Bond Math: Duration Risk at the Zero Boundary

There seems to be lots of confusion surrounding Bill Gross' latest Investment Outlook, Life and Death Proposition. First, some background of what Bill Gross stated...

Investors aren't only concerned with credit risk (i.e. the ability to get paid back), but also duration risk (the risk of lending for an extended period of time in fear that rates may rise).

In Bill's words:

What perhaps is not so often recognized is that liquidity can be trapped by the “price” of credit, in addition to its “risk.” Capitalism depends on risk-taking in several forms. Developers, homeowners, entrepreneurs of all shapes and sizes epitomize the riskiness of business building via equity and credit risk extension. But modern capitalism is dependent as well on maturity extension in credit markets. No venture, aside from one financed with 100% owners’ capital, could survive on credit or loans that matured or were callable overnight. Buildings, utilities and homes require 20- and 30-year loan commitments to smooth and justify their returns.

Investors had been willing to take on this duration risk because they would be compensated with additional yield AND (this is important) because bonds could appreciate if rates fell (i.e. when yields fall, bonds rise).

Back to Bill:

Because this is so, lenders require a yield premium, expressed as a positively sloped yield curve, to make the extended loan. A flat yield curve, in contrast, is a disincentive for lenders to lend unless there is sufficient downside room for yields to fall and provide bond market capital gains.

And although the yield curve is steep, it is very low in nominal terms (i.e. there is less room for rates to move down).

Last time to Bill for his main argument:

Even if nodding in agreement, an observer might immediately comment that today’s yield curve is anything but flat and that might be true. Most short to intermediate Treasury yields, however, are dangerously close to the zero-bound which imply little if any room to fall: no margin, no air underneath those bond yields and therefore limited, if any, price appreciation. What incentive does a bank have to buy two-year Treasuries at 20 basis points when they can park overnight reserves with the Fed at 25? What incentives do investment managers or even individual investors have to take price risk with a five-, 10- or 30-year Treasury when there are multiples of downside price risk compared to appreciation? At 75 basis points, a five-year Treasury can only rationally appreciate by two more points, but theoretically can go down by an unlimited amount. Duration risk and flatness at the zero-bound, to make the simple point, can freeze and trap liquidity by convincing investors to hold cash as opposed to extend credit.

Now my oversimplified explanation using two interest rate scenarios...

Scenario one... bonds yielding 5%.

In this scenario, bonds with maturities 1 year through 5 are yielding 5%. Should rates stay at 5%, the bonds are worth PAR (i.e. $100) in all scenarios. However, the bonds have the potential to appreciate should yields move lower. In fact, should rates fall all the way to 1% (a huge decline, but this is meant to illustrate the point), the bonds actually appreciate almost 20% in the case of the 5 year Treasury. Compare that to the one year Treasury that gained less than 5%.

In other words, in a flight to quality scenario there is a HUGE incentive to own the longer duration bond when yields have room to compress.

Scenario two... bonds yielding 1%.

In this scenario, bonds with maturities 1 year through 5 are yielding 1% (yes the yield curve is upward sloping in "real life", but this isn't far off). Should rates stay at 1%, the bonds are again worth PAR (i.e. $100), but in this case they have limited room to move due to the zero boundary. Should rates move all the way to 0%, the five year bonds don't appreciate 20% like in scenario 1, they appreciate only 5%, while the one year Treasury appreciates around 1%.

In other words, in a flight to quality scenario the potential benefit of a longer duration Treasury is 75% lower than in scenario one and only 4% higher than the one year maturity bond.

The example above is close to current rates (as of this writing, a five year bond yields 0.82%). The result, as Bill Gross points out, is a lack of incentive for a lender to lend and take that risk as they can get roughly the same yield just putting their money in a mattress without the risk of rates moving higher (0% isn't far from 0.82%). In addition, for an investor that is allocating to bonds to diversity their equity holdings, fixed income will no longer appreciate in a flight to quality scenario to offset equity losses. As a result, businesses should in theory be having a hard time getting money for their businesses outside of equity financing.

But, the evidence doesn't point to any of this being an issue. As far as I know, investors are still willing to extend the duration of their investments to pick up this incremental yield. And why not? The Fed has made it clear there is zero risk that rates will rise going out to at least 2014. So why not pocket that additional 82 bps regardless of the lack of capital appreciation?

The Impact of Low Rates Through 2014

Bloomberg details the latest from the Fed:

Chairman Ben S. Bernanke said the Federal Reserve is considering additional asset purchases to boost growth after extending its pledge to keep interest rates low through at least late 2014.

Policy makers are “prepared to provide further monetary accommodation if employment is not making sufficient progress towards our assessment of its maximum level, or if inflation shows signs of moving further below its mandate-consistent rate."

The immediate market reaction was a risk asset rally, a huge rally in gold (per Calculated Risk: Bernanke made it clear that even if inflation moved above the target - and unemployment was still very high - the Fed would only slowly pursue policies to reduce the inflation rate), and a rally at the belly of the yield curve (the yield curve flattened out to five years... shorter rates couldn't fall as they are already at or near zero). Why? The "late 2014" date is much later than the June 2013 date previously projected by Bernanke last summer.

The impact of this announcement (and the previous projected rates) can be seen in the chart below that shows the Fed Funds rate curve (implied by EuroDollar futures) for March 2013 through December 2014, as of various dates over the past year.

What do we see? We see an initial drop between March and June of last year as Bernanke indicated low yields for the foreseeable future, then a huge drop (mid-summer) after Bernanke stated rates would remain zero through June 2013. Today's announcement really did nothing through June 2013 (that was already projected), but was felt further out along the curve.

The key question is what is the Fed trying to accomplish?

In "normal" times, low yields = cheap financing = increased consumption (it creates an incentive for individuals to borrow and banks to lend), but in today's zero-bound world the impact is minimal. Increased consumption is limited as individuals are trying to rebuild their own balance sheets and those that might benefit most from borrowing, don't necessarily have the credit to qualify for a loan. In terms of impact on unemployment, GYSC (of Economic Disconnect fame) states:

Unemployment is a structural problem, not a cyclical one, but the FED is still stuck in the past.

In addition, there are some theories that consumption may actually be negatively impacted by zero bound rates. As I outlined over the summer, I think it is possible that negative real interest rates may actually cause individuals to save more, while Kid Dynamite outlined yesterday that low rates forecasted may cause individuals to hold off from making a loan fueled purchase:

Let me explain: right now, one appealing factor of home buying/selling decisions is that interest rates are very low – you can afford to buy more house. If I think that interest rates are going to remain low for a long period of time, I will be in no hurry to lock in this low rate on the debt I’m borrowing – I will be in no hurry to go out and buy a house.

So what is it then? Corporations!

There is one sector that I think will be positively impacted by the latest announcement.... corporations. Don't let their record profits as a percent of GDP (while personal income is at record lows) fool you into thinking they don't need help at the populations expense. Seriously though... my initial reaction upon hearing that rates would be held down near zero through 2014... buy credit... WITH duration out to around ten years (the secondary impact is positive for equities, as explained below).

While Treasury yields are at all-time lows, corporate spreads remain at elevated levels (when yields fell during the summer when we had to deal with the US downgrade and Europe, spreads widened significantly).

In "normal" times, when markets calm these spreads would be expected to narrow, which I still believe is the case. One would also "normally" expect Treasury yields to rise as investors shift out of Treasuries, causing the hard interest rate component of corporate yields (rate + spread = yield) to rise, but this risk has been removed for the foreseeable future out to around ten years. The result is that corporate bonds seem like a very safe investment. This decreased risk should mean even cheaper financing for longer dated maturity corporate bond issuance.

So will this finally set off a round of corporate fueled expansion? If they don't see aggregate demand improving, then I don't see how this will impact the underlying economy. But, with the cost of equity high (i.e. what I perceive as fair to cheap equity valuations) and cost of debt low (i.e. these lower yielding corporate bonds), we may see significant change in capital structures (perhaps via private equity).

Source: Barclays Capital

Race to the Bottom

Reuters details:

U.S. Treasuries rose broadly and the five-year yield hit a record low on Wednesday, supported by prospects of further monetary easing by the U.S. Federal Reserve.

* The five-year Treasuries yield fell to a record low of 1.179 percent at one point.

* Treasuries have been supported by market expectations that the Fed could unveil a second round of quantitative easing as early as November and make new purchases of Treasuries.

* An additional factor supporting Treasuries was a rally in Japanese government bonds in the wake of the Bank of Japan's decision on Tuesday to ease monetary policy, said a trader for a European brokerage house.

Sean from Dead Cats Bouncing details the why:

The purpose of QE is to increase inflation expectations and support growth, so success would be reflected in the long-run real rate (a proxy for real trend GDP growth) to mean-revert back towards the 2-2.5% range as happened in 2009.

The inflation expectations component of yields will have to move higher if central banks start chucking hundreds of billions of new money around. In other words, even with the Fed as bond ‘buyer of last resort’, nominal yields are unsustainably low, particularly as commodity markets are on fire in anticipation.

What is remarkable is that the Fed is going nuclear when the US economy is by no means in freefall (as evidenced by yesterday’s ISM non-manufacturing survey).

He finishes with a sentence that sums this all up perfectly.

We’re heading into uncharted waters and we’re traveling at full speed.

Source: Federal Reserve

Swap Curve Whacked

At a very basic level, interest rate swaps allow the exchange of a fixed rate for a floating rate across maturities. When viewed in the form of a swap curve (below), we can see what the market is pricing in for this fixed for floating across maturities, similar to a Treasury curve (i.e. the level in which you can get paid over various maturities on one side, while paying 3-month LIBOR on the other).

Below we see the swap curve at spot (i.e. current levels) and what the market is pricing in one, three, five, and ten years into the future.

What is the below chart showing?

1) The swap curve is currently steep, though not as steep as the Treasury curve (as long swaps are currently trading well through Treasuries)
2) The market is pricing in rates to rise rather dramatically at the front-end of the yield curve over the next five to ten years (though not much at all over the next 12 months)
3) The yield curve is actually inverted at the very long-end as early as three years out

Why? For one, investors that were underweight (or short) duration got themselves caught majorly off-guard over the course of the past few weeks as the long-end has taken a cliff-dive and now need duration at any cost.




Source: Bloomberg

IBM Borrows on the Cheap

Bloomberg details:

International Business Machines Corp. raised $1.5 billion at the lowest interest rate on record as the credit rally that began in June extended into August on investor confidence the economy won’t slip back into recession.

The 1 percent, 3-year notes from IBM, the world’s biggest computer-services company, have the lowest coupon of the more than 3,400 securities in the Barclays Capital U.S. Corporate Index of investment-grade company debt. Dearborn, Michigan-based Ford Motor Co.’s credit rating was lifted two steps by Standard & Poor’s.

Source: Barclays Capital

Get Low, Get Low, Get Low, Get Low

Thanks to Lil Jon for the headline of the post... Peter Boockvar via The Big Picture details:

Outside of the late ‘08, early ‘09 panic into US Treasuries where the 10 yr yield got to 2.06%, the 10 yr bond yield is now at the lowest level since at least 1962 (as far back as Bloomberg goes) at 3.07%, breaking the June ‘03 level of 3.11% less than 2 weeks before Greenspan cut the fed funds rate to 1%.

Add high quality spread to the equation and we get an even lower figure. The aggregate bond index (i.e. the Barclays Capital Aggregate made up mainly of Treasuries, Corporates, and Agency MBS), which EconomPic detailed a few weeks back:

We have a new milestone to watch... the Barclays Capital Aggregate Bond Index (i.e. the most popular US dollar fixed income benchmark) closed at a mere 3.08% on May 21st. That is the lowest level EVER (well, at least since the benchmark's January 1973 inception).

Hit a new 2.94% low as of yesterday's close.



Source: Barclays Capital

Money Market Funds Yielding Nada... In Other Words "Solid" Real Returns

USA Today reports on the (lack of) returns in money market space:

Money isn't everything, at least to investors in money market funds. Yields are at all-time lows, and nearly a quarter of funds yield nothing at all.

The average money fund yielded an annualized 0.08% the week ended Aug. 4, the latest data from iMoneyNet, which tracks funds, show. At that rate, a $10,000 investment would return 15 cents a week. But 275 taxable funds have no yield, 23% of the 1,180 funds iMoneyNet tracks.

With that as a background, this won't surprise you. Over the past twelve months, the Lipper Money Market Index has returned 1.01% (higher than 0.08%, but minuscule none-the-less).

However, this may. Over that same period, inflation (as measured by CPI) has DECREASED 2.1% year over year, which has resulted in real returns in money market space (i.e. returns less inflation OR importantly returns + deflation) up more than 3%.



With the economy shrinking and expected by many to grow at 2-3% when it does rebound (in real terms), 3% real returns don't seem so bad.

Source: Lipper / BLS

Yield Curve to Predict Equity Markets? Yes and No

Interesting article in Bloomberg about the yield curve accurately forecasting economic conditions:

• First, it’s a leading economic indicator, officially added to the index designed to predict the economy’s ebbs and flows in 1996. It was a leader well before that, even though it was unofficial.
• Second, what you see is what you get. The spread is never revised, always available and in no way proprietary.
• Third, and most curious, the majority of economists don’t get it. They see rising bond yields in isolation -- without paying attention to what that price-setter, the Fed, is doing at the front end of the curve.
• It’s the juxtaposition of short and long rates, not their level, that conveys information about monetary policy.

Crossing Wall Street makes the case that the yield curve can also help predict the stock market:

Two years ago, I looked at the impact of the yield curve on the stock market and I was stunned to find:

Probably the most fascinating stat is that all of the stock market’s net capital gains have come when the 10-year yield is 65 or more basis points above the 90-day yield (that happens about 70% of the time). The yield curve hasn’t been that positive in 15 months.

Anything less than 65 basis points, including a negative yield curve, works out to a net equity return of a Blutarsky. Zero Point Zero.

Today the spread is out to nearly 300 basis points.

Yes, over the past 25 years (all the data I was able to pull) a flat yield curve did equate to a poor performing equity market over the subsequent two year period. However, a high spread between the 10 year and 90 day yield did not necessarily mean strong returns were on the horizon (see 1992 and 2002 noting that the red line indicate the two year FORWARD return).



What did? Sustained periods of a steep yield curve.

So the question becomes, what type of economic conditions usually persist in order to have SUSTAINED periods of a steep yield curve? My quick answer... expectations of higher growth for an extended period that is reinforced by a rebound in the economy (allowing long rates to STAY higher than short term rates).

My concern this time around isn't around short-term rates (they will likely stay low), but long term rates may now be influenced not only by expectations of economic growth, but by issuance and inflation expectations.

"Maturity Premium" Approaching 20 Year High

Across the Curve details:

The 2 year/10 year spread has reached 225 basis points. That is approaching the very wide end of the range which has prevailed for that spread for the lat three decades. So a little history.

The cycle wide in this market iteration was achieved in November when it touched 261 basis points.

The 2year/30 year spread currently sits at about 318 basis points. In 2004 it peaked at 364 basis points.

Returning to the fixed income markets, I think that the record spreads which I have cited are in peril aas the market cchokes on the burden of supply from the Treasury.

Ten Year Yields: Higher or Lower?

Higher --> Supply: Across the Curve

Treasury bonds are taking a severe drubbing and the yield on the benchmark 10 year note is approximately at the level which prevailed on the day when the Federal Reserve announced quantitative ease (2.96 percent currently).

One participant noted that the 200 day moving average on the Long Bond was 3.798 percent and the market penetrated that level this morning as a sharp knife would melting butter.

Lower --> Quantitative Easing / Continued Economic Deterioration: Zero Hedge

There has been a lot of criticism of Big Ben (us included) but one thing that has come out is he is not afraid to take relatively risky moves to combat whatever he perceives as the biggest threat. As we have noted before, he has clearly revealed his playbook in the past and we see little indication that he will stray from it going forward. On the balance between inflation and deflation, much has been made of the Chinese response if we try to print our way out of this situation but the much larger problem has always been deflation. Combining what we know about the available policy options and the effectiveness of the last round of QE, we have to believe that more purchases of long rates are on the table as a serious consideration.

Source: Yahoo

Real Yields Matter

Paul Krugman comments:

The really striking thing about corporate borrowing rates isn’t that they’re high by historical standards, although they are, but the fact that they’re high even though interest rates on government debt are very, very low. Below I show the spreads on AAA and Baa debt against 30-year Treasuries: they really have spiked.

Also bear in mind the decline in expected inflation: real corporate rates are very high.

That last sentence is key. Even though Treasury rates have rallied significantly in nominal terms over the past 1 1/2 years, they still yield more in real terms than when the financial crisis began. Corporates, as Paul points out, are the greater issue. Real yields on Investment Grade Corporate Bonds are now 2.5x higher than they were just six months ago.



Throw in a declining economy and the diminished end-user demand we are witnessing across industries, and it is very easy to see why corporations are having such a difficult time.

Are Treasuries Really in a Bubble?

A Barron's video posted at The Big Picture warns to 'Stay Away From Treasury Bonds'. I'll agree that Treasury bonds look awfully rich and I have no intention of going long, but I do feel there is danger to outright shorting treasuries in this environment (though as I post this, 30 year yields have blown out 20 bps today). First lets look at some data that shows at a minimum long bonds (i.e. 30 year Treasuries) appear rich.

30 year treasury yields have rallied dramatically over the past 25+ years, but the most recent rally is unprecedented over that time.



In terms of pricing, long bonds have rallied more than 30% in the past 3 months. Supporting the case that these bonds are ready to sell off... long bond prices have historically sold off ("mean reverted") following smaller, yet similar rallies.



However, it is important to remember that the current market is not "normal" and mean reversion is not a certainty. Off the top of my head, I can think of many reasons why long bond yields may not only stay at current levels, but may actually continue to rally.

1. Real yields are not abnormally low (a deflationary environment makes those puny yields much better in real rather than nominal terms)
2. The Fed can (and will likely be) purchasing Treasury bonds to keep rates artificially low; likely starting in the 5-7 year space, but possibly out along the curve
   
3. The economy can continue to get worse / companies will default in the coming year at substantial levels, creating the possibility of another "flight to quality"

As Larry MacDonald states in his post Shorting The Bond Bubble? Hold On:

Shorting government bonds would thus appear to be a no brainer as risk appetite responds to signs of an upturn in economic growth and inflation worries arise anew. But what might not be so obvious is the timing of the trade.

Lags in the impact of stimulus measures could mean deflationary news will linger for awhile yet. More importantly, the Federal Reserve has stated it is committed to buying Treasuries to keep interest rates low until the crisis and economy stabilizes. China too will likely be a buyer of U.S. Treasuries as part of its strategy of suppressing the yuan to enhance the competitiveness of its exports.

So watching from the sidelines may be the strategy for now.

Update: My post was all set to go when I saw Credit Writedowns had an eerily similar post. Always nice to be in good company.

Real Yield of Treasuries vs. Corporates

T-Bills practically yield nothing and moving out along the curve we see a similar flight to the quality of Treasuries. However, real yields tell a different story (real as in removed the inflation within 5 year inflation swaps). While corporates look awfully cheap if you don't expect the Great Recession, the 2% real yield over five years of Treasuries is the highest figure we've seen in a year and a half.