Hedging Interest Rate Margins on Demand Deposits - PowerPoint PPT Presentation

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� Presentation related to: � Hedging Interest Rate Margins on Demand Deposits � Working paper available on SSRN (to be updated soon) � Presentation Outlook � Modeling framework � customer rates � customer rates � deposit amounts � Interest rate margins � Optimal strategies � The blinkered investor � Integrated risk management � Conclusion 2

Prolegomena � Demand Deposits involve huge amounts � Bank of America Annual Report – Dec. 2007 Average Balance (Dollars in millions) 2007 2006 Assets Federal funds sold and securities purchased under agreements to resell $ 155,828 $ 175,334 Trading account assets 187,287 145,321 Debt securities 186,466 225,219 Loans and leases, net of allowance for loan and lease losses 766,329 643,259 All other assets 306,163 277,548 $ $ 1,602,073 1,602,073 Total assets Total assets $ $ 1,466,681 1,466,681 Liabilities Deposits $ 717,182 $ 672,995 Federal funds purchased and securities sold under agreements to repurchase 253,481 286,903 Trading account liabilities 82,721 64,689 Commercial paper and other short-term borrowings 171,333 124,229 Long-term debt 169,855 130,124 70,839 All other liabilities 57,278 Total liabilities 1,465,411 1,336,218 Shareholders’ equity 136,662 130,463 Total liabilities and shareholders’ equity $ 1,602,073 $ 1,466,681 � Demand deposits involve both interest rate and liquidity risks 3

Prolegomena � Can we think of a market value or a “fair value” of demand deposits? � Clearly not for practical, accounting and financial theory reasons � No real market to compute “exit values” � As for loans, affectio sociatatis effects : contractors identities (bank and customer) are essential elements of demand deposits customer) are essential elements of demand deposits � Money does smell! � Not a “law invariant contract” � One cannot only rely on cash-flows � This is not only a matter of bank credit risk � Think of the simplest case � No interest bearing, one USD deposit at t=0, withdrawn at some random time t � Unlike a term deposit where the repayment date is known 4

Prolegomena � Standard mathematical finance approach � � � � τ � � � Q � � − − � Value of the contract: 1 E exp r s ds ( ) � � � � � � 0 � Q stands for a “risk-neutral” probability � Obvious problem : t is not adapted to the usual filtration related to interest rates interest rates � Not a standard interest rate contract � Assume that is a stopping time adapted to some larger filtration λ with intensity � Risk-neutral withdrawal intensity � Similar to the valuation of defaultable securities � One has no idea of the risk premia associated with the uncertainty of the closing date � Since unlike liquid defaultable bonds, there is no liquid reference market 5

Prolegomena � Standard mathematical finance approach � We end-up with an arbitrary choice of risk-neutral probability (or risk premia) due to market incompleteness � Mark-to-Model valuation with large model risk � Can this issue be mitigated at a portfolio level? � Large pool and diversification effects Large pool and diversification effects � Insurance ideas related to the law of large numbers � Infinitely granular portfolios (Gordy, 2003) � Well diversified portfolios (Björk and Naslünd, 1998, De Donno, 2004) � Along this view, the uncertainty on the amortizing scheme of demand deposits as sampling fluctuation could be neglected for large portfolios � This contradicts empirical evidence � Demand deposit amounts at a bank level are not fully correlated to interest rates 6

Prolegomena � There exists some extra risk whatever its name � Liquidity risk � Business risk � As stated in the regression model relating demand deposit amounts to interest rates in Jarrow & Van Deventer, 1998 � The computation of the “value” of demand deposits through the The computation of the “value” of demand deposits through the expected discounted approach is flawed � Implicitly assumes no risk premia for liquidity or business risk � Minimal martingale measure � Which seems rather unrealistic, given relationships between monetary aggregates, stock markets and real economy � Let us remark that the same issue holds for the valuation of the mortgage prepayment option 7

Prolegomena � Accounting framework of deposit accounts involve mainly: � IASB (International Accounting Standards Board) : IAS 39 � FASB (US Financial Accounting Standards Board) � FASB mention that demand deposits “involves consideration of non financial components” and propose to postpone recognition of those liabilities at fair value � Approaches differ but the two boards are connected � Financial Crisis Advisory Group, G20, European Commission, Financial Stability Forum also involved � Amortized cost versus Fair value � Fair value measurement is likely to be updated � Exposure draft, May 2009 � Accounting boards, SEC, Basel Committee on Banking Supervision, European Banking Federation favour the amortizing cost approach for demand deposits � One should thus focus on interest rate margins rather than fair value 8

Modeling Deposit Rate – Examples � We assume the customer rate to be a function of the market rate. � Affine in general (US) / Sometimes more complex (Japan) ( ) ( ) { } ( ) = α + β ⋅ ⋅ ≥ 1 g L L L R = α + β ⋅ g L L T T T T T �����&�.����� �� �� 0,9 3.00% M2 Own Rate JPY Libor 3M 0,8 Japanese M2 Own Rate 2.50% 0,7 0,6 �������'� ��&���� 2.00% 0,5 1.50% 0,4 0,3 ������5����������6 1.00% 0,2 0,1 0.50% 0 USD 3M Libor Rate mars-99 sept-99 mars-00 sept-00 mars-01 sept-01 mars-02 sept-02 mars-03 sept-03 mars-04 sept-04 mars-05 sept-05 mars-06 sept-06 mars-07 0.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 9

L Dynamics for Market Rate : forward Libor rate t � Market Model for forward Libor rate(s) dL ( ) t = µ + σ dt dW t L L L L t µ µ ≠ ≠ ����������,���������������������� ����������,���������������������� 0 0 L � Coefficient specification assumptions: µ , L σ � Our model: constant L � Assumptions can be relaxed: � Time dependent coefficients � CEV type Libor models 10 10

Deposit Amount Dynamics � Diffusion process for Deposit Amount � � = µ + σ dK K dt dW ( ) t � � t t K K K ���������������� � Sensitivity of deposit amount to 680 4 660 3,5 market rates 640 3 � Money transfers between deposits � Money transfers between deposits 620 2,5 2,5 600 and other accounts 2 580 � Interest Rate partial contingence. 1,5 560 1 540 � Business risk, … US Demand Deposit Amount 0,5 520 US M2 Own Rate � Incomplete market framework 500 0 oct-00 janv-01 avr-01 juil-01 oct-01 janv-02 avr-02 juil-02 oct-02 janv-03 avr-03 juil-03 oct-03 janv-04 avr-04 juil-04 oct-04 janv-05 avr-05 juil-05 oct-05 janv-06 avr-06 juil-06 oct-06 janv-07 avr-07 juil-07 ( ) ( ) ( ) 2 = ρ + − ρ dW t dW t 1 dW t − < ρ < 1 0 K L K 11