Bank for International Settlements, April 2016, Interest rate risk in the banking book, here.
CCAR and Dodd Frank have mandated that Bank Holding Companies enumerate the securities and contracts in the banking book for various quarterly and semiannual risk simulation reports on the banking book portfolio. One side effect of globally gathering the individual security information is that P&L attribution for interest rate, credit, and FX ( in addition to reinvestment, liquidity, capital plan implementation, gap, and option risk) can be allocated by model to the individual securities and contracts. Certainly there will be some aggregation in the bank book position reporting, however, the point is that despite deposits with no contractual maturity date, prepayment, and other quantitative modeling issues the Banking Book is subject to standard P&L Attribution explanatories and thus Net Interest Margin Optimization is possible. If the explanatory power of the realized P&L is sufficient the ability to computationally optimize NIM at the security level will be profitable.
P&L Attribution in the trading book is well studied and widely practiced. The individual traded securities typically have robust valuation models depending on publicly available market and econometric data. Certainly there are exceptions: synthetic CDOs and CDX tranches come to mind. The credit default correlation is not currently observable market data. The internal correlation calibration of the Gaussian Copula have forced banks to take significant losses in multiple reported cases in the past 25 years. Since the trading book is focused on daily mark to market Front office quants spend much of their time working with security valuation models.
P&L Attribution in the banking book is not as well studied and practiced (see BIS Interest Rate Risk in the Banking Book). The Banking Book follows accrual accounting, there is no daily mark-to-market requirement. You can see from the BIS document that there are not even standard cashflow models for some securities. Many, but not all, of the quantitatively problematic securities include deposits with no contractual maturity and Securities with optional terminations or prepayments. With the current low interest rate environment the error rate in estimates for deposit funding of loan positions despite their substantial size is not quite a big a problem as it used to be. Banking Book securities need cash flow models (for accrual accounting) rather than full blown valuation models (like those used in the trading book).
The quantitative cash flow models can be much simpler than the corresponding valuation model. A US Treasury Fixed coupon par bond mark to market (aka price) may change daily and require a simple Yield Curve valuation model to price. The cash flow model is even simpler. The bond owner gets a fixed coupon every six months followed by a payment of par. It is very deterministic and the cashflow payment date are negotiated in advance, contractually. The expected cashflow model for a Mortgage Backed Security typically requires a prepayment model, same thing for a Mortgage loan. This is a well studied quant modeling problem. There are still more complex modeling securities like multi currency loan facilities and credit cards. The Banking book holds risk (and the NIM is subject to risk) of the following types:
Interest Rate risk – Banking book faces fixed float mismatch risk, Basis risk.
Credit risk – Banking book faces default and failure to pay risk. Credit Spread is not such a big problem since the securities are buy and hold but on the other hand you know JPM was hedging Bank Book Credit Spread Risk with CDX tranches in 2012. Traditionally credit risk is managed in the banking book by maintaining aggregated loss reserves. One of the things that change post CCAR is the the banking book credit risk can be managed at the security level.
FX risk – Banking book faces risk free rate identification risk, inflation risk, for non G10 currencies. All non USD securities and cashflows are subject to FX spot rate volatility.
Reinvestment risk – ALM funding and payments may not be aligned for the purpose of new business reinvestment ( capital plan implementation). Low Interest rate funding may be most plentiful when the aggregate interest and credit rates are lowest and Funding may be least plentiful when interest rates are highest.
Execution risk – the Banking book is subject to the risk of planned purchases lagging or exceeding predetermined targets in notional amount and time of booking.
Liquidity risk – Banking book faces the risk that its Asset cash flows do not cover its Liabilities funding requirement.
Gap risk – Banking book faces mismatched maturity risk between Assets and Liabilities.
Optionality risk – From BIS
arises from option derivative positions or from optional elements embedded in a bank’s assets, liabilities and/or off-balance sheet items, where the bank or its customer can alter the level and timing of their cash flows. Option risk can be further characterised into automatic option risk and behavioural option risk.
We discuss/note the details of some of these risks with an eye toward their explanatory value in matching expected NIM to realized NIM. Note at a security level we would like a cashflow model covering the Interest rate, credit, FX and Option risk. LP optimization on top of the security models can address Reinvestment, liquidity, and gap risk.
Credit Risk Premium notes from Hull
A feature of credit markets is the large difference between probabilities of default calculated from historical data and probabilities of default implied from bond prices (or from credit default swaps). Consider, for example, a seven-year A-rated bond. As we will see the average probability of default backed out from the bond’s price is almost ten times as great as that calculated from historical data.
Real-world default probabilities are usually less than risk-neutral default probabilities. This means that bond traders earn more than the risk-free rate on average from holding corporate bonds. Risk-neutral default probabilities are used when credit dependent instruments are valued. Real-world default probabilities are used in scenario analysis and in the calculation of bank capital under Basel II.
Altman (1989) was one of the first researchers to comment on the discrepancy between bond prices and historical default data. He showed that, even after taking account of the impact of defaults, an investor could expect significantly higher returns from investing in corporate bonds than from investing in risk-free bonds. As the credit rating of the corporate bonds declined, the extent of the higher returns increased.
The idea underlying equation (1) is that the excess return of a corporate bond over a similar risk-free bond compensates the holder for the cost of defaults. However the estimates produced by the equation depend critically on the choice of the risk-free rate, r.
A natural choice for r is the Treasury rate. Treasury rates are yields on bonds that have no default risk and the bond yield spreads that are quoted in the market are usually spreads relative to a Treasury bond that has a similar maturity. However, Treasury rates tend to be lower than other rates that have a very low credit risk for a number of reasons:
- Treasury bills and Treasury bonds must be purchased by financial institutions to fulfill a variety of regulatory requirements. This increases demand for these Treasury instruments driving the price up and the yield down.
- The amount of capital a bank is required to hold to support an investment in Treasury bills and bonds is substantially smaller than the capital required to support a similar investment in other very low-risk instruments.
- In the United States, Treasury instruments are given a favorable tax treatment compared with most other fixed-income investments because they are not taxed at the state level.
This leads many market participants to regard swap rates as better proxies for risk-free rates than Treasury rates.3
The credit default swap (CDS) market provides a way of estimating the benchmark risk- free rate used by participants in credit markets. If a five-year par yield corporate bond provides a yield of 6% and five-year protection can be bought against the issuer for 150 basis points a year, an investor can obtain an (approximate) risk-free return of 4.5% by buying the bond and buying credit protection. This suggests that the risk-free rate being used by market participants is 4.5%. Using this type of analysis across many corporations Hull et al (2004) estimate that the benchmark risk-free rate being used by market participants is the swap rate less 10 basis points. 4 This is similar to estimates that have been made by Moody’s KMV.5
Default Correlation Hull
Bonds do not default independently of each other. There are periods of time when default rates are very low and periods of time when they are very high. Evidence for this can be obtained by looking at the default rates in different years published by Moody’s. Between 1970 and 2003 the default rate per year ranged from a low 0.09% in 1979 to a high of 3.81% in 2001. The average over the whole period was 1.27%. These results mean that there is systematic risk in bond returns that cannot be diversified away. Bond traders should demand an extra return for bearing this risk.
Liquidity Risk notes from Hull
Part of the risk-premium in Table 2 is to compensate bondholders for liquidity risk. Estimates of liquidity risk premiums are difficult to obtain. Fleming (2001) looks at on- the run and off-the run bonds and concludes that the yield on off-the-run bonds for a five to ten year maturity is about 10 basis points higher than the yield on on-the-run bonds on average. The maximum spread observed was about 25 basis points.
Longstaff (2004) measures the size of what he terms the “flight to liquidity premium” on Treasury bonds by comparing yields on RefCorp and Treasury zero-coupon bonds. RefCorp bonds are bonds issued by the Resolution Funding Corporation (RefCorp), a government agency created by the Financial Institutions Reform, Recovery, and Enforcement Act of 1989 (FIRREA). RefCorp bonds have the same credit risk as Treasury bonds since their principal is fully collateralized by Treasury bonds and full payment of coupons is guaranteed by the Treasury under the provisions of FIRREA. RefCorp bonds receive the same tax treatment as U.S. Treasury bonds, but are less liquid. Longstaff finds that the spread of seven-year RefCorp bonds over seven-year Treasuries to be about 10 basis points on average. The highest spread observed was 35 basis points.
There is some evidence that the liquidity premium on corporate bonds may be higher than that on off-the-run Treasury bonds or RefCorp bonds. For example, Driessen (2004) decomposes the expected excess return over Treasuries from corporate bonds into several components and produces higher estimates for the average impact of liquidity than those produced by Fleming and Longstaff.6
Based on the available evidence, a reasonable estimate of the average liquidity premium on corporate bonds would seem to be between 10 and 25 basis points. Liquidity is therefore likely to be an important component of the risk premium for bonds with relatively high credit ratings.
The point is even though there are not standard models for all the Banking Book securities – the fact that CCAR and Dodd Frank mandate that the Banks collect and report on their accrual portfolios means two things: 1. we can run P&L attribution on a security basis across the banking book, and
2. we can optimize the capital plan additions to the banking book according to the interest rate, credit, and FX risk of the portfolio securities.
It turns out we can do this across all the US Commercial Bank Assets and Liabilities reported to the US Federal Reserve. It is something like 10 billion positions in aggregate. Both the attribution and NIM Optimization problems are interesting. The part of the optimization problem that is interesting (even restricted to USD assets and liabilities, exclusively) is when you provide both credit and interest rate data on a security by security level the LP problem must balance the realized and unrealized credit losses with the expected credit and interest rate premium (realized and expected). Moreover, the P&L attribution problem and the optimization problem are linked. The better the P&L attribution model can explain the realized P&L, the more accurate the LP optimization of the capital plan in the buy and hold Banking Book portfolio.
We expect that this can be done deterministically on data reported to the US Federal Reserve and well as on an expected forecasting basis. In this historically low NIM environment, we expect that additional basis points of optimized NIM will be priced at a premium across the BHC’s reporting to the Fed.
The Basel Committee on Banking Supervision has today issued standards for Interest Rate Risk in the Banking Book (IRRBB).
The standards revise the Committee’s 2004 Principles for the management and supervision of interest rate risk, which set out supervisory expectations for banks’ identification, measurement, monitoring and control of IRRBB as well as its supervision.
Hull et.al. References
Altman, E. I., 1989 “Measuring Corporate Bond Mortality and Performance” Journal of Finance, 44, 902-22.
Amato, J. D. and E. M. Remolona, 2004 “The Credit Spread Puzzle” BIS Quarterly Review, 5, Dec 2003, 51-63.
Bernt, A., R. Douglas, D. Duffie, M. Ferguson, and D. Schranz, 2004 “Measuring Default Risk premia from Default Swap Rates and EDFs’’ Working Paper, Stanford University.
Collin-Dufresne, P., R.S. Goldstein, and J.S. Martin, 2001 “The Determinants of Credit Spread Changes” Journal of Finance, 56, 2177-2207.
Collin-Dufresne, P., R. Goldstein, and J. Helwege, 2003 “Is Credit Event Risk Priced? Modeling Contagion via the Updating of Beliefs” Working Paper, Carnegie Mellon University.
Cornell, B. and K. Green, 1991 “The Investment Performance of Low-Grade Bond Funds” Journal of Finance, 46, 29-48.
Driessen, J., 2003 “Is Default Event Risk Priced in Corporate Bonds?” Review of Financial Studies (forthcoming).
Duffee, G. R., 1996 “Idiosyncratic Variation of Treasury Bill Yields” Journal of Finance, 51, 527-551.
Fama, F. and K. French, 1993 “Common Risk Factors in the Returns on Stocks and Bonds” Journal of Financial Economics, 33, 3-56.
Fleming, M., 2001 “Measuring Treasury Market Liquidity” Working Paper, Federal Reserve Bank of New York.
Hamilton, D.T., P.Varma, S. Ou and R. Cantor, 2004 “Default & Recovery Rates of Corporate Bond Issuers: A Statistical Review of Moody’s Ratings Performance 1970- 2003” Moody’s Investors Service, January.
Hull, J., M. Predescu, and A. White, 2004 “The Relationship Between Credit Default Swap Spreads, Bond Yields, and Credit Rating Announcements” Journal of Banking and Finance (forthcoming).
Longstaff, F., 2004 “The Flight-To-Liquidity Premium in U.S. Treasury Bond Prices” Journal of Business, 77, 511-526
Merton, R., 1974 “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates” Journal of Finance, 29, 449—70.