainty is when you do not know the odds. Risk refers to unambiguous bets. • Ellsberg paradox, 1961: agents prefer unambiguous bets over ambiguous bets, that is agents are uncertainty averse • Gilboa Schmeidler (1989): multiple prior approach, Max-Min-Expected Utility (MMEU): probabilities are represented by intervals, rather than numbers. • Gilboa (1987), Schmeidler (1982,1989): Choquet utility (sub-additive measures represent uncertainty aversion)

33. Ambiguity and the crisis • Toxic assets are ambiguous bets. The effect of ambiguity is that: • Investors require a premium for uncertainty • Bid-ask spread larger • Portfolio inertia (people do not participate in the market when uncertainty increases) • Ambiguity reduces market liquidity. • Changes in ambiguity can be triggered by events specific to a single issuer (or issue), or by shocks affecting other issuers (or issues). This is called information-based contagion (i.e. Enron).

34. Counterparty risk and the crisis • In 2008 the market was expecting a default of a big bank. On March 15 Bear Stearns was rescued. On September 15 Lehman Brothers was left to his destiny and went bust • The crisis was a test for the risk mitigating system applied in the banking practice. The system was severely shaked, but in the end it worked (we do not know whether with the help of Governments, and what would have happened without). • It is difficult to say whether the counterparty risk emergency is over or not.

35. Counterparty risk (long position) • Assume a forward contract CF.for the long party A. The value of credit exposure (CVA) is recovered as CFA(T) = max[S(T) – F(0),0](1 –1B) + max[S(T) – F(0),0]RRB1B – – max[F(0) –S(T),0] = CF(T) – LgdB1Bmax[S(T) – F(0),0]

36. Counterparty risk (short position) • For the short position we have instead CFB(T) = max[F(0) – S(T),0](1 –1A) + max[F(0) – S(T),0]RRA1A – – max[S(T) – F(0),0] = – CF(T) – LgdA1Amax[F(0) – S(T),0]

37. Credit Valuation Adjustment (CVA) • Counterparty risk requires a correction in the valuation of the CF contract, called CVA which amounts to a short position in a vulnerable option. EQ[P(t,T)Lgdi1imax[(S(T) – F(0)),0]]

38. A CVA Algorithm • In order to allow for default at arbitrary time before maturity, consider the following algorithm • 1. Partition the lifetime of the contract in a grid of times {t1,t2,…tn} • 2. For every time period from ti-1 to ti compute the exposure, that is the short position in the option • 3. For every time period from ti-1 to ti compute the expected loss from default of the counterparty [Q(ti-1) – Q(ti)] X LGD X Option with Q(ti) the survival probability beyond time Q(ti) • 4. Sum the expected losses

39. Risk mitigating techniques • In order to reduce the credit risk in their derivative transactions, banks apply risk mitigating techniques that are inspired by futures market. These are implemented in the so called ISDA standard Credit Annex • The risk mitigating techniques are: • Net exposure of the all open contracts (open interest account, in futures market jargon) • Deposit of collateral of profit and losses every week (margin in the language of futures)

40. A simple example • Assume a counterparty A has p forward contracts CFi open with counterparty B. • The value of each exposure is given by CFi = max([Si(t) – P(t,Ti)Fi],0) where  = 1 represents long positions and  = – 1 denotes short positions. • Notice that the exposure is a short position in a portfolio of call options for long positions and put options for short positions.

41. Netting • Assume that counterparty B defaults at time . In the presence of a netting agreement, exposure in this case will be given by a an option of a basket, rather than a basket of options

42. Monte Carlo simulation • Counterparty risk is evaluated by Monte Carlo simulation • Algorithm: • Choose a set of dates: {t1,t2,…tn} and for each one of these evaluate a basket option (counterparty risk exposure) • For each date tithe value of counterparty risk will be [Q(ti-1) – Q(ti)]Basket (S1, …Sp, ti; A(ti), ti) with Q(ti) the survival probability beyond time Q(ti)

43. Collateral • The impact of collateral amounts to resetting the strike in favor of the party that receives the deposit (again as it happens in the futures markets). • Collateral is deposited in cash or very safe securities. In come cases, however, the senior tranches were actually used as collateral. • If one accounts for collateral, the CVA amounts to a short position in cliquet options. • If risky collateral is used, it is typical to apply a “haircut” (a given amount of collateral provides guarantee for a lower amount of exposure)

44. What went wrong? • Risk mitigating arrangements: the Lehman Bros default provided a test. It seems that it took about 15 days to compute and notify losses, due to negatives externalities: shortage of lawyers, difficulty to have third party fair valuation. • Interbank market: the interbank market was left outside the risk mitigating arrangement. Credit risk haunted to the Euribor/Libor rates (difference between 3m Euribor/OIS)

45. From credit to liquidity • If you do not trust your neighbor and do not trust your assets, you are in liquidity trouble • Funding liquidity: you must come up with funding for your assets, but the market is dry. Solutions: i) chase retail investors ii) rely on quantitative easing (won’t last long) • Market liquidity: you are forced to unwind positions in periods of market stress, and you may not be able to find counterparts for the deal, unless at a deep discount. Solution: quantitative easing (place illiquid bonds as collateral)

46. From liquidity to accounting • Fair value accounting: bonds available for sale must be evaluated at fair value and profits and losses must be reported in the balance sheet. • What is fair value? The price as close as possible to the market evaluation? But: what is a market? • Types of assets: • Type 1. Price is available on a transparent market • Type 2. A variable needed to compute the price can be calibrated from a liquid market • Type 3. Neither the price or market parameters can be observed

47. Accounting and the crisis I • What is a market? Two people exchanging one good is a market? Or do we need more people to say that we have a market? Sorites paradox (how many grains make a heap of sand?) • In a market in which people do not trust their neighbors (counterparty risk) and do not trust their assets (ambiguity) accounting may have a perverse effect • Assume counterparty A is in desperate need of cash and is obliged to unwind a position worth 100 overnight (say a senior tranche). Say no one wants to buy, and finally one finds a counterpart for 70. If this is considered a market, all institutions in the world will record a loss of 30 on the same asset. And tomorrow many others will be in need of cash…

48. “Lite accounting” • Lite accounting was a term used for Enron to denote the fact that much of Enron’s debt and most of Enron managers’ bonuses where hidden in about 1 000 companies controlled by Enron, but not consolidated in its balance sheet. Enron crisis was triggered by the request of consolidation from the auditing company (Arthur Andersen) • SIV (Structured Investment Vehicle): lite accounting for banks. Off-balance sheet institutions, controlled by banks, issuing short term liabilities (commercial paper) and investing on long term bonds (senior tranches) to earn the difference in spread (carry). A receipe to boost leverage.

49. Accounting and the crisis II • Reconsider the modern version of Sorites paradox with lite accounting and SIV. • Financial institution A has SIV , and in an illiquid market has difficulty to raise commercial paper to fund the assets. Then it is forced to look for a financial institution B to sell the assets. But financial institution B should buy the asset through its vehicle  which is also struggling to place commercial paper to fund his own assets. • Notice: the first SIV in history were launched by Citigroup in 1988 and were given the names Alpha and Beta Finance Corporations.

50. Where did the crisis end? • The crisis could end nowhere but in the only balance sheet that is not computed at fair value, namely Government and municipal entities balance sheets. • Bail-out from the Government: special purpose interventions (see AIG, Fortis, and the like) and general purpose committments • Central bank intervention: quantitative easing, to provide liquidity to the system and prevent contagion. It is almost over in Europe, still alive in the US.