Starving the Beast: Convexity Hedges and Bond Market Distortion

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March has undoubtedly been a wild month for the markets. We have witnessed the largest daily point gain ever occurred in history in the S&P500, followed by a record negative net change three days later, when the Dow Jones Industrial Average also recorded its biggest point drop ever. The same index hit an all-time high on February 12, and its rise stopped just short of the 30,000 milestone.  The VIX, also known as Wall Street’s “fear gauge”, reached levels never seen before on March 27. Circuit breakers halted trading time and again, several countries issued short selling bans amid severe turmoil.

Monetary policy was the only game in town. A surprise cut delivered by the Federal Reserve on March 3 – the first of its kind after the 2008 financial crisis – triggered an unprecedented rally in U.S. Treasuries. The yield on the 10-year note plummeted below 1% for the first time and hit a historic low of 0.318% after days of free fall.

The measures implemented by the central bank could not help but spread panic in the markets. Investors brushed off the positive results of the U.S. February job report, pricing in dismal expectations about the impact of Covid-19 on the economy. But there is more to the story than the investors’ flight to safety. A strange beast was hunting the markets and its name is indeed obscure: convexity hedging.

I am confident that our readers are well aware of the inverse relation between bond prices and yields. The next step towards an understanding of this fascinating phenomenon is the concept of duration. This measure can be defined as the sensitivity of the price of a debt instrument to changes in interest rates. This means that the longer the duration of a bond, such as a Treasury note, the sharper the decline in yield as interest rates fall. The rate we are most interested in is the Federal Funds rate set by the Federal Open Market Committee. The factors affecting duration are the maturity and the coupon payments of the bond.

Duration uses a linear approximation of the nonlinear price-rate function to measure the change in price of a fixed-income instrument given a change in rates. In mathematical terms, this means using the first derivative (slope) in lieu of the actual function, as illustrated in the chart. Convexity, the second derivative of the price-rate function, is a better measure of interest rate risk. Usually the convexity of bonds is positive, but for some assets it can be negative: this means that as rates fall, their value falls more sharply, while they do not decrease their value as fast as other bonds when rates rise.

The prime example to illustrate this pattern are mortgages: in a low interest rate environment, they are likely to be prepaid and refinanced with more attractive terms for the borrower, leading to a shortened duration. This clearly has an effect on mortgage-backed securities as well. Therefore, the holders of the aforementioned assets face a significant interest rate risk that needs to be hedged. Hedging means taking an offsetting position in order to mitigate the risk arising from an existing one.

It is no surprise that the most prominent convexity hedgers out there are mortgage servicers. This includes two main categories: banks and Government-Sponsored Enterprises (GSEs) such as the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac). Commercial banks face a mismatch: their liabilities (deposits) reprice at less favourable terms when rates fall and so do their assets (mortgages).

These institutions need to compensate for the assets whose value fails to rise when rates decline and, thus, they need to “add duration”: the higher the duration, the greater the sensitivity to changes in interest rates under the assumption that yields move inversely to prices. When it comes to fixed income instruments for commercial banks, corporate bonds, mortgages and Treasuries are on their menu. They typically refrain from massively investing in corporate bonds due to high capital requirements. As mortgages are the problem, they clearly cannot be an eligible solution. Buying bonds is not necessarily the best option, due to significant balance sheet costs. Moreover, the supply of U.S. Treasury notes is not sufficient to cover the needs of the banking system.

Players affected by the issue can also resort to the derivates market, with a focus on Interest Rate Swaps (IRS). IRSs are contracts for exchanging a stream of future payments (cash flows) with another and their “plain vanilla” version involves receiving fixed-rate payments against floating ones.

Confused readers might now wonder why servicers continue to offer mortgages and what prevents investors at large from losing faith in MBSs. The reason is that the hunt for duration is only second to the hunt for yield: in a world where entire yield curves can plunge into negative territory market players are recalibrating their risk appetite.

It is hard to overestate the relevance of these factors: they can heavily affect the market for U.S. sovereign debt as they explain who is buying the 10-year Treasury note and make clear that this trade is a risk management decision, rather than an investment one. This is the rationale behind an apparent paradox: as the prices of the longer-maturity end of the yield curve rally, investors crave even more and keep buying in spite of sky-high prices.

Is this a newly established relation? Not in the slightest, as it appears to have triggered several sell-off over the years. Its effects are most evident subsequently to rate cuts and their impact was exacerbated with the introduction of new regulations after 2008. August 2018 is an ideal case study: not only did the Federal Reserve decrease its benchmark rate by 25 basis points, but it did so in a move largely unforeseen by most players.  While there is no shortage of explanations for the turmoil that now keeps hitting the headlines, economic events at the end of the third quarter of 2018 fail to explain the slide in Treasury yields. Convexity hedging is estimated to be responsible for more than half of the market move.

Some experts at the time advanced the hypothesis that the Fed purchasing MBSs could mitigate the phenomenon, as the transactions would not be hedged in the same way as servicers do. The latest developments fail to confirm such view: the New York arm of the American central bank has now embarked in an MBS buying spree and the yield on the 10-year Treasury note is falling again.

The same rationale applies when, instead, rates surge: many experts point the finger to convexity hedging as one of the drivers of what is known as the “bond market massacre of 1994”, when the Fed surprised investors with a rate hike. A similar event occurred in 2003.

Perhaps the most important implication of this kind of distortion is its ability to cast doubts over the reliability of the yield curve as an indicator of recession. Every U.S. recession in history was preceded by an inversion of the curve (which plots the yield on U.S. Treasury for different maturities) and each time such inversion occurs, economists and commentators scramble to illustrate how, instead, it has lost its prophetic powers.

Time will tell what impact the potentially distorting convexity hedges will have. What we know for sure is that the “this time is different” argument will not cut it, under these circumstances. A much scarier beast is ravening growth prospects and hopes of escaping a severe recession are vanished.

Dal cartaceo di maggio 2020

Author profile

I’ve been part of Tra i Leoni since my first semester at Bocconi up to becoming Deputy Director. I’m a third year BIEF-Economics student and I mainly cover finance and campus life. In 2019 I wrote “Word on the Street”, a weekly column about the story behind the names of campus buildings and spots, while last semester I was the head of our Global Edition.

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