Little Wing? US Rate Increases Alter Treasury And MBS Hedging

As the US Treasury 10-year yield approaches 2% … again, we begin to worry about issues such as extension risk and convexity risk (collectively known as “The Wings”) given their propensity to drive hedging.

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Extension Risk
Historically, the risk of sudden yield curve movements has greatly affected the market for MBS, which represent claims on a pool of underlying residential mortgages. The interest rate risk of MBS differs from the interest rate risk of Treasury securities because of the embedded prepayment option in conventional residential mortgages that allows homeowners to refinance their mortgages when it is economical to do so: When interest rates fall, homeowners tend to refinance their existing loans into new lower-rate mortgages, thereby increasing prepayments and depriving MBS investors of the higher coupon income. However, when rates rise, refinancing activity tends to decline and prepayments fall, thereby extending the period of time MBS investors receive below-market rate returns on their investment. This is commonly known as “extension risk” in MBS markets.

Duration and Convexity
The effect of the prepayment option can be seen in the chart below, which displays the relationship between yield changes (x-axis) and changes in the value of an MBS (black) and a non-prepayable ten-year Treasury note (red). The sensitivity of each instrument to small changes in yields (essentially the slope of each yield-price relationship at the point at which the MBS was last hedged, indicated by the dashed line) is known as the effective duration, while the rate at which duration changes as yields change (the curvature of the price-yield relationship) is known as its convexity. In the example shown below, the MBS and Treasury security are duration matched in the sense that they will tend to move one-to-one for small changes in yields.

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    When interest rates increase, the price of an MBS tends to fall at an increasing rate and much faster than a comparable Treasury security due to duration extension, a feature known as the negative convexity of MBS. Managing the interest rate risk exposure of MBS relative to Treasury securities requires dynamic hedging to maintain a desired exposure of the position to movements in yields, as the duration of the MBS changes with changes in the yield curve. This practice is known as duration hedging. The amount and required frequency of hedging depends on the degree of convexity of the MBS, the volatility of rates, and investors’ objectives and risk tolerances.

    Duration hedging of MBS can be done with interest rate swaps or Treasury bonds and notes. When rates decline, hedgers will seek to increase the duration of their positions. This can be achieved by buying Treasury notes or bonds, or by receiving fixed payments in an interest rate swap. Conversely, MBS holders will find the duration of their MBS extending when rates increase, which they may choose to offset by selling Treasury notes or bonds, or by paying fixed in swaps. If sufficiently strong, this hedging activity can itself cause interest rates to rise further, and further increase duration for MBS holders, inducing another round of selling of Treasuries.

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A Convexity Event Averted
A sudden initial rise in medium- to long-term rates can therefore trigger a self-reinforcing sell-off in Treasury yields and related fixed income markets, fueled by MBS hedging—a phenomenon known as a convexity event. During a convexity event, MBS hedgers collectively attempt to decrease duration risk by selling Treasury securities or paying fixed in swaps. The two most important factors that determine the likelihood of a convexity event are the size of the MBS portfolio held by duration hedgers and the convexity of that portfolio. The large-scale purchases of MBS initiated by the Federal Reserve in November 2008 as part of the post-crisis LSAPs have had a profound impact on both these determinants.

    MBS investors, broadly speaking, fall into two categories: those holding MBS on an unhedged or infrequently hedged basis and those that actively hedge the interest rate risk exposure. Unhedged or infrequently hedged investors include the Federal Reserve, foreign sovereign wealth funds, banks, and mutual funds benchmarked against an MBS index. MBS holders who actively hedge include real estate investment trusts (REITs), mortgage servicers, and the government-sponsored enterprises (GSEs).

Mortgage bonds are often held by large investors such as money managers and banks. They tend to prefer stable returns and constant duration as a means to reduce risk in their portfolios. So when interest rates drop, and mortgage bond duration starts to shorten, the investors will scramble to compensate by adding duration to their holdings, in a phenomenon known as convexity hedging. A hedge is basically investing in something that tends to go up when the first thing goes down (or vice versa). To add duration, so as to extend payments into a longer period, investors could buy U.S. Treasuries, which would further push down yields in the market. Or they could use interest-rate swaps, which are a contract between two parties to exchange one stream of interest payments for another.

Here are the dollar swaps and US Treasury actives curves today and from December 2005 to illustrate the decline in both curves of around 300 basis points at the ten year tenor.

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Today’s US Treasury curve upward sloping … again having retreated from the inverted curve.

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Here is a snap shot of MBS hedge ratios by coupon.

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Of course, interest rates are influenced by the Voodoo Children themselves, the Central Banks like The Federal Reserve.

US Treasury Yield Curve Un-inverts (Can’t Turn The Fed Loose) Sag Gone In Treasuries, Not Swaps

Federal Reserve Chair Jerome Powell has said that the US economy is in a good place, and further rate cuts are not warranted. That is, Trump can’t turn The Fed loose.

Various US Treasury yield curves are un-inverting and are all positive.

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The Treasury actives curve is no longer sagging, but the Dollar Swaps curve continues to sag.

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But in terms of Treasury futures, the volatility for 2 year, 10 year and 30 year (Ultra) contracts   are progressively warping for 10 Delta Puts as maturity increases.

2-year:

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10-year:

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30-year (Ultra):

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Every investor needs The Fed to keep propping up asset bubbles!

Of course, the yield curve can revert to a negative state if … the China trade agreement becomes unglued, Democrats succeed in impeaching President Trump, etc.

 

How Negative Rates Broke Black-Scholes, Pillar of Modern Finance (How About SABR?)

I suggest that students at George Mason University ask their finance professors how negative interest rate impact their use of the famous Black-Scholes model.

(Bloomberg) — Negative interest rates have quite literally broken one of the pillars of modern finance.  

As economists and central bankers weigh the pros and cons of sub-zero rates and their impact on the world, traders have been contending with a rather more mundane, but fundamental issue: How to price risk on trillions of dollars of financial instruments like interest-rate swaps when their complex mathematical models simply don’t work with negative numbers.

Out are certain variations of the Black-Scholes model, the framework that allowed derivatives to flourish in the past four decades. In are a hodgepodge of approximations and workarounds, including one dating to the 19th century.

Granted, the current state of affairs is more a nuisance than a serious problem. And it’s one that has been largely confined to Europe and Japan.

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But with sub-zero interest rates becoming a long-term economic feature and the number of negative-yielding bonds reaching $15 trillion, it’s an issue more and more traders, particularly in the U.S., are trying to wrap their heads around.

“I was quite surprised that I’ve started getting questions from U.S. clients wondering, ‘What’s the impact of negative rates? What are the mathematics?’” said Sphia Salim, a London-based rate strategist at Bank of America.

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The issues are most apparent in the market for interest-rate swaps. (This market allows professional investors to lock in interest rates and lets speculators bet on whether rates on bonds or loans will rise or fall.) That’s because the Black 76 model, the main tool to price options for interest-rate derivatives, and its variants are so-called log-normal forward models.

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For those who aren’t math nerds, it can essentially be boiled down to this: the formula breaks because it requires users to calculate a logarithm, and a logarithm of a negative number is undefined, or meaningless.

One option has been to dust off a framework that was first proposed nearly 120 years ago. Known as the Bachelier model, it’s named after the French mathematician Louis Bachelier, who laid out his approach in his 1900 thesis “Theory of Speculation.” The model is best known for solving the math behind a theory from physics known as Brownian motion (some five years before Albert Einstein did the same in his revolutionary work on thermodynamics), and applying it to finance, according to a 2016 paper by Ian Thomson.

All is not lost. There is the SABR Model that is a stochastic volatility model.

The SABR model describes a single forward , such as a LIBOR forward rate, a forward swap rate, or a forward stock price. This is one of the standards in market used by market participants to quote volatilities. The volatility of the forward is described by a parameter . SABR is a dynamic model in which both and are represented by stochastic state variables whose time evolution is given by the following system of stochastic differential equations:

with the prescribed time zero (currently observed) values and . Here, and are two correlated Wiener processes with correlation coefficient :

The constant parameters satisfy the conditions . is a volatility-like parameter for the volatility. is the instantaneous correlation between the underlying and its volatility. thus controls the height of the ATM implied volatility level. The correlation controls the slope of the implied skew and controls its curvature.

The above dynamics is a stochastic version of the CEV model with the skewness parameter : in fact, it reduces to the CEV model if The parameter is often referred to as the volvol, and its meaning is that of the lognormal volatility of the volatility parameter .

A SABR model extension for Negative interest rates that has gained popularity in recent years is the shifted SABR model, where the shifted forward rate is assumed to follow a SABR process

for some positive shift . Since shifts are included in a market quotes, and there is an intuitive soft boundary for how negative rates can become, shifted SABR has become market best practice to accommodate negative rates.

The SABR model can also be modified to cover Negative interest rates by:

for and a free boundary condition for . Its exact solution for the zero correlation as well as an efficient approximation for a general case are available.[2]

An obvious drawback of this approach is the a priori assumption of potential highly negative interest rates via the free boundary.

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U.K. Bank Credit Rallies as Johnson Strikes Brexit Deal With EU (UK CoCo Prices Jump, But Not Deutsche Bank’s 6% CoCo)

While the UK Parliament has to sign off on the Brexit agreement, bank credit rallies after Boris Johnson reached an agreement with the EU.

U.K. lenders’ riskiest notes jumped, leading a credit rally, after Prime Minister Boris Johnson reached a Brexit agreement with the European Union.

Barclays Plc’s 1.25 billion pound ($1.6 billion) 5.875% CoCo reversed earlier losses and hit 99.5 pence on the pound, the highest since May 2018, according to data compiled by Bloomberg.

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Nationwide Building Society’s 600 million-pound perpetual bond, sold last month, hit a record. Oddly, NBS’s perpetual bond started rising on October 10th, well before PM Boris Johnson announced his Brexit agreement.

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A contingent convertible bond (CoCo), also known as an enhanced capital note (ECN) is a fixed-income instrument that is convertible into equity if a pre-specified trigger event occurs.

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A famous CoCo bond is the Deutsche Bank 6% Perpetual.

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While issued at par (100), the G-spread on the Deutsche’s 6% CoCo bond is … 11%.

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Odd, that DB’s CoCo bond remained relatively calm after the Brexit deal was announced.

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Is that UK PM Boris Johnson or Martin Kernsten, the Nipple King from Parks and Recreation?

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Its always sunny in the UK!

A Horse Is A Horse … Fed Chair Powell Announces New QE … That Is Not QE?

A horse is a horse, of course, of course, but no one can talk to a horse, of course. Unless, of course, that certain horse is … Jerome Powell!

(Bloomberg) Federal Reserve Chairman Jerome Powell said the central bank will resume purchases of Treasury securities in an effort to avoid a repeat of recent turmoil in money markets, while hinting at the possibility of another interest rate cut.

“My colleagues and I will soon announce measures to add to the supply of reserves over time,” he told a National Association for Business Economics conference in Denver on Tuesday.

The Fed chief suggested that the purchases would be made up of Treasury bills and stressed the buying should not be seen as a return of the crisis-era quantitative easing programs that the Fed engaged in a decade ago to boost the economy. Three-month bill yields fell on the comments.

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“I want to emphasize that growth of our balance sheet for reserve management purposes should in no way be confused with the large-scale asset purchase programs that we deployed after the financial crisis,” he said. “Neither the recent technical issues nor the purchases of Treasury bills we are contemplating to resolve them should materially affect the stance of monetary policy.”

“In no sense, is this QE,” Powell said in a moderated discussion after delivering his speech.

The Fed has cut interest rates twice this year to shelter the U.S. economy from weak global growth and trade-policy uncertainty. Traders in federal funds futures are betting that the Federal Open Market Committee will reduce rates again at its Oct. 29-30 meeting from the current target range of 1.75% to 2%.

Another Cut
In the question and answer period after his speech, Powell compared the current period to two instances in the 1990’s when the Fed cut rates three times in a successful effort to keep an economic expansion on track.

Powell’s comments suggest the Fed is inching closer to reducing rates at the upcoming meeting “but it’s not a done deal,” said Michael Gapen, chief U.S. economist at Barclays Plc.

“Another rate cut as early as this month remains a real possibility,’’ agreed Sarah House, senior economist, Wells Fargo & Co., who attended the Denver conference.

Powell told the gathering that the actions the Fed has already taken “are providing support for the outlook,” which remains favorable but faces risks, principally from global developments such as trade and Brexit.

“The broader geopolitical risks are important right now,’’ Powell said. “You have to be watching those carefully and assess the implications.”

Slowing Economy
The economy has recently shown signs of slowing as weakness overseas has spread to the U.S. and moved from domestic manufacturing industries to services.

The job market has also downshifted, even as unemployment has fallen to a half-century low of 3.5%. Nonfarm payrolls grew by an average of 157,000 per month in the third quarter, compared with gains above 200,000 earlier in the expansion.

Powell said that work done by the Fed mining private-sector data suggested the most recent job gains may ultimately be revised lower, but that the pace would still be above the level needed to hold unemployment steady.

He voiced confidence though that the economic expansion would remain on track. “This feels very sustainable,’’ [That’s what she said!]

Repo Market
Money markets were roiled last month as a combination of corporate tax payments and the settlement of Treasury debt purchases temporarily sent short-term interest rates skyrocketing.

The Fed announced last week that it will extend through October the ad hoc liquidity lifeline that it’s been offering to U.S. funding markets since then.

“We will not hesitate to conduct temporary operations if needed to foster trading in the federal funds market at rates within the target range,” Powell said.

“As we indicated in our March statement on balance sheet normalization, at some point, we will begin increasing our securities holdings to maintain an appropriate level of reserves,” he added. “That time is now upon us.”

Well, maybe not right now.

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The NEW logo for The Federal Reserve.

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Free Cat? World’s Best-Run Pension Funds Say It’s Time to Start Worrying (Not Enough Revenue Thanks To ECB Policies And Inflated Liabilities)

State and Federal pension funds are plagued by extravagant promises to pensioners and low yields on pension assets caused, in part, by Central Banks, like the European Central Bank and Federal Reserve.

(Bloomberg) Back in 2012, the world’s best-managed pension market was thrown a lifeline by the Danish government to help contain liabilities. That was when interest rates were still positive.

Seven years later, with rates now well below zero, even Denmark’s $440 billion pension system says the environment has become so punishing that it may be time for a change in European rules.

Henrik Munck, a senior consultant at Insurance & Pension Denmark, an umbrella organization, says the way liabilities are currently calculated “could cause a negative spiral” that forces funds to keep buying low-risk assets, drive yields lower and the value of liabilities even higher.

The warning comes as pension firms across Europe struggle to generate the returns they need to cover their growing obligations. In Denmark, some funds saddled with legacy policies guaranteeing returns as high as 4.5% have had to use equity to meet their obligations.

To calculate liabilities, pension firms use a complex mathematical formula constructed by the European Insurance and Occupational Pensions Authority (EIOPA). The formula is intended to shield funds from erratic market swings that artificially inflate or hollow out balance sheets. But with negative rates more entrenched, there are signs the EIOPA curve, as it’s called, may not be working as intended.

“When pension funds across Europe de-risk simultaneously, it may actually become pro-cyclical: it increases the price movements, and it could result in yet more downward pressure on the EIOPA yield curve, exacerbating the problem,” Munck said.

The curve is comprised of several elements. Its backbone — the euro interest-rate swap curve — has sunk since its implementation about four years ago, driving up the value of liabilities.

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PFA, like many Danish pension funds, started scaling back guaranteed products for retirees many years ago. That’s given it a buffer to help absorb some of the shock of growing liabilities. But not everyone’s as well prepared. “If the discount curve is more volatile and you can’t hedge it, you can — if you don’t have enough capital — be forced to lower risk on the more hedgeable space, to compensate,” Damgaard said.

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Low volatility assets like sovereign debt?? Pretty soon, government pensions will have to deliver cheaper payments to pensioners.

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Green Man! Fed’s Balance Sheet Climbs As 10-year Treasury Note Yield Falls Back To Obama Swan Song Of 2016

The Federal Reserve’s Balance Sheet has reversed its unwind and is now rising again.

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The 10-year Treasury Note yield is now back to the waning years of President Obama, just prior to President Trump’s election.

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Thanks to The Fed’s massive injections of “green” into the repo market, repo rates are lower today in 2018/2019.

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Yes, the Federal Reserve is officially “green man.”

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Treasury, Swap And SOFR Curves Remain Inverted Compared To 1 Year Ago (Venezuela’s 6M Yield At 17,500%)

Foul Powell on the prowl? 

The US Treasury actives curve certainly is different than one year ago. It was upward sloping, but not it is downward sloping to 5 years then upward sloping again.

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The US dollar swaps curve was steeply upward sloping a year ago, but now is deeply downward sloping up to 18 months.

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At least the great rum-producing nation of Venezuela looks pretty much the same as 1 year ago, with the exception of the short end where the 6 month sovereign yield is … 17,500%.

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The Crazy World Of Jerome Powell: Fed’s FOMC Lowers Target Rate By 25 BPS As Repo, SOFR Rates Balloon, Dow Drops Over 150 Pts

The Fed is the God of Hellfire!

The FOMC lower the Fed’s target rate by 25 basis points to 2.00%.

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The NY Fed’s SOFR rate ballooned to 5.25%.

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The GCF Repo Index ballooned to 6%.

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The US Treasury and Dollar Swaps curves remain … kinky.

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On the news, the Dow tanked over 160 points. Is the market signaling too little for the rate cut?

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The Crazy World of … Jerome Powell.

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