I ran into some discussions about “doom loops” involving mortgage hedging in the USD rates market. I am quite distant from current market conditions, so I cannot give market advice, nor am I completely on top of the current dynamics. Instead, this article gives a background explanation why mortgage hedging causes difficulties in USD rates markets.
One point to note that this is largely a phenomenon in the U.S. rates markets, the other major developed markets do not have as consumer-friendly mortgages as U.S. conventional 30-year mortgages. The U.S. conventional mortgage market was developed with the help of the government-sponsored enterprises (GSEs), that bought standardised mortgages. As will be discussed in this article, hedging the risk of the prepayment option in conventional mortgages is difficult, and securitisation (placing the mortgages in mortgage-backed securities — MBS) was the way to offload the risk of mortgage hedging for banks.
A conventional 30-year mortgage is amortising — the principal is paid down during the lifetime of the mortgage, which involves a fixed periodic payment. (As opposed to a bullet structure where the principal is only paid off at maturity. The standard bond structure is a bullet.) The interest rate is fixed, which means that we can guarantee that the principal is paid off by maturity at the latest. However, the borrower has the option to prepay the mortgage (in whole or in part), which is extremely convenient for consumers. If mortgage rates drop enough, they can refinance the mortgage at a lower rate. (There are fees associated with doing this, so the interest rate drop has to be enough to cover the fees.) Other countries either do not issue mortgages with fixed interest rates for 30 years (e.g., the effective maximum fixed rate available in Canada is (was?) 5 years, and so the rate had to be reset during a typical 25-year amortisation) and/or there are financial penalties associated with prepayment.
One small aside, which I have noted in the past. The amortising structure means that 30-year mortgages align closer to 7- to 10-year Treasury bullet securities. A 30-year Treasury has much longer duration than a 30-year mortgage, so it is not the proper comparison for mortgage/Treasury spreads.
Why Is Prepayment Bad (For Banks)?
A standard story is that banks “borrow short and lend long” — that is, they (allegedly) borrow at the overnight rate via deposit liabilities to finance long-dated assets like mortgages. The usual story is then the banks get wrecked if the deposit rates rise above the rate of interest on their assets.
This story is based on folk memories of the situation in the 1970s. Interest rates were regulated, and so banks could ensure that they had positive interest rate spreads without doing a whole lot of analytical work. (This led to the classic “3-6-3 rule” for small American savings and loans — pay 3% on deposits, get 6% on mortgages, hit the golf course at 3. It was a system that made so easy to run a bank that pretty much anyone could run one (and pretty much anyone did).
Once interest rates were deregulated, banks could no longer guarantee that short-term funding rates were below asset returns. In the 1970s, the beginning of the Savings and Loan crisis was driven by the rise in short-term rates squeezing small banks. (Fraud and financial speculation in the deregulated industry created far greater financial damage than the initial interest rate shock; the interest rate shock set up the psychology for risk-seeking behaviour that led to the fraud.)
How Do Banks Deal With the Risk?
I have written about this before, but the “borrow short/lend long” story misses three key strategies used to manage duration risk.
Dump the long-dated assets off the balance sheet via securitisations. The MBS market is very large for a very good reason.
Issue longer-dated liabilities (bank bonds, term deposits).
Use derivatives (interest rate swaps, or options on swaps — swaptions). Liability-matching investors are structurally short duration (not enough long-dated bonds), so they are willing to take the other side of derivatives trades where banks offload duration.
This means that dealing with duration/prepayment risk at banks is optional — they can either offload most of the risk, or they can let their treasury desk go wild with hedging strategies if they feel they are sophisticated enough.
How Do (Most) Bond Managers Deal With the Risk?
As an immediate disclaimer, I was involved in Canadian rates management, so my comments here are based on vibes. The easy way to deal with the prepayment risk on MBS (that were offloaded by banks) is to have MBS in your benchmark. If you are a bond fund manager, you are managing against an implicit liability — your benchmark. (Fixed income strategies and analytics are portable because everyone is managing against implicit/explicit liabilities.) So to deal with MBS, you just have MBS in your benchmark. If you have a market weighting in MBS, your aggregate prepayment risk is the same as the index — i.e., not a source of risk.
Since everyone other than index managers attempt to outperform the index courtesy of taking risks versus the benchmark weighting, it is up to the manager to decide how much mortgage risk to take. From what I saw, a fairly common strategies for smaller bond managers was to allocate the risk budget to corporate bonds (or duration decisions), or outsource their MBS allocation to a large institutional fund (if they are something like a pension fund and not competing directly with other fund managers).
How Do Asset Allocators Deal With This?
The standard way large investors manage their portfolios is to have a hierarchical system with an asset mix layer sitting on top of asset-class specific portfolio managers. The distinction between these two levels can be blurred, as senior portfolio managers possibly also have an input into the asset mix decisions, but the two roles are tracked independently. Nevertheless, it is probably a mistake to say that “bond portfolio managers make bond allocation decisions,” rather that is an asset allocator decision (although the asset allocators may be those portfolio managers wearing different hats).
At the asset mix level at firms that have actuarial liabilities, we tend to see that actuarial liabilities typically have a longer duration than their fixed income portfolios on two grounds. Firstly, it is “expensive” to have too high a bond portfolio weight, since expected returns are lower. Secondly, there is not enough long duration supply to allow many large investors to duration match (as was run into when the U.K. mandated pension fund liability matching).
Amortising mortgages are a bad fit to match against the cash flows needed to immunise required payments to pensioners whose life spans get distressingly long courtesy of improvements in medical science. As such, it is unlikely that anyone at the asset mix level is going to say “we should specifically load up on mortgages.” This means that decisions about mortgages get left at the level of portfolio managers.
Who’s Left?
If we look through the previous categories of investors who invest in fixed income, we have covered most of them in terms of the number of management firms. However, we are missing a small number of fixed income investors who do care about mortgage prepayment risk — and those investors are quite large. Given that influence on the market is weighted by portfolio size, the point about it being a small group may seem pointless. This is just me being pedantic about writing style — mortgage hedging is not really a major concern for “bond investors,” rather the subset that is “mortgage hedgers” (which is tautologically true).
Historically, the GSE’s were the largest mortgage hedgers, but there are also the big banks, investment banks, and mortgage (hedge) funds that have a mismatch between mortgage assets and their (implicit) liabilities. My understanding was that this activity was dialled down after the Financial Crisis (which saw a couple of the GSE’s put into receivership), but I am not on top of recent developments.
The Hedging Problem
Interest rate risk — in the absence of optionality — is the easiest/second easiest risk to hedge (foreign exchange hedging might be easier). All fixed income assets have a pricing sensitivity to the interest rate curve. The first order hedge to interest rate risk is to determine each portfolio asset’s sensitivity to a 1 basis point (0.01%) rise in rates across the curve (“DV01” — dollar value of .01%) and then add each DV01 value up, giving the DV01 of the portfolio.1 For example, if your have a portfolio of bonds with a DV01 of $-10,000, you expect to lose about $100,000 if there is a parallel rise of interest rates of 10 basis points across the curve. You then pick some hedging instruments (bond or short rate futures, swaps, or benchmark bonds) and then just do a trade to bring your DV01 back to its liability benchmark (e.g., the DV01 of an index portfolio that has the same market value as your portfolio).
If you want to be fancier, you decompose your interest rate exposure across the curve into maturity buckets, and you handle each independently — “key rate duration.”
DV01 and “duration” are related concepts, but in general, people refer to “duration risk” even when their concern is DV01. The advantage of duration is that it is return sensitivity for the portfolio (measured in percent) that is invariant to the size of the portfolio. However, the people managing portfolios care more about the dollar value of risks, and DV01 is a better fit. Duration is also not well defined for anything other than bonds, while DV01 can be used for any asset.
The ease of hedging results from the fact that market value changes are very close to linear with respect to shocks in interest rates. You will lose roughly twice as much money if rates rise 2 basis points instead of one, and you will get a profit roughly equal to the magnitude of the DV01 if rates fall one basis point instead of rising.
Fixed income options — and bonds with embedded options, such as prepayable mortgages — are not linear with respect to interest rate shocks. In the case of mortgages, they have the ugly property that the duration extends (the magnitude of the DV01 goes up) if interest rates rise. This means that if interest rates change by more than insignificant amounts, the actual gain/loss is no longer well approximated by (initial DV01)×(yield change).
(Vanilla option-free bond durations also change as yields change, but the duration change is beneficial. In the case of rising rates, this means that the duration drops very slightly as the yield goes up, so you lose less money than predicted by multiplying the starting DV01 times the yield change in basis point. Going the other way, the duration extends as yields fall, so you make more money than predicted. In practice, you need a rate move of 50 basis points to really notice this effect. This means that bond returns outperform what is predicted by the linear sensitivity — there is a positive second order return sensitivity that is called convexity. Since bonds with embedded options always underperform what is predicted by linear extrapolation, practitioners will say that they have negative convexity.)
Hedging Embedded Options
There are two strategies for hedging the risks of embedded options.
Buy interest rate options that roughly align with the embedded options in your mortgage portfolio.
Dynamically hedge the risk.
Buying options to cancel out the risk from mortgage prepayments is generally expensive, but it does reduce other risks. However, options trading is zero sum: for every buyer, there needs to be a seller. Although there is some structural demand for selling volatility due to dubious academic finance theories,2 there is not enough to cover the demand created by large mortgage portfolios. So, in aggregate, the hedgers are forced to dynamically hedge at least part of their aggregate option risk.
Dynamic hedging requires periodically adjusting your hedging ratio (DV01) so that it risk is neutralised. (This is done at a relatively high frequency, but typically not intraday.)3 To avoid excessive transactions, there will be a “dead zone” (yay for control systems terminology) where small hedging mismatches are ignored. However, this implies that if rates rise, the hedgers need to take actions that are equivalent to selling bonds (sell bonds, sell futures, pay fixed in swaps). Which means that they are doing a transaction that reinforces the current trend in yields.
Note: This description is probably too brief, so I expect that I will do a “dynamic hedging” primer as a follow up.
We therefore end up with the situation if the U.S. bond market tanks, the mortgage hedgers are piling on sell orders. Which reinforces volatility — the U.S. market has the tendency to adjust faster than other developed markets as a result.
Although that sounds like a plot right out of Monster Chiller Horror Theatre (now available on Netflix), we typically do not see interest rates march off to infinity. Sooner or later, valuation matters, and people step in to halt the rout.
As such, I do not see this as a “doom loop,” rather the reality that interest rate adjustments occur in on accelerated time span. We might lose a hedge fund or two, but that’s what happens when markets move.
Concluding Remarks
The structural need to hedge prepayment risks means that the USD rate market is a bit livelier than other markets when rates break out of a trading range. Although this is entertaining when it happens (if you are not on the wrong side of the trade), the effect typically burns out, so do not expect this effect to drive interest rates to infinity.
Remember that for bonds, “yield up” -> “price down.” So the DV01 is a negative number if the shock is a 1 basis point rise in rates. However, everyone orally gives DV01 as a positive number, which is the magnitude of the DV01. Some shops might give up and define DV01 as the dollar value of a 1 basis point drop in rates. However, the DV01 that people care about in practice is the DV01 gap between their portfolio and the index, which swings back and forth between positive and negative depend on duration views.
Modern portfolio theory says that the optimal portfolio manager generates steady outperformance. Do you know what generates steady outperformance? Strategies that effectively “sell volatility”: selling options, buying short-term credit products, carry trades. These strategies make money until they blow up, typically because everyone herds into the because everyone is judged on the basis of wanting steady outperformance.
If rates go in one direction then return to their starting point, dynamically hedging an option generates losses. In our example, if rates first rise, the hedger needs to sell to get back to neutral DV01. But if rates go back to where they were, they will need to undo that sale to return to neutral — which implies that they need to buy at a higher price than they sold. The reason why the Black-Scholes model was a big deal is that it related the price of an option to the cost of hedging the option — the more rates jump back and forth randomly, the greater the hedging losses. So, option prices depend upon the volatility of prices.
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