Prices of Collateralized Debt Obligations: An Overview. Gerald P. Dwyer Federal Reserve Bank of Atlanta University of Carlos III, Madrid

Transcription

1 Prices of Collateralized Debt Obligations: An Overview Gerald P. Dwyer Federal Reserve Bank of Atlanta University of Carlos III, Madrid

2 Only an Overview These brief notes provide only an overview of some of the literature that analyzes prices of collateralized debt obligations and one empirical paper

3 Pricing of Individual Deals Charles Smithson, Valuing Hard-to-value Assets and Liabilities: Notes on Valuing Structured Credit Products Journal of Applied Finance, Issues 1 and 2, 2009 Discusses general valuation problem and then context of hard-to-value illiquid assets Pricing of CDOs starts at cash flows and models to tranches cash flows and then values these cash flows

4 An Empirical Analysis of the Pricing of CDOs Longstaff and Rajan (2008) Build a model of CDX prices and estimate it for a three-factor model October 2003 to October 2005 Suggest the three factors can be approximately interpreted as Firm-specific default risk: 64.6% of the total CDX index spread Clustered industry or sector risk: 27.1% of the spread Economy-wide default risk: 8.3% of the spread Bhansali, Gringrich and Longstaff (2008) show a substantial increase in systemic risk in

5 Why Are Securitization Issues Tranched? Firla-Cuchra and Jenkinson (2006) Test theoretical explanations Create separating equilibrium in which higher-rated tranches are less informationally intensive and lower-rated tranches are more informationally intensive Pooling can overcome adverse selection problem by concentrating losses in lower tranche (Lender holds equity tranche Chiesa 2006) Market incompleteness can create gain from stripping off nearly risk-free part Data from comprehensive data on European securitizations from 1987 to 2003 Find evidence consistent with all these explanations

6 Tranching and Rating Brennan, Hein and Poon (2009) Explain arbitrage CDOs Build pricing model in which CDOs are priced with same distribution as a typical corporate issuer of a bond with the same probability of default or expected losses Default probabilities (S&P and Fitch) Expected losses (Moody s) CDO distribution is not really the same; buyers are wrong Theory and numerical examples Show this can explain tranching, not that it is only plausible explanation or most likely one

7 Economic Catastrophe Bonds Coval, Jurek, and Stafford (2009) Build model of rating and tranching Low payoffs on highly rated tranches are likely to come in bad states of the world Bad states of the world here maps into high stochastic discount factors (high marginal utility) Buyers ignore shift of payments from high value periods into low value periods Use CDX data on credit default swaps to suggest that the price data are consistent with prices based on ignoring the state in which various payoffs are made September 2004 to September 2007

8 ABX and Valuing CDOs Stanton and Wallace (2009) ABX index used by some to value CDOs Are prices credible? ABX price changes uncorrelated with changes in values of underlying securities Prices not credible in terms of underlying Prices consistent with recovery rate of 21 percent if all mortgages default 21 percent much too low in U.S. experience

9 Pricing of ABX Fender and Scheicher (2009) Regressions of returns on Housing and related indicators Ratings downgrades Interest rates Risk appetite and liquidity Risk appetite measured by ratio of VIX to realized volatility over a forward 20-day window Liquidity measured by spreads on $ 10-year swaps and CDX

10 Pricing of ABX (2) Fender and Scheicher (2009) Results indicate that liquidity and risk appetite are important determinants in addition to the fundamental ones

11 ABX and Housing Futures Mizrach (2009) Looks at jumps in ABX and housing futures Finds they are related, mostly through news

12 Did ABX Prices Reflect Liquidity Problems during the Financial Crisis? Dungey, Dwyer and Flavin (2011) Systematic and Liquidity Risk in Subprime Mortgage-backed Assets Overall strategy Estimate a common factor related to the financial crisis Examine how this factor is related to long-term and short-term factors

13 06-1 vintage ABX Indices by Vintage 06-2 Vintage /2/06 1/2/08 1/2/ Vintage AAA AA A BBB BBB- - 1/2/06 1/2/08 1/2/ Vintage /2/06 1/2/08 1/2/10 Sources: Markit Group Limited/Haver Analytics - 1/2/06 1/2/08 1/2/10

14 Modelling Framework Define return as change in logarithm of index value Returns on each tranche and vintage are modelled as a linear combination of a common, credit rating, vintage and idiosyncratic factor, Returns are pre-filtered to account for ARCH in residuals

15 Modelling Framework t j i t j i t i t i t i t j k t j r t j t w t w t f k k w w,,,,,, 1,,,, 1,,, 1 ; ; ;,,,,,,,,,, i j t i j t i j j t i j i t i j i j t y w k f f

16 Estimation Data from start of vintages to December 31, 2009 AAA, AA and BBB- tranches , , and vintages Estimate IGARCH for each Then estimate factors by quasi-maximum likelihood

17 06-1 vintage ABX Indices by Vintage 06-2 Vintage /2/06 1/2/07 1/2/08 1/2/ Vintage AAA AA A BBB BBB- - 1/2/06 1/2/07 1/2/08 1/2/ Vintage /2/06 1/2/07 1/2/08 1/2/09-1/2/06 1/2/07 1/2/08 1/2/09 Sources: Markit Group Limited/Haver Analytics

18 Table 1 Summary Statistics for Asset Returns by Vintage Rating Mean Standard Min Max Skewness Excess Number Deviation Kurtosis of observations Vintage 06-1 AAA AA A BBB BBB Vintage 06-2 AAA AA A BBB BBB Vintage 07-1 AAA AA A BBB BBB

19 Table 1 Summary Statistics for Asset Returns by Vintage Rating Mean Standard Min Max Skewness Excess Number Deviation Kurtosis of observations Vintage 06-1 AAA AA A BBB BBB Vintage 07-1 AAA AA A BBB BBB Vintage 07-2 AAA AA A BBB BBB

20 Table 2 Correlations of Returns across Credit Ratings within Vintages Rating AAA AA A BBB BBB- AAA AA A BBB BBB- Vintage 06-1 Vintage 06-2 AAA 1 1 AA A BBB BBB Vintage 07-1 Vintage 07-2 AAA 1 1 AA A BBB BBB

21 V1_AAA -20 1/1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/2010 Adjusted Returns Vintage 06-1 V1_BBB /1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/2010 V1_AA /1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/2010

22 V3_AAA -10 1/1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/ Adjusted Returns Vintage /1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/ V3_BBB- V3_AA -8 1/1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/2010

23 V4_AAA -10 1/1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/ Adjusted Returns Vintage /1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/ V4_BBB- V4_AA -8 1/1/2006 1/1/2007 1/1/2008 1/1/2009 1/1/2010

24 Factors V06-1

25 Factors 07-1

26 Factors V07-2

27 Common Factor Rating AAA AA BBB Vintage 06-1

28 Common Factor s Importance over Time AAA:06_1 AA:06_1 BBB:06_1 AAA:07_1 AA:07_1 BBB:07_1 AAA:07_2 AA:07_2 BBB:07_ first half second half first half second half

29 Integrated Logarithm of Common Factor for AAA /1/2006 7/1/2006 1/1/2007 7/1/2007 1/1/2008 7/1/2008 1/1/2009 7/1/2009

30 VIX and REIT VIX Jan-06 1-Jan-07 1-Jan-08 1-Jan-09 REIT Jan-06 1-Jan-07 1-Jan-08 1-Jan-09

31 30-Day Commercial Paper and Treasury Rates January 1, 2007 through February 07, Run on Northern Rock Run on Money Market Funds AA Asset Backed AA Financial AA Nonfinancial A2/P2 Nonfinancial Treasury AA Asset Backed AA Financial AA Nonfinancial A2/P2 Nonfinancial Treasury /1/07 7/1/07 1/1/08 7/1/08 1/1/09 7/1/09 1/1/10 7/1/10 1/1/11 Source: Federal Reserve Board, Haver Analytics

32 Libor-OIS Libor-OIS 1 Mo Libor-OIS 3 Mo /1/06 1/1/08 1/1/10 Sources: Financial Times/Bloomberg/Haver Analytics

33 Libor- Tbill Libor-Tbill 1 Mo Libor-Tbill 3 Mo /1/06 1/1/08 1/1/10 Sources: Financial Times/Bloomberg/Haver Analytics

34 OIS-Tbill OIS-Tbill 1 Mo OIS-Tbill 3 Mo (50.0) 1/1/06 1/1/07 1/1/08 1/1/09 1/1/10 Source: Federal Reserve Board/Bloomberg/Haver Analytics

35 Preliminary Evidence Some simple regressions On unit roots and cointegration Log integrated common factor, log index of reit index and log vix have unit roots There exists one cointegrating vector among these variables I have done this and just am estimating ecm and computing relationships

36 Regression Results Dependent variable: Ifw_AAA061 R-Square Parameter Standard Variable Estimate Error t Value Pr > t Intercept <.0001 DJAREIT <.0001 AAABCPmTbill1mo LiborMOIS1m <.0001

37 Regression with TED Spread Dependent variable: Ifw_AAA061 R-Square Parameter Standard Variable Estimate Error t Value Pr > t Intercept <.0001 DJAREIT <.0001 AAABCPmTbill1mo <.0001 LiborMTbill1m <.0001

38 Regression with Libor-OIS and Ted Spread Dependent variable: Ifw_AAA061 R-Square Parameter Standard Variable Estimate Error t Value Pr > t Intercept <.0001 DJAREIT <.0001 AAABCPmTbill1mo <.0001 LiborMTbill1m <.0001 OISMTbill1m

39 Conclusions We find an increasing role for the common factor and the escalating vulnerability of AAA tranche to common factors

40 Conclusions Preliminary evidence common factor is related to Real estate values Signals of financial stress Libor minus OIS Commercial paper less Tbill rate How important? Housing prices may be the predominant factor Liquidity and flight to quality probably played a role