The Price for Bearing Default Risk Darrell Duffie, Stanford - PowerPoint PPT Presentation

The Price for Bearing Default Risk Darrell Duffie, Stanford University Q Group, October, 2005 Based on collaboration with: Antje Berndt Rohan Douglas Mark Ferguson David Schranz Stanford University, 2005

Main Objective • How much are investors in corporate debt paid for taking default risk, above their expected default loss? • Our analysis is based on Moodys KMV estimates of default probabilities and CIBC data on default swap (CDS) prices. • The default risk premium is bigger, per dollar of expected default loss, for high-quality firms. • The default risk premium, at fixed credit quality, was dramatically reduced from mid-2002 to the end of 2003, especially in the broadcasting and entertainment sector. Stanford University, 2005

20 risk−neutral 18 actual 16 14 Default probability (percent) 12 10 8 6 4 2 0 Dec01 Jul02 Jan03 Aug03 Feb04 Sep04 Mar05 Figure 1: Estimated actual and risk-neutral 1-year default probabilities for Royal Caribbean Cruises. Stanford University, 2005

14 12.16 12 10 Default Rate (percent) 7.98 8 6 3.58 4 2.23 2 0.70 0.67 0.48 0.13 0.10 0.07 0.00 0.02 0.00 0.00 0.00 0 Ba1 Ba3 B1 B2 Aaa Aa1 Aa2 Aa3 A1 A2 Baa1 Baa2 Baa3 Ba2 B3 Figure 2: Default Rate by Moody’s Modified Credit Rating. Stanford University, 2005

70% 60% Last rating change: Upgraded 50% Unchanged 3-year default rate Downgraded 40% 30% 20% 10% 0% Investment-Grade B Caa Ba Figure 3: Upgrade-downgrade momentum (1996-2003 data). Source: Moody’s, 2004. Stanford University, 2005

Moody’s KMV Estimated Default Frequency • Asset value and volatility are computed jointly from a modified Black-Scholes options pricing model, treating equity as a call on assets struck at liabilities. • The liability default boundary point is measured as short-term debt plus a fraction (half) of long-term debt. • The “distance to default” is the number of standard deviations by which the expected asset value exceeds the default point. • This firm’s current EDF is the fraction of those firms in previous years with the same distance to default that actually did default within one year. Stanford University, 2005

0.05 0.04 Frequency of default within one year 0.03 0.02 0.01 0 −0.01 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Distance to default Figure 4: The dependence of empirical default frequency on distance to default. (Source: Duffie, Saita, Wang (2005). Stanford University, 2005

+ 350 + + + 300 + Number of Observations 250 + + 200 + + 150 + + + 100 + + + + + + 50 + + 10 20 30 40 50 60 70 80 90 100 Post Default Prices in US Dollars Figure 5: Distribution of senior unsecured recovery rates, 1982 - 2002. Source: Moody’s Default and Recovery Report (2003). Stanford University, 2005

60% 50% 40% Recovery rate 30% Value-Weighted Mean 20% Issuer-Weighted Mean Long-Term Issuer Mean 10% 0% 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 Year Figure 6: Time variation in average recovery rates, 1982 - 2003. Source: Moody’s. Stanford University, 2005

60% 1987 1997 50% 1984 1986 1992 1994 2003 Recovery rate 1996 40% 1998 1988 1991 1982 1999 1989 30% 2002 1990 2000 2001 20% Recovery rate = 50.3 - 6.3 Default rate £ 10% 2 R = 0.60 0% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% Default rate Figure 7: Correlation of Speculative Grade Default and Recovery Rates. Source: Moodys Default and Recovery Report (2004). Stanford University, 2005

Figure 8: Default swap: buyer of protection pays the CDS rate U quarterly, and at the default time τ delivers bond worth Y ( τ ) in exchange for notional (100). Stanford University, 2005

16 14 12 Number of quote providers 10 8 6 4 2 0 < 200 200-400 400-800 800-1,600 1,600-3,200 3,200-6,400 6,400-12,800 12,800-25,600 > 25,600 Figure 9: Distribution of CDS quote providers by number of quotes provided. Data source: CIBC. Stanford University, 2005

55 50 45 40 35 30 25 20 15 10 5 0 Aaa Aa A Baa Ba B Caa Ca C Unrated Figure 10: Distribution of firms by median credit rating during the sample period. Sources: CIBC and Moody’s. Stanford University, 2005

CDS 5-year rate (mid-quote, basis points) 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Moody’s KMV 5-year EDF (basis points) Figure 11: Scatter plot of EDF and CDS observations and OLS fitted relation- ship. Source: CIBC (CDS) and Moody’s KMV (EDF). Stanford University, 2005

Logarithm of CDS 5-year rate (mid-quote) 0 −1 −2 −3 −4 −5 −6 −7 −8 −7 −6 −5 −4 −3 −2 −1 Logarithm of Moody’s KMV 5-year EDF Figure 12: Scatter plot of EDF and CDS observations, logarithmic, and OLS fitted relationship. Source: CIBC (CDS) and Moody’s KMV (EDF). Stanford University, 2005

CDS versus EDF (5-year) For 33,912 paired daily median observations over 2000-2004: � ˆ log CDS i = 1 . 45 + 0 . 76 log EDF i + β j D month , sector ( i ) + z i , (0 . 05) (0 . 02) • Standard errors estimated for panel correlation. • R 2 = 74 . 4% . • One-sigma confidence band for a given CDS rate places it between 59% and 169% of the fitted rate. Stanford University, 2005

3.00 2.50 Oil and gas Broadcasting Healthcare Time effect on risk premium 2.00 1.50 1.00 0.50 0.00 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - - - - - - - - - - - - - - - - - - - - - - - - - c b r n g t c b r n g t c b r n g t c b r n g t c p c p c p c p c e e u u e e u u e e u u e e u u e O O O O D A D A D A D A D F J A F J A F J A F J A Month Figure 13: Monthly dummy multipliers in CDS-to-EDF fit. Stanford University, 2005

60 50 Mean recovery rate 40 30 20 10 0 Healthcare Media, Broadcasting Oil and Oil Services Utility-Gas and Cable Figure 14: Sectoral recovery differences. Stanford University, 2005

Default Intensity • λ t is the conditional mean arrival rate of default. R t � 0 λ ( s ) ds � • The probability of survival for t years is p ( t ) = E . e − • The risk-neutral probability of survival for t years is R t p ∗ ( t ) = E ∗ � 0 λ ∗ ( s ) ds � . e − • p ∗ ( t ) < p ( t ) because t > λ t . – λ ∗ – E ∗ ( λ ∗ t ) > E ( λ ∗ t ) . Stanford University, 2005

Dynamic Default Intensity Models • Actual intensity, λ t log-normal with mean reversion, fitted from 12 years of monthly observations of 1-year EDFs by maximum likelihood. • Sector homogeneity of volatility and mean reversion. • Risk-neutral intensity: log λ t = a + b log λ t + u t , where u t is an independent gaussian auto-regressive process. • Fit a, b , and dynamic parameters from 1-year and 5-year CDS. Stanford University, 2005

20 risk−neutral actual 18 16 default intensity (%) 14 12 10 8 6 4 2 0 Dec01 Jul02 Jan03 Aug03 Feb04 Sep04 Mar05 date Figure 15: Implied default intensities for Royal Caribbean Cruises. Stanford University, 2005

5.0 4.5 4.0 λ ∗ ( t ) /λ ( t ) 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Dec01 Jul02 Jan03 Aug03 Feb04 Sep04 Mar05 Figure 16: Estimated default risk premia, λ ∗ /λ , for Royal Caribbean Cruises. Stanford University, 2005

9 risk-neutral-to-actual default probability instantaneous 1 year 8 5 year 7 6 5 4 3 2 1 0 Jul02 Oct02 Jan03 Apr03 Aug03 Nov03 Feb04 Jun04 Sep04 Dec04 date Figure 17: Median default risk premia, broadcasting-entertainment. Stanford University, 2005