Tag Archives: duration

Digging For Value in a Pile of Manure

A special thank you to Brett Freeze of Global Technical Analysis for his analytical rigor and technical expertise.

There is an old story about a little boy who was such an extreme optimist that his worried parents took him to a psychiatrist. The doctor decided to try to temper the young boy’s optimism by ushering him into a room full of horse manure. Promptly the boy waded enthusiastically into the middle of the room saying, “I know there’s a pony in here somewhere!”

Such as it is with markets these days.

Finding Opportunity

These days, we often hear that the financial markets are caught up in the “Everything Bubble.” Stocks are overvalued, trillions in sovereign debt trade with negative interest rates, corporate credit, both investment grade, and high yield seem to trade with far more risk than return, and so on. However, as investors, we must ask, can we dig through this muck and find the pony in the room.

To frame this discussion, it is worth considering the contrast in risk between several credit market categories. According to the Bloomberg-Barclays Aggregate Investment Grade Corporate Index, yields at the end of January 2020 were hovering around 2.55% and in a range between 2.10% for double-A (AA) credits and 2.85% for triple-B (BBB) credits. That means the yield “pick-up” to move down in credit from AA to BBB is only worth 0.75%. If you shifted $1 million out of AA and into BBB, you should anticipate receiving an extra $7,500 per year as compensation for taking on significantly more risk. Gaining only 0.75% seems paltry compared to historical spreads, but in a world of microscopic yields, investors are desperate for income and willing to forego risk management and sound judgment.

As if the poor risk premium to own BBB over AA is not enough, one must also consider there is an unusually high concentration of BBB bonds currently outstanding as a percentage of the total amount of bonds in the investment-grade universe. The graph below from our article, The Corporate Maginot Line, shows how BBB bonds have become a larger part of the corporate bond universe versus all other credit tiers.

In that article, we discussed and highlighted how more bonds than ever in the history of corporate credit markets rest one step away from losing their investment-grade credit status.

Furthermore, as shared in the article and shown below, there is evidence that many of those companies are not even worthy of the BBB rating, having debt ratios that are incompatible with investment-grade categories. That too is troubling.

A second and often overlooked factor in evaluating risk is the price risk embedded in these bonds. In the fixed income markets, interest rate risk is typically assessed with a calculation called duration. Similar to beta in stocks, duration allows an investor to estimate how a change in interest rates will affect the price of the bond. Simply, if interest rates were to rise by 100 basis points (1.00%), duration allows us to quantify the effect on the price of a bond. How much money would be lost? That, after all, is what defines risk.

Currently, duration risk in the corporate credit market is higher than at any time in at least the last 30 years. At a duration of 8.05 years on average for the investment-grade bond market, an interest rate increase of 1.00% would coincide with the price of a bond with a duration of 8.05 to fall by 8.05%. In that case a par priced bond (price of 100) would drop to 91.95.

Yield Per Unit of Duration

Those two metrics, yield and duration, bring us to an important measure of value and a tool to compare different fixed income securities and classes. Combining the two measures and calculating yield per unit of duration, offers unique insight. Specifically, the calculation measures how much yield an investor receives (return) relative to the amount of duration (risk). This ratio is similar to the Sharpe Ratio for stocks but forward-looking, not backward-looking.

In the case of the aggregate investment-grade corporate bond market as described above, dividing 2.55% yield by the 8.05 duration produces a ratio of 0.317. Put another way, an investor is receiving 31.7 basis points of yield for each unit of duration risk. That is pretty skinny.

After all that digging, it may seem as though there may not be a pony in the corporate bond market. What we have determined is that investors appear to be indiscriminately plowing money into the corporate credit market without giving much thought to the minimal returns and heightened risk. As we have described on several other occasions, this is yet another symptom of the passive investing phenomenon.

Our Pony

If we compare the corporate yield per unit of duration metric to the same metric for mortgage-backed securities (MBS) we very well may have found our pony. The table below offers a comparison of yield per unit of duration ratios as of the end of January:

Clearly, the poorest risk-reward categories are in the corporate bond sectors with very low ratios. As shown, the ratios currently sit at nearly two standard deviations rich to the average. Conversely, the MBS sector has a ratio of 0.863, which is nearly three times that of the corporate sectors and is almost 1.5 standard deviations above the average for the mortgage sector.

The chart below puts further context to the MBS yield per unit of duration ratio to the investment-grade corporate sector. As shown, MBS are at their cheapest levels as compared to corporates since 2015.

Chart Courtesy Brett Freeze – Global Technical Analysis

MBS, such as those issued by Fannie Mae and Freddie Mac, are guaranteed against default by the U.S. government, which means that unlike corporate bonds, the bonds will always mature or be repaid at par. Because of this protection, they are rated AAA. MBS also have the added benefit of being intrinsically well diversified. The interest and principal of a mortgage bond are backed by thousands and even tens of thousands of different homeowners from many different geographical and socio-economic locations. Maybe most important, homeowners are desperately interested in keeping the roof over their head

In contrast, a bond issued by IBM is backed solely by that one company and its capabilities to service the debt. No matter how many homeowners default, an MBS investor is guaranteed to receive par or 100 cents on the dollar. Investors of IBM, or any other corporate bond, on the other hand, may not be quite so lucky.

It is important to note that if an investor pays a premium for a mortgage bond, say a 102-dollar price, and receives par in return, a loss may be incurred. The determining factor is how much cash flow was received from coupon payments over time. The same equally holds for corporate bonds. What differentiates corporate bonds from MBS is that the risk of a large loss is much lower for MBS.


As the chart and table above reveal, AAA-rated MBS currently have a very favorable risk-reward when compared with investment-grade corporate bonds at a comparable yield.

Although the world is distracted by celebrity investing in the FAANG stocks, Tesla, and now corporate debt, our preference is to find high quality investment options that deliver excellent risk-adjusted returns, or at a minimum improve them.

This analysis argues for one of two outcomes as it relates to the fixed income markets. If one is seeking fixed income credit exposure, they are better served to shift their asset allocation to a heavier weighting of MBS as opposed to investment-grade corporate bonds. Secondly, it suggests that reducing exposure to corporate bonds on an outright basis is prudent given their extreme valuations. Although cash or the money markets do not offer much yield, they are always powerful in terms of the option it affords should the equity and fixed income markets finally come to their senses and mean revert.

With so many assets having historically expensive valuations, it is a difficult time to be an optimist. However, despite limited options, it is encouraging to know there are still a few ponies around, one just has to hold their nose and get a little dirty to find it.

A Traders’ Secret For Buying Munis

Believe it or not, any domestic bond trader under the age of 55 has never traded in a bond bear market. Unlike the stock market, which tends to cycle between bull and bear markets every five to ten years, bond markets can go decades trending in one direction. These long periods of predictable rate movements may seem easy to trade, especially in hindsight, but when the trend changes, muscle memory can trump logic leaving many traders and investors offside.

If you believe higher yields are upon us in the near future, there are many ways to protect your bond portfolio. In this article, we present one idea applicable to municipal bonds. The added benefit of this idea is it does not detract from performance if rates remain stubbornly low or fall even lower.  Who says there is no such thing as a free lunch?


Municipal bonds, aka Munis, are debt obligations issued by state and local government entities. Investors who seek capital preservation and a dependable income stream are the primary holders of munis. In bear markets, munis can offer additional yield over Treasury bonds, still maintain a high credit quality, and avoid the greater volatility present in the corporate bond or equity markets.

Munis are unique in a number of ways but most notably because of their tax status. Please note, munis come in taxable and tax-exempt formats but any reference to munis in this article refers to tax-exempt bonds.

Because of their tax status, evaluating munis involves an extra step to make them comparable to other fixed income assets which are not tax-exempt. When comparing a muni to a Treasury, corporate, mortgage backed security, or any asset for that matter, muni investors must adjust the yield to a taxable equivalent yield. As a simple example, if you are in a 40% tax bracket and evaluating a muni bond yielding 2%, the taxable equivalent yield would be 3.33% (2.00% / (1-40%). It is this yield that should be used to equate it to other fixed income securities.

Negative “Tax” Convexity Matters

Thus far, everything we have mentioned is relatively straight-forward. Less well-understood is the effect of the tax rate on muni bonds with different prices and coupons. Before diving into tax rates, let’s first consider duration. Duration is a measure that provides the price change that would occur for a given change in yield. For instance, a bond with a duration of 3.0 should move approximately 3% in price for every 1% change in yield.

While a very useful measure to help quantify risk and compare bonds with different characteristics, duration changes as yields change. Convexity measures the non-linear change in price for changes in yield. Convexity helps us estimate duration for a given change in yield.

For most fixed rate bonds without options attached, convexity is a minor concern. Convexity in the traditional sense is a complex topic and not of primary importance for this article. If you would like to learn more about traditional convexity, please contact us.

Munis, like most bonds, have a small amount of negative convexity. However, because of their tax status, some muni bonds have, what we call, an additional layer of negative tax convexity. To understand this concept, we must first consider the complete tax implications of owning munis.

The holder of the muni bond receives a stream of coupons and ultimately his or her invested principal back at par ($100). The coupons are tax free, however, if the bond is sold prior to maturity, a taxable capital gain may occur.

The table below illustrates three hypothetical muni bonds identical in structure and credit quality. We use a term of 1 year to make the math as simple as possible.

In the three sample bonds, note how prices vary based on the range of coupons. Bond A has the lowest coupon but compensates investors with $2.41 ($100-$97.59) of price appreciation at maturity (the bond pays $100 at maturity but is currently priced at $97.59). Conversely, Bond C has a higher coupon, but docks the holder $2.41 in principal at maturity.

For an uninformed investor, choosing between the three bonds is not as easy as it may appear. Because of the discounted price on bond A, the expected price appreciation ($2.41) of Bond A is taxable and subject to the holder’s ordinary income tax rate. The appropriate tax rate is based on a De minimis threshold test discussed in the addendum. Top earners in this tax bracket pay approximately 40%.

Given the tax implication, we recalculate the yield to maturity for Bond A and arrive at a net yield-to-maturity after taxes of 4% (2.50% + (2.50 *(1-.40). Obviously, 4% is well below the 5% yield to maturity offered by bonds B and C, which do not require a tax that Bond A does as they are priced at or above par. Working backwards, an investor choosing between the three bonds should require a price of 95.88 which leaves bond A with an after tax yield to maturity of 5% and on equal footing with bonds B and C.

Implications in a rising yield environment and the role of “tax” convexity

Assume you bought Bond B at par and yields surged 2.50% higher the next day. Using the bond’s stated duration of .988, one would expect Bond B’s price to decline approximately $2.47 (.988 * 2.5%) to $97.53. Based on the prior section, however, we know that is not correct due to the tax implications associated with purchasing a muni at a price below par. Since you purchased the bonds at par, the tax implication doesn’t apply to you, but it will if anyone buys the bond from you after the 2.5% rise in yields. Therefore, the price of a muni bond in the secondary market will be affected not just by the change in rates, but also the associated tax implications. Assuming the ordinary income tax rate, the price of Bond B should fall an additional $1.65 to $95.88.  This $1.65 of additional decline in Bond B’s price is the penalty we call negative tax convexity.

The graph below shows how +/- 2.50% shifts in interest rates affect the prices of bonds A, B, and C. The table below the graph quantifies the change in prices per the shocks. For simplicity’s sake, we assume a constant bond duration in this example.

It is negative tax convexity that should cause investors, all else being equal, to prefer bonds trading at a premium (such as bond C) over those trading at par or a discount. It is also worth noting that the tax convexity plays an additional role in the secondary market for munis. Bonds with prices at or near par will be in less demand than bonds trading well above par if traders anticipate a near term rise in yields that will shift the par bond to a discounted price.


Yields have fallen for the better part of the last thirty years, so muni investors have not had to deal with discounted bonds and their tax implications often. Because of this, many muni investors are likely unaware of negative tax convexity risk. As we highlighted in the table, the gains in price when yields fall are relatively equal for the three bonds but the negative deviation in price in a rising yield environment is meaningful. Given this negative divergence, we recommend that you favor higher coupon/ higher priced munis. If you currently own lower priced munis, it may be worth swapping them for higher priced (higher coupon) bonds.

Addendum: De minimis

The tax code contains a provision for munis called the de minimis rule. This rule establishes the proper tax rate to apply to capital appreciation. The following clip from Charles Schwab’s Bond Insights provides a good understanding of the rule.

The de minimis rule

The de minimis rule says that for bonds purchased at a discount of less than 0.25% for each full year from the time of purchase to maturity, gains resulting from the discount are taxed as capital gains rather than ordinary income. Larger discounts are taxed at the higher income tax rate.

Imagine you wanted to buy a discount muni that matured in five years at $10,000. The de minimis threshold would be $125 (10,000 x 0.25% x five years), putting the dividing line between the tax rates at $9,875 (the par value of $10,000, minus the de minimis threshold of $125).

For example, if you paid $9,900 for that bond, your $100 price gain would be taxed as a capital gain (at the top federal rate of 23.8%, that would be $23.80). If you received a bigger discount and paid $9,500, your $500 price gain would be taxed as ordinary income (at the top federal rate of 39.6%, that would be $198).

It is important to note that some bonds are issued at prices below par. Such bonds, called original issue discount (OID), use the original offering price and not par as the basis to determine capital gains. If you buy a bond with an OID of $98 at a price of $97.50, you will only be subject to $0.50 (the difference between the OID price and the market price) of capital gains or ordinary income tax.

The Worst Place To Be For Bond Investors

Last week, Jeffrey Gundlach of DoubleLine Funds noted in a webcast that investment grade corporate bonds are terrible. There is no way to win with them, he said. As much as half the investment grade universe could be downgraded to junk, and that will take buyers out of the market who can’t buy junk bonds. On some basic ratios, Gundlach argued, a lot of investment grade debt should already be rated junk.

Yesterday, DoubleLine Capital Portfolio Manager Monica Erickson was quoted in a Reuters piece arguing similarly that the investment grade corporate bond market is the worst place to be for bond investors. That part of the market has delivered negative returns this year. For example, the iShares Investment Grade Corporate Bond ETF (LQD) is down 5.50% for the year through November 15. The main investment grade bond index, the Bloomberg Barclay’s US Aggregate Bond Index, is down 2.23% over the same period. This year, investment grade corporates have underperformed lower quality junk bonds.

Interestingly, it’s not that investment grade companies are ready to default, noted Erickson. It’s that the starting yield on investment grade corporates is so low that there is a lot of duration risk in them. That risk reflects how soon or long it takes for an investor to receive their money back in interest and principal payments. If interest rates increase, bonds with higher durations (fewer payments coming back to the investor sooner) suffer more because it takes an investor longer to receive their money back and invest in new prevailing higher rates.

In addition to the higher-than-usual duration risk, investment grade corporates are yielding less over comparable Treasuries than they have previously. Echoing Gundlach’s point, Erickson said BBB-rated (the lowest rung of investment grade) bonds had increased from 20% of the investment grade universe in 2008 to 50% of the universe today. In a downturn, bonds moving from BBB to BB may not find buyers easily since many institutions have prohibitions against owning junk bonds. The BBB-rated universe is around $3 trillion, while the entire junk bond universe is a little over $1 trillion.

The Reuters article said that Erickson favored bank loans over investment grade corporates, since bank loans have a floating rate feature. But they aren’t foolproof either because of their extra dollop of credit risk.

Investors should have a handle on their bond allocations. It may not be a bad time to overweight Treasuries.

Please click here if you have questions about how we manage bond portfolios.

Higher Rates Are Crushing Investors

There is an old saying that proclaims, “it’s not the size of the ship, but the motion of the ocean.” Since this is a family-friendly publication, we will leave it at that. However, the saying has a connotation that is pertinent to the bond market today. Much of the media’s focus on the recent surge in yields has been on the absolute increase in numerical terms. The increase in rates and yields, while important, fails to consider the bigger forces that can inflict pain on bond holders, or sink the ship. When losses accumulate and fear of further losses mount, volatility and other instabilities can arise in the bond market and bleed to other markets, as we are now beginning to see in the equity markets.

Since 1983, fixed-income investors have been able to put their portfolios on autopilot, clip coupons and watch prices rise and yields steadily fall. Despite a few bumps on this long path, which we will detail, yields, have declined gradually from the mid-teens to the low single digits.

In this piece, we discuss the effect that higher yields are having on debt investors today and compare it to prior temporary increases in yield. It is from the view of debt investors that we can better appreciate that the “motion” is much bigger today than years past.

The Motion of the Bond Ocean

As we alluded in the opening, the losses felt by bond investors cannot be calculated based solely on the amount that yields rise. For instance, if someone told you that yields suddenly rose by 1%, you have no way of estimating the dollar losses that entails for any investor or the entire universe of bond holders. For example, an investor holding a 1-month Treasury bill will have a temporary and inconsequential loss of less than 0.10%, but it will be erased when the bill matures next month. Conversely, a holder of a 30-year bond will see the bond’s value drop by approximately 20%. This example demonstrates why a bond’s duration is so important. In addition to duration, it is critical to know the cumulative amount of bonds outstanding to understand the effects of changes in yields or interest rates.

Comparing yield changes to prior periods without respect for duration and amount of debt outstanding is a critical mistake and has led to an under-appreciation of the losses already incurred by the recent rise in rates and the potential future losses if rates increase further. The importance of this analysis comes back to the central premise of an investor’s objective – wealth is most effectively compounded by avoiding large losses. In the end, we care less about the change in interest rates than we do the impact of that change on the value of a portfolio.

Amount of Debt Outstanding: Since 1993 total U.S. debt outstanding, including federal government, municipalities, consumers, and corporations have risen from about $14 trillion to nearly $60 trillion, a 318% increase as graphed below. The table below the graph compares the surge in outstanding debt among the various issuers of debt as well as the nation’s GDP.

Data Courtesy: Bloomberg

Duration of Debt Outstanding: The duration of a bond is a measure of the expected change of a bond’s price for a given change in yield. For example, the U.S. Treasury 10-year note currently has a duration of 8.50, meaning a 1% change in its yield should result in an approximate 8.50% decline in price. Since it quantifies the price change of a bond for a given change in interest rates, it affords a pure measure of risk. For simplicity’s sake, we omit a discussion of convexity, which measures the second order effect of how duration changes as yields change.

Think of duration as a fulcrum as shown below.

As illustrated, an investor of these cash flows would receive the weighted average of the present value of all of the expected cash flows at the three year mark.

Duration is a function of the current level of yields, the nominal coupon of the security, and the time to maturity of the debt issued.

The following graph highlights that the weighted average duration of total U.S. debt outstanding (including Federal, consumer, municipal and corporate) has increased by approximately 1.30 years to almost 6 years since 1993. All else equal, a 1% increase in yields today would result in an approximate 6.0% loss across all U.S. debt versus a 4.7% loss in the early 1990’s.

Data Courtesy: Bloomberg

The table above shows the changes in duration for various classes of fixed-income instruments since 1993. Consumer debt includes mortgages, credit cards and student loans. As an aside, the increase in yields since 2016 has caused the duration of mortgage-backed securities (MBS) to increase by over 3.0 years from 2.25 to 5.30 years.

Duration and Amount of Debt Outstanding

If we combine the duration and debt outstanding charts, we gain a better appreciation for how fixed-income risk borne by investors has steadily increased since 1993. The following graph uses the data above to illustrate the sensitivity of bond investors’ wealth to a 1% change in yields. For this analysis, we use the change in 5-year U.S. Treasury yields as it closely approximates the aggregate duration of the bond universe.

Data Courtesy: Bloomberg

The table below displays the way that the recent uptick in bond yields has been commonly portrayed over the prior few months.

Tables like the one above have been used to imply that the 2.13% increase in the 5-year U.S. Treasury yield since 2016 is relatively insignificant as three times since 1993 the trough to peak yield change has been larger. However, what we fear many investors are missing, is that the change in rates must be contemplated in conjunction with the amount of debt outstanding and the duration (risk) of that debt.

The table below combines these components (yield change, duration, and debt outstanding) to arrive at a proxy for cumulative dollar losses. Note that while yields have risen by only about two-thirds of what was experienced in 1993-1994, the dollar loss associated with the change in yield is currently about three times larger. Said another way, yields would have needed to increase by 9.73% in 1993-1994 to create losses similar to today.

Data Courtesy: Bloomberg


We have often said that our current economic environment is much more sensitive to changes in interest rates because of the growth in debt outstanding since the financial crisis and the recent emergence from the ultra-low interest rate period that crisis produced. Although 5-year yields have only risen by 2.13% from the 2016 lows, losses, as shown above, are accumulating at a faster pace than in years past.

Furthermore, because of the difference between the amount of debt outstanding and the actual currency in the economic system, most of that debt represents leverage. It is beyond the scope of this article to explore those implications but, as illustrated in the table above, rising rates will decidedly reveal the instabilities we fear are embedded in our economy but have yet to fully emerge.

If we are near the peak in interest rates for this cycle, then unrealized losses are likely manageable despite the anxiety they have induced. On the other hand, if we are in the process of a secular change in the direction of rates and they do continue higher, then nearly every fixed-income investor, household, corporation and the government will be adversely impacted.

How’s Your Bond Fund Doing?

It’s been a tough year for bonds so far. Of course, a tough year for bonds can be a tough day for stocks. But investors seem equally disturbed by a 2% loss in bonds as by a 10% or more loss in stocks, so it’s worth looking at how bond funds have weathered the most recent storm. We looked at some of the most popular funds that reside in Morningstar’s intermediate term bond fund category. That category contains funds whose duration is moderate and whose holdings tend to be almost all investment grade, and so those funds tend to be the workhorses of most investors’ portfolios.

Through May 1, the BloombergBarclays US Aggregate is down 2.42%. That’s a total return number, so it includes the difference in price plus interest payments. The Morningstar intermediate term bond fund category average is down 2.11%, a slightly better showing likely owing to the higher corporate bond exposure and slightly lower duration of many funds compared to the Treasury -heavy index.

Duration Hurts

First, all of our selected funds have beaten the index so far this year except for the Western Asset Core Bond fund. The fund’s portfolio doesn’t appear unusual, although it has more of its assets in Agency Pass-Throughs than its peers (35% versus 21%), according to Morningstar. It has nearly 22% of its portfolio in Government bonds, according to Morningstar. Almost all of that is in U.S. Treasuries with a small part scattered in U.S. Agencies and Non-U.S. government debt. Nearly 8% of the fund’s portfolio is in emerging markets debt.

However, the fund’s average effective duration, a measure of interest rate risk, is nearly seven years, and that has likely contributed to its underperformance. No other fund’s duration is over seven, and the next highest three are barely over six. Five of the funds have durations around 4 years, and they’ve tended to hold up better this year.

Things Besides Duration Matter Too

Two funds stand out for bucking the trend of duration dictating performance. First, the Delaware Diversified Income Fund clocks in with a duration of 6.09, but the fund has still been able to eke out a gain over the Morningstar intermediate term category average and the Bloomberg Barclays U.S. Aggregate. This fund has traditionally held a lot of corporate bonds, including more high yield bonds than its peers. Currently the fund has 13% of its portfolio in BB-rated bonds (the highest level of junk or high yield), and those have held up better than more highly rated bonds this year. So the fund’s credit risk has likely helped it in an environment when interest rate risk has inflicted more pain.

Second, PIMCO Total Return has the lowest duration of the group at 3.99 years, but has lost more than the category average. The fund has been lighter in corporates than its peers – 19% versus 30%, according to Morningstar. It also has a significant allocation to what it classifies as “US Government Related,” which, according to PIMCO’s website, could include “nominal and inflation-protected Treasuries, Treasury futures and options, agencies, FDIC-guaranteed and government-guaranteed corporate securities, and interest-rate swaps.” Morningstar has its Agency MBS Pass-Through allocation at 39%, relative to 22% for its peer average. The fund’s most recent quarterly commentary mentions that positions in Agency MBS along with short exposure to the Japanese Yen, short exposure to duration in Japan and Canada, and exposure to high yield corporates” detracted from performance. The fund’s most recent monthly commentary lists non-U.S. rate strategies, positions in non-Agency MBS, and high yield corporates as the largest detractors.

It should be said that the new managers of PIMCO Total Return have done quite well since taking over in the fall of 2014. The new management team has been running the fund for a little over three years now, and, after a choppy start, the fund ranks in the 28th percentile of Morningstar’s intermediate term category for the three-year period ending in April 2018. A quarter’s worth of underperformance shouldn’t discourage any investor from choosing a particular fund or manager, though it’s useful to check in on asset classes and particular funds from time to time.