Bond Economics: Primer: Bank Interest Rate Risk

This also does not include losses that are created by the yields on certain classes of credit instruments rising while the risk-free curve does not move (or even falls). Such a scenario represents the risk of credit spreads widening, and once again, is treated as a separate risk to be analysed. (The reader may have noticed a pattern – risk management generally takes the principle of decomposing all risks facing the bank into distinct risks that are quantified separately. Although real world bank failures result from a few causes, trying to mush the distinct risks into a single quantitative analysis does not offer any guidance as to how to hedge against the aggregated risk scenario.)

DV01

The main building block of interest rate risk analysis is the measure known as the dollar value of one basis point (DV01). If we have a portfolio of fixed income instruments, how much money do we lose (or possibly gain, if we use fixed income derivatives) if the quoted yield on every single instrument in the portfolio rises by one basis point (0.01%)? This is a scenario where the risk-free interest rate yield curve rises by one basis point, and the spread for every instrument remains the same. In fixed income markets, people will quite often use “duration” as a loose stand-in for the DV01. (The advantage of “duration” as a sensitivity measure is that it is independent of the value of the portfolio – modified duration tells us about percentage gains/losses on the portfolio. This is useful when writing for a general audience. But if you are managing a portfolio or firm, dollar losses end up being more meaningful. I jump back and forth between DV01 and duration in this text based on which requires the least text.)

Unless you are doing something insane, you are not going to worry about a one basis point movement in yields. However, we can approximate the losses (gains) that would be generated by larger movements by multiplying the yield change (in basis points) by the DV01. (Fixed income nerds might object that multiplying the yield change by the DV01 is using a first order approximation to the loss, we need to apply a correction due to the convexity of the portfolio. Although that is correct, convexity only matter for yield changes that will already have torched your portfolio if you are on the wrong side of the trade.)

Calculating the DV01 of a portfolio of assets is straightforward if you have software tools that can price all the instruments in your portfolio. You just re-price everything, and then add up all the gains and losses. This was a standard exercise I had to work on at my old day jobs. (One might ask – why would anyone own fixed income assets that they are unable to price? Is that not totally crazy? Well, that is exactly what people did in the early 1990s and explains why the 1994 bond bear market was seared into people’s memories.)

The trick to looking at interest rate of a firm (as opposed to a bond fund) is that we need to calculate the DV01 of the liabilities as well as the assets. Since the liabilities are what the company owes (and not owns), they work backwards as opposed to assets. (Using market parlance, they are a short position.) That is, if interest rates rise and the bank has issued bonds, the market value of those bonds declines. Those losses will show up as a gain in the calculation.

Booking “gains” because the market value of your liabilities drops offends some people of a bearish disposition, but it needs to be done to get a useful picture of a bank’s risk position. Imagine that you own $1 million in 5-year loans that pay 7% interest, and the position is funded by issuing $1 million in 5-year bonds issued at 5%. So long as the borrowers keep up their payments, you are pocketing a net interest margin of 2% every year, and the proceeds from the maturing loans will pay off the bond you issued. There is no interest rate risk associated with holding the position to maturity, and the risk analysis should reflect this. If you just looked at the sensitivity of the asset side of the position, the analysis would suggest that you would lose (gain) money if interest rates rose (fell), which is incorrect.

As a final reminder, longer maturity instruments have a greater sensitivity to interest rate changes than short maturity ones. The DV01 of $10 million of 2-year bonds is much less the DV01 of $10 million of 10-year bonds. You adjust the DV01 (or duration) of a portfolio of fixed dollar size by adjusting the average maturity of the portfolio.

Key Rate Duration

A variant of DV01 analysis is to look at the interest rate sensitivity of a portfolio with respect to yield changes at benchmark maturities (e.g., 2-, 5-, 10-, 30-year maturities). For example, what is the gain/loss for the portfolio if the 30-year maturity rises by one basis point, which other benchmark maturities remain unchanged? (Such an analysis is more complicated than calculating the DV01, as we need to interpolate yield changes across the yield curve for bonds at intermediate maturities.)

The usefulness of this sensitivity analysis is that we can piece together the sensitivities to answer questions like “what happens if the 2-year rises by 100 basis points, and the 10-year rises by 50 basis points?” That is, we can see whether we have risks associated with a flattening of the yield curve which might be hidden in scenarios where we assume the yield curve moves in a parallel direction.

Scenarios

Top management does not want to be multiplying large numbers by fifty when discussing interest rate risk, and so risk analysis reports tend to be based on scenarios featuring large interest rate “shocks” – 50, 100 basis points, or interest rate shifts that happened historically. This will generate a chunky number that can be compared to the bank’s annual profits or equity. Regulators are also interested in the analysis of such shock scenarios.

Scenario analysis in useful for providing easily understood context for understanding the interest rate risk the bank is running. Although it is possible to develop fancier probabilistic models for interest rate risk, I was not too convinced that the other methodologies I ran into added much value for most discussions.

Although scenarios help focus the mind on the scale of potential losses, there are two open questions. Will the future resemble any analysed scenario? And even if we know how much yields will change, what exactly can we do about it? Although the first question can only be answered with access to a time machine, the second can be addressed by the bank’s hedging strategy.

Hedging

The standard situation for banks is that economic forces tend to push them into a duration mismatch: assets have longer duration than liabilities. Non-term deposits are floating rate and thus do not drop in value when interest rates rise. On the asset side, residential mortgages are typically fixed rate (although the 30-year conventional mortgage that is a standard feature of American finance is an outlier), as are many loans. As a result, banks generally face losses if interest rates rise.

This risk can be reduced via hedging. Using non-standard terminology, you can divide interest rate hedging into passive and active hedging. However, the phrase passive hedging is not usually used, rather people would refer to it asset-liability matching.

Asset-liability matching is a strategy of modifying the structure of balance sheet items to bring the interest rate sensitivity of assets and liabilities closer together.

On the asset side, a few things can be done.

• Remove long-duration assets from the balance sheet (most likely by selling into securitisations).

• The bank can own shorter-duration bonds in its liquidity/investment portfolio.

• Adjust the pricing offered to customers to induce more to take on floating-rate loans.

• Change the strategic mix of lending to markets where floating rates are more commonly used.

On the liability side, the main strategy is to issue longer-term debt. This includes issuing bonds or term deposits. This is generally more expensive, since there are greater risk premia on long-term debt.

Asset-liability matching was the traditional way for banks to manage interest rate risk. However, it was discovered that these traditional methods were unable to cope with the high level of interest rate volatility that banks faced after the financial system was deregulated. (In the immediate post-World War II era in most developed countries, interest rates were regulated. These regulations started to be dismantled in the 1970s and 1980s, with the deregulation timing varying by jurisdiction.) Interest rate derivatives (what I spend most of my day job looking at) came to the rescue (sort of).

There are two main variants of interest rate hedges: futures versus over-the-counter derivatives (mainly interest rate swaps). Bond futures are somewhat exciting as a speculative vehicle, but they are not that well suited for a hedging programme that needs to be maintained for a long time. Swaps feature higher trading costs but are multi-year instruments that do not need to be rolled over. (This long life is a disadvantage if you ever have to unwind a swaps book.)

Describing the details of an interest rate swap is beyond the scope of this text. However, it is fairly easy to understand their economic effect (as long as you know what a short or long position is…). A swap is a contract between two counterparties, who are liable to pay each other cash flows based on the contract terms. The structure is zero sum: the gain of one party is the loss of the other.

• One side will “receive fixed.” This party gets an economic payoff that is equivalent to buying a bond with the maturity that matches the tenor of the swap contract using 100% leverage at the floating rate.

• The other side “pays fixed.” This party has the economic payoff of being 100% short the bond, receiving the floating rate on the proceeds of the short sale.

The DV01 of a short bond position is the negative of the DV01 of a long position (you “own” a negative amount of the bond). Which means that bank could use “pay fixed” swap transactions to cancel out the excessive DV01 position of its assets versus its liabilities.

Although it is possible to cancel out interest rate risk with derivatives, large derivatives exposures have side effects that create other risks. The first risk is that the positions can lose money, and these losses create a need to post collateral. Since the offsetting capital gains on other assets will not generate cash inflows, this represents a liquidity drain for the derivatives user. The second risk is that it is easy to hedge against changes of the market value of assets, but the value of assets used in accounting is often not the same as the market value. (Although how banks account for assets is important, it is beyond the scope of this text to cover.) As such, hedging programmes may be targeted at the accounting exposures of the bank, which is not the same thing as its true economic exposure (i.e., if all items on the balance sheet are valued at their market value).

In practice, even banks that use swaps will not cancel out all their interest rate risk. However, they can be used to get the risks to a more reasonable level. However, not all banks use swaps to a significant extent. Financial derivatives require extremely close risk management – there are many institutions that blew themselves up with so-called “rogue traders.” (I am in the camp that some of the “rogue traders” situations were the result of some segments of firm management quietly benefiting from the trader’s massive trading positions, who then threw the trader under the bus when the positions blew up.) Additionally, you need to have a large trading volume in swaps to overcome transaction costs and the fixed costs of employing a swaps desk. As such, smaller banks tend to stick to more traditional asset-liability matching strategies.

The article “Why Don’t Banks Hedge More?” by Kiah Lau Haslett gives an example of the thinking of smaller banks. The article refers to the results of the 2024 Bank Director Survey, based on interviewing American banks. In the survey, 91% of banks with assets between $250 million and $500 million did not undertake (active) hedges, and the same was true for 89% of banks between $500 million and $1 billion in assets. A bank with $1 billion assets is a minnow when compared to Bank of America ($3.18 trillion in assets at the end of 2023) or even Canada’s RBC (C$2.004 trillion at the end of 2023). Nevertheless, not all respondents to the survey were negative. Todd Cuppia, a Managing Director at Chatham Financial offered the following quote: “Derivatives do their best work when the environment changes more quickly than you can adjust your pricing or lending strategy or your portfolio in general.”

Embedded Options

The option to pre-pay a loan greatly complicates fixed income pricing. Normally, if you own a long maturity instrument with a fixed interest rate, you get a large positive return if interest rates markedly drop. But if the borrower can pre-pay the loan, they can refinance at a lower interest rate and repay your loan at par value. This wipes out the market value gains you would have had. The most important class of instruments with a pre-pay option are American 30-year conventional mortgages.

This situation is dealt with by pricing the instrument with a pre-pay option using option pricing theory. Option pricing theory is highly complex and beyond the scope of this text, but the effect can be summarised. What happens is that the apparent sensitivity to interest rates (duration/DV01) drops as interest rates fall below the level where refinancing the instrument is attractive.

Imagine that you have a portfolio of conventional mortgages, and you start out at an interest rate where it is not attractive to refinance. You have matched the DV01 of these assets to your liabilities, thinking that this has removed your interest rate risk. This is not the case if interest rates fall to a level where refinancing activity starts. The duration of your assets will collapse, while the duration of liabilities is unchanged. (As a technical note to appease fixed income nerds, the duration of instruments without embedded options will tend to rise somewhat as interest rates fall, courtesy of convexity.)

This means that you are no longer hedged against interest rate movements – you lose money if interest rates drop significantly. This is despite the fact that you were allegedly hedged against interest rates when yields were higher.

The only way to completely hedge out this risk is to embed options in your liabilities (expensive) or buy options from you local friendly fixed income option dealer (also expensive). Hedging a portfolio of mortgages using options is something a hedge fund (or relative value team) might do if pricing is attractive, but it is not a sensible long-term strategy.

The low-cost way to deal with embedded options is to just accept the risk. The sensible strategy is to have a somewhat longer asset duration than liabilities when interest rates are “high” so that you do not face serious losses if interest rates fall. (Of course, this means that you are facing losses if interest rates rise.) This strategy helps explain why banks will tend to avoid completely hedging out interest rate risk and leave asset duration longer than liabilities.

Sensible Interest Rate Management

One problem with reading popular descriptions of banking – as well as texts by some economists – is that it is argued that banks permanently run a massive duration mismatch between assets and liabilities, based on the theory that “banks borrow short, and lend long.” This folklore is not baseless – developed banking systems run on traditional lines ran into a lot of trouble in the 1970s and 1980s because of a duration mismatch. The bond bear market in 1994 also wreaked havoc for many banks that decided it was a good idea to speculate on interest rate derivatives (that they were often unable to price correctly). Recently, some American regional banks ran into issues in 2023 due to interest rate losses.

Nevertheless, banking practices – as well as regulatory practices – have changed a lot since 1994. The amazing power of digital computers has been unleashed in risk management, and interest rate risk is the easiest risk to manage. (Currency risk would be easier, but currency traders have decided to take advantage of the simplicity of currency pricing to trade wacky exotic derivatives that brings the complexity back. If you do not have exotic derivatives exposure, currency risk management is easier than for rates.) Currently, at any competent bank, the treasury desk, top management, and the risk teams know exactly the bank’s interest rate risk (which was not even true at some sizable, dedicated bond funds as late as the early 1990s).

The post-pandemic bond bear market demonstrated that the folklore belief that banking systems are systemically vulnerable to interest risk is not the case. The bear market was quite violent (the 10-year U.S. Treasury rose from a low of around 0.5% in 2020 to just under 5% in 2023, and similar rate rises happened in other markets outside Japan). The major banks weathered the bond bear market. Large banks do take interest rate risk seriously. The following comments explain why. I am expressing them using my biases, and it is entirely likely that many bankers might have differing opinions on some of my points.

The sensible attitude for a bank is to realise that its core competitive advantages are in liquidity management and credit risk analysis (as well as whatever financial activities its non-traditional banking units do). Conversely, there is no reason to believe that a bank is going to have a great deal of success in guessing the direction of the next movement of interest rates. As such, the bank should attempt to use asset-liability matching as well as active hedging programmes to get its accounting exposure to interest rates as low as possible. Perfect hedging is not expected, as the bank needs to trade off the risk versus the costs of hedging unusual risk exposures as well as the risks posed by large notional positions in derivatives. Realistically, the bank has to set a target duration mismatch that is lower what the natural tendency of its balance sheet would imply and accept that it will face interest rate losses that are manageable in adverse scenarios.

• It is extremely difficult to make money betting on the direction of interest rates as a systemic trading strategy. This is in complete contrast with the extreme confidence that commentators and Chief Economists have in discussing their forecasts for bond yields. In general, bond portfolio managers outperform based upon taking risks other than duration, even the bond gurus who are regularly quoted on financial media. To the extent that the people managing the interest rate risk at a bank are aware if this reality, their willingness to bet the bank’s future on interest rate risk diminishes.

• Bonds are a universally hated asset class. The consensus view since the early 1980s was to be bearish on bonds. (I can personally attest to this courtesy of being a secular bond bull when I was employed in finance.) There is no reason to believe that top bank managements were on the other side of that consensus.

• Regulators have figured out that interest rate risk is easy to measure, and they have clamped down on it. As noted below, there were some disastrous exceptions made by American regulators that predictably were uncovered in 2023.

• Bank bonus schemes often are based on the profits of business units. Such schemes cannot create holes in coverage where it is possible that all the individual business units are profitable and get bonuses while the bank in aggregate loses money. The profits and losses due to interest rate risk has to go somewhere in the compensation scheme – and the influential managers in lending and investment banking divisions do not want to risk their bonuses based on other managers’ hare-brained theories about interest rates.

Ruining my story is the exceptions – U.S. regional banks ran into problems due to interest rate losses. However, these banks were operating under “light touch regulation” that the powerful American banking lobby demanded for the “non-systemically important banks.” Although most banks weathered the storm, the population of banks in the United States is large enough to produce a few failures.

This episode also deflates some of the libertarian silliness regarding the lack of necessity of bank regulation. The 2023 episode demonstrated that it is possible for a bank to cultivate a clientele of rich stupid people who should not be allowed to manage more than $1000 in cash. These clients are not going to properly monitor the health of the bank while it is operating “normally.” However, these clients – despite allegedly being ardent free marketeers – will scream loudly to politicians demanding a bailout when their bank goes belly up.

Concluding Remarks

Interest rate risk is easily measured and relatively easy to hedge. Folklore about banks running massive duration mismatches does reflect the pre-1994 experience, but there has been progress in risk management since then.

Appendix: Who are the Swap Counterparties?

One apparent issue with arguing that banks can hedge away their long duration risk in the swap market is that if this is widespread, it implies that there needs to be large counterparties taking the other side of the trade. Although textbooks by academics in finance have delightful theories about “speculators” taking the other sides of derivatives trades, taking “directional exposure” in interest rate swaps are a balance sheet intensive activity. (Speculators make relative value trades: take positions in similar swaps that generally cancel out if the yield curve shifts in parallel.)

Since banks need to take the economic equivalent of a “short bond” position, we need to find counterparties that want the equivalent of a “leveraged long” bond position. Such entities are easy to find. They are investors that have actuarial liabilities to match, but do not want to buy long-dated government bonds since the prospective returns on them are believed to be much lower than the expected returns on risk assets. (The investors with actuarial liabilities are pension funds, as well as insurance companies.) By taking the other side of banks’ swap positions, they get the economic equivalent of bond exposure while being able to buy whatever fad investment products the best and bright of Wall Street sales teams are selling them.

References and Further Reading