Discussion: Bank Risk Dynamics and Distance to Default

Transcription

1 Discussion: Bank Risk Dynamics and Distance to Default Andrea L. Eisfeldt UCLA Anderson BFI Conference on Financial Regulation October 3, 2015

2 Main Idea: Bank Assets Bank assets Payoff Bank debt Bank asset value Bank equity Borrower asset value Figure 1: Payoffs at maturity in the simplified model with perfectly correlated borrower defaults to common factor shocks as well as idiosyncratic risk. We then view the assets of the bank as T = 10, σ = 0.2, ρ = 0.5, r = 0.01, δ = 0.005, and F1 = 0.8. Unlike in Figure 1, there is no sharp kink in the bank s asset value in Figure 2. There are two reasons for the lack of sharp kink. First, contingent claims on borrower assets, and equity and debt of the bank as contingent claims on in this case, loans in the bank s portfolio are not at maturity. For H < τ T, loans have not these contingent claims. matured yet, while for 0 τ < H, they have been rolled over into new loans. Second, the existence This options-on-options feature of bank equity and debt has important consequences for the of idiosyncratic borrower risk makes the borrower s default option more valuable and the loan less implied default risk and equity risk dynamics. To illustrate the main intuition, it is useful to valuable to the bank, particularly when the asset value is close to the face value of the debt. consider the simplified case without idiosyncratic risk in which all borrowers are identical with perfectly correlated defaults. Assume further that the maturity of the (zero-coupon) debt issued aggregate borrower asset value Aggregate borrower asset value Figure 2: Bank asset value at bank debt maturity as a function of aggregate borrower asset value. Simulated bank asset values shown as dots. Dashed line shows the kinked payoff that would result with perfectly correlated borrower asset values and without staggering of loan maturities Moreover, unlike in Figure 1, there is dispersion in the bank asset value conditional on the The reason is that for loans that have been rolled over into a by the bank equals the maturity of the (zero-coupon) loans made by the bank. In this case, the second generation of loans, the face value of the loan depends on the common factor realization up to the roll-over date τ. For example, if Wτ is low, there will be more defaults at τ and hence the payoffs at maturity as a function of borrower asset value are as shown in Figure 1. In this example,

3 Discussion: Two Main Points 1 Are banks different because of their assets or their liabilities? 2 How does banks change in σ A from Oct 07 to Oct 08 compare to that of non-financial firms? All firms DI (and DD) deteriorate together, and to a similar extent. Most of the decline is due to an increase in (idiosyncratic) volatility. For banks, the change in leverage contributes relatively more.

4 What, if anything, is special about banks? Different assets? All firms likely face decreasing returns to scale or scope. Implies firm value concave in underlying asset value. How much of bank asset value comes from existing loans? Banking is a (pro) cyclical business. Missing: Bank assets may have much lower value in second best use. Important connection to liability side. Different liabilities? Deposits and other short term debt finance. Tiny equity cushions. Subject to runs. V A V B V A small. Important interaction b/t asset value, fragile capital structure.

5 Bank Assets: Betas are Procyclical Table 1: An EW index of the 50 top nancial rms are constructed. Monthly observations from July 1926March 2015 are split into quintiles according to the return on the CRSP VW index by year. The CAPM beta for the nancial index overall, for the 20% best years, and for the 20% worst years are shown below. CRSP VW returns are from Ken French's website. Dependent variable: excess return on EW index of top 50 n Overall index Bottom quintile years Top quintile years CAPM β (0.016) (0.033) (0.060) Constant (0.001) (0.002) (0.005) Observations 1, R Adjusted R Residual Std. Error (df = 1063) (df = 266) (df = 175) F Statistic 3, (df = 1; 1063) (df = 1; 266) (df = 1; 175) Note: p<0.1; p<0.05; p<0.01

6 Bank Assets: What s Missing in Model Banks scale loan portfolio up and down with aggregate state.

7 Bank Assets: What s Missing in Model Bank assets more varied. BofA Book Assets 06/30/2010 Cash and balances due from depository ins5tu5ons: Securi5es Federal funds sold and securi5es purchased under agreements to resell: Loans and Leases Trading assets Premises and fixed Assets Other RE Unconsolidated Subsidiaries Intangible Assets Other Assets

8 Bank Liabilities Good State Assets Liabili/es Bad State Assets Liabili/es Cash 20 STD 80 Cash 20 STD 80 Loans 80 Equity 20 Loans 65 Equity 5 Total 100 Total 100 Total 85 Total 85 Crisis State Assets Liabili/es Cash 20 Loans 50 STD 70 Equity 0 Crisis State with Par/al Run Assets Liabili/es Total 70 Total 70 Cash 20 STD 40 Loans 20 Equity 0 Total 40 Total 40 Note: Must reconcile with lower correlation with market in bad times.

9 Bank Assets = A(L) Bank Asset Value V DEF V B V RUN Underlying Asset Value

10 Discussion: Two Main Points 1 Are banks different because of their assets or their liabilities? 2 How does banks change in σ A from Oct 07 to Oct 08 compare to that of non-financial firms? All firms DI (and DD) deteriorate together, and to a similar extent. Most of the decline is due to an increase in (idiosyncratic) volatility. For banks, the change in leverage contributes relatively more.

11 DI = V A V B 1 V A σ A 1 σ E % change in asset value which renders firm insolvent, measured in units of σ A. I.e. How many σ A s is a firm s equity cushion? Use the structural measure to decompose changes in financial soundness into lvg and vol. How does 07/08 change in σ A for banks and non-banks compare? 7 DI (LHS) DD (RHS) Mar- 26 Apr- 28 May- 30 Jun- 32 Jul- 34 Aug- 36 Sep- 38 Oct- 40 Nov- 42 Dec- 44 Jan- 47 Feb- 49 Mar- 51 Apr- 53 May- 55 Jun- 57 Jul- 59 Aug- 61 Sep- 63 Oct- 65 Nov- 67 Dec- 69 Jan- 72 Feb- 74 Mar- 76 Apr- 78 May- 80 Jun- 82 Jul- 84 Aug- 86 Sep- 88 Oct- 90 Nov- 92 Dec- 94 Jan- 97 Feb- 99 Mar- 01 Apr- 03 May- 05 Jun- 07 Jul- 09 Aug- 11 Sep- 13 0

12 1 σ E = DI Are Banks Different? V A V B V A 1 σ A top 50 Non- Financials top 50 Financials Dec- 62 Dec- 64 Dec- 66 Dec- 68 Dec- 70 Dec- 72 Dec- 74 Dec- 76 Dec- 78 Dec- 80 Dec- 82 Dec- 84 Dec- 86 Dec- 88 Dec- 90 Dec- 92 Dec- 94 Dec- 96 Dec- 98 Dec- 00 Dec- 02 Dec- 04 Dec- 06 Dec- 08 Dec- 10 Dec- 12 Figure 22: A comparison of the log median measured DI for the largest 50 financial and non-financial firms in terms of market capitalization, The horizontal lines indicate the position of our benchmark cutoffs (DI=1,2,3,4) on the log scale.

13 1 σ E V A V B V A 1 σ A = DI 1.6% 1.4% No%LT%Debt% With%LT%Debt% 1.2% 3% 1% 0.8% 2% 0.6% 0.4% 0.2% 1% 0%!0.2% M!72% D!73% S!75% J!77% M!79% D!80% S!82% J!84% M!86% D!87% S!89% J!91% M!93% D!94% S!96% J!98% M!00% D!01% S!03% J!05% M!07% D!08% S!10% J!12% Figure S8: The median of log DI for those firms with no long term debt (in blue) and those firms long term debt (in red), Punch line: Banks, non-financials, tech firms experience similar DI declines. Larger for firms with more debt. But, is it lvg or vol?

14 07 08 ln(di) = ln( V A V B V A ) ln( 1 σ A ) variable change in log(leverage) change in log(1/siga) top financials top non financials

15 07 08 ln(di) = ln( V A V B V A ) ln( 1 σ A ) variable change in log(leverage) change in log(1/siga) with debt without debt

16 07 08 ln(di) = ln( V A V B V A ) ln( 1 σ A ) variable change in log(leverage) change in log(1/siga) Port1 Port2 Port3 Port4 Port5 Smallest equity cushion is portfolio 1 (banks) Largest equity cushion is portfolio 5 (tech)

17 Decomposition Take Aways Overall, 1 σ A More Important More blue then red on previous slides! There does appear to be systematic variation in the relative contribution of lvg vs. vol. Firms with more leverage (and banks) attribute more of their decline to equity cushions shrinking with falling asset values.

18 Bond spreads, CDS spreads, DI and DD similar Jan- 02 May- 02 Sep- 02 Jan- 03 May- 03 Sep- 03 Jan- 04 May- 04 Sep- 04 Jan- 05 May- 05 Sep- 05 Jan- 06 May- 06 Sep- 06 Jan- 07 May- 07 Sep- 07 Jan- 08 May- 08 Sep- 08 Jan- 09 May- 09 Sep- 09 Jan- 10 May- 10 Sep- 10 Jan- 11 May- 11 Sep- 11 Jan- 12 May- 12 Sep- 12 Jan- 13 May- 13 Sep- 13 Jan- 14 May- 14 Sep Bond DI 0 Not a problem with structural models, bond spreads look the same. The crisis appears to be a surprise increase in idiosyncratic volatility.

19 2 1 σ E V A V B 1 V A σ A = DI Median DI Total Volatility Median DI Idiosyncratic volatility Jan-26 Jan-30 Jan-34 Jan-38 Jan-42 Jan-46 Jan-50 Jan-54 Jan-58 Jan-62 Jan-66 Jan-70 Jan-74 Jan-78 Jan-82 Jan-86 Jan-90 Jan-94 Jan-98 Jan-02 Jan-06 Jan-10

20 Does not mean banks don t matter Need to understand large variation in quantity of idiosyncratic risk that drives variation in firms financial soundness.

21 Discussion: Two Main Points 1 Are banks different because of their assets or their liabilities? 2 How does banks change in σ A from Oct 07 to Oct 08 compare to that of non-financial firms? All firms DI (and DD) deteriorate together, and to a similar extent. Most of the decline is due to an increase in (idiosyncratic) volatility. For banks, the change in leverage contributes relatively more. Note: Fragility affects both first and second moments.

22 Takeaway from Paper Extremely worthwhile to put a model on the table. Log normality is clearly a simplifying assumption. Useful to rigorously explore the implications of alternative assumptions with micro foundations.