Bond Theory From the Bond Squad

bondsquadwebbannerOur focus this year has been on economic data, fiscal and monetary policy and financial market conditions. However, we have received many questions from readers regarding the callability and price sensitivity of fixed income securities. As such, the focus of this week’s “In the Trenches” report is bond theory.

Back to School

Let’s start off with definitions of common bond terminology. Definitions provided by Bloomberg and Investopedia (no need to reinvent the wheel) followed by our commentary:

To see a list of high yielding CDs go here.

Duration: Also known as MacCauley’s duration. The weighted average maturity of the security’s cash flows, where the present values of the cash flows serve as the weights. The greater the duration of a security, the greater its percentage price volatility.

Bond Squad: This is duration in its simplest form. When one looks up the duration of a bond or a portfolio of bonds, it is the MacCauley calculation which is usually provided.

Modified Duration: The percentage price change of a security for a given change in yield. The higher the modified duration of a security, the higher its risk. Ad/ModDuration = [duration / {1 + (IRR/M)}]; where IRR is the internal rate of return and M is the number of compounding periods per year.

Bond Squad: This is the duration calculation which is of interest to most financial advisors and investors as it measures the price volatility of a bond or bond portfolio versus moves in interest rates. However, the difference between the Modified Duration and MacCauley’s duration of a bond or portfolio is usually negligible.

Effective Duration: A duration calculation for bonds with embedded options. Effective duration takes into account that expected cash flows will fluctuate as interest rates change.

Investopedia Definition: Effective duration can be estimated using modified duration if the bond with embedded options behaves like an option-free bond. This behavior occurs when exercise of the embedded option would offer the investor no benefit. As such, the security’s cash flows cannot be expected to change given a change in yield. For example, if existing interest rates were 10% and a callable bond was paying a coupon of 6%, the callable bond would behave like an option-free bond because it would not( be) optimal for the company to call the bonds and re-issue them at a higher interest rate.

Bond Squad: Effective Duration calculations attempt to clarify something that tends to vex advisors and investors, the effects of a call (or put) option on a bond or preferred security. As the Investopedia definition states, if interest rates available to an issuer were higher than the coupon on an outstanding callable bond, that bond would behave similarly as a non- callable bond. The call option would have basically no value to the issuer.

Convexity: The second derivative of a security’s price with respect to its yield, divided by the security’s price. A security exhibits positive convexity when its price rises more for a downward move in its yield than its price declines for an equal upward move in its yield.

Bond Squad: Convexity is not discussed much among financial advisors and investors, but it is a topic which affects everyone who participates in callable securities, such as preferred stocks, hybrids and callable bonds. Callable securities tend to be negatively convexed. By this we mean: When rates rise, prices of callable securities tend to fall similarly as non-callable securities with similar maturities. However, when interest rates fall, the potential price increase is limited by the call option.

Let’s tie this all together.

I keep the ends out for the tie that binds (Bond Squad walks the line)

Investors and advisors (particularly those who have entered the business during the past decade, a time when capital markets training of new advisors was de-emphasized), often confuse duration with maturity. Although the maturity of a bond or average maturity of a portfolio will affect duration calculations, it is not the sole determinant factor. We must consider coupon/average coupon as well. Remember the formula for Modified Duration (the measure of a bond’s price volatility) is:

“ [duration / {1 + (IRR/M)}]; where IRR is the internal rate of return and M is the number of compounding periods per year.”

In other words, the larger and more frequent a bond’s coupon payments, the shorter its duration. The shorter its duration the lower its price sensitivity to rising interest rates for a given maturity. This is why prices of bonds and preferreds with large coupons tend to hold up better in rising rate environments than their lower coupon brethren. A the duration of a zero coupon bond matches its maturity as it provides no timely coupon payments (cash flows) which can be reinvested.

Recently, we reviewed a portfolio with an average maturity of 13.56 years, an effective maturity (when call options are considered) of 8.45 years, but the modified duration of the portfolio is just 6.45 years. Even the option-adjusted duration (effective duration) is only 7.10 years. This in spite of only having only 15% of the portfolio invested in bonds with maturities of seven years and in. How was this possible? The relatively-low portfolio duration was the result of high coupons and bond callability. The average coupon of the portfolio is 4.92% with some of the longer-dated bonds sporting coupons of between 6.00% and 8.00%. We should also mention that about half the portfolio consists of municipal bonds, making the after tax coupons and average yield somewhat higher. Also helping to keep the effective duration down is the combination of call options and high coupons, which increase the odds that a bond might be called, even after a moderate rise in rates. In this case, a callable bond with a so-called “fat” coupon tends to behave like a non-callable bond of similar quality with a maturity matching the callable bonds “worst” (lowest yield) call date. For years we have listened to theories of when and if a security might be called put forth by both financial professionals and investors. We have heard theories which have opined that whether a bond is or isn’t called depends on the difference between “Libor and the long bond” or “issuers call in securities and issue replacements to keep investors interested.” However, it truly comes down to one factor: Is the outstanding callable debt expensive?

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The Cost of Everything

When considering whether or not a callable fixed income security is likely to be called in, we must consider whether or not it is expensive versus where new debt could be issued or, in the case of a corporation seeking to reduce its outstanding debt, versus other debt issued by that corporation. It really is that simple. Just as you would refinance your home mortgage when you can save a sufficient amount of money or payoff your debt carrying the highest interest rate first, corporations have a similar viewpoint. Even the Investopedia’s definition of effective duration alludes to this when it states:

“(I)f existing interest rates were 10% and a callable bond was paying a coupon of 6%, the callable bond would behave like an option-free bond because it would not (be)optimal for the company to call the bonds and re-issue the at a higher interest rate.”

What Investopedia is saying is: A callable bond with a coupon of 6.00% is unlikely to be called if the debt must be refinanced at 10.00%. As such, the 6.00% bond would trade like a non-callable bond to its maturity date.

A 5.00% callable bond would be very unlikely to be called in a 6.00% world. It is for this reason that we are not sanguine on perpetual preferreds with low fixed coupons (6.00% and lower). A 100 basis point rise in long-term rates could result in a 16%+ decline of the price of these low coupon perpetual preferreds. Keep in mind that a 100 basis point rise in long-term rates would only put the yield of the 10-year U.S. Treasury at about 3.20% and the yield of the 30-year government bond at about 3.95%. We are not talking about a return to the “old normal” to see perpetual preferreds get “hit.” Another problem with perpetual preferreds is that they are perpetual. As there is no maturity, duration volatility potential never lessens as it would with a security with a stated maturity. A security with a stated maturity rolls in on the yield curve every year until it matures, thereby shedding duration-related volatility each year.

Double Trouble

Some investors have tried to hedge out duration risk (or take advantage of rising rates) by purchasing floating rate or fixed-to-float securities linked to Libor rates, with the idea that they would at least “always” price near par and could offer increasing income streams as rates rise. However, many (most) Libor- adjustable preferreds are both callable and perpetual (or have very long maturities). This presents two potential problems for investors.

The first problem is that coupons of Libor floaters adjust versus a short-term benchmark (such as the three-month USD Libor rate) and, due to their perpetual or long- dated nature, can also be subject to movements of long-term rates.

The second problem is that because these securities tend to be callable, issuers might choose to call in a floater or a fixed-to- float rather than pay a higher coupon.

One might ask: If rates are higher, why would a company call in a floater when the coupon increased? Wouldn’t the company have to refinance the floating rate debt at higher rates as well? Not necessarily. Remember, most of these Libor floaters have long-dated maturities or are perpetual. This means that there is a disconnect between interest rates of which coupons adjust and interest rates off which these long- dated/perpetual securities might trade.

In a scenario in which the yield curve is positively-sloped (short-term rates are lower than long-term rates), an issuer is unlikely to call in a Libor floater as it would have to pay a higher interest rate for long-term fixed-rate debt than it is paying on the Libor floater. This is “advantage issuer.” For the investor, the scenario is not as desirable. Depending on the floater,s spread over Libor, one might own a floater paying a low coupon (say 5.00%) when long-term fixed-rate corporate debt and preferreds offer yields of 7.00%. In this scenario, the floater could trade at a significant discount to par. It is for this reason that Libor floaters tend to perform better in a curve- flattening scenario.

However, the benefits of a flattening (or inverted) yield curve also have limits. Let’s say one owns a Libor floater during a time of Fed tightening. In this scenario, the yield curve usually flattens as the Fed raises short-term rates in an effort to stabilize growth and manage inflation. Ebbing inflation pressures tend to slow, stop and eventually reverse the rise of long-term rates, thus the yield curve flattens. In this scenario the Libor floater should perform quite well. Rising short-term rates and slowing, stable or falling long-term rates tend to be positive for bond prices (higher coupons + stable yields=higher prices). However here is where benefits become limited.

Just as a call option allows an issuer to call in a fixed-rate security when it becomes expensive versus prevailing borrowing costs, the call option on the Libor floater allows the issuer to call in the floater before its coupon rises too far for comfort. The issuer might either refinance at a fixed rate or to simply retire the debt if the floater represents one of the costlier outstanding public debt issues.

Since the yield curve tends to be positively-sloped most of the time, the interest rate volatility risk can remain present even when rates are rising. It is for this reason that we prefer floaters with wide (300 basis points or more) spreads over Libor. Whereas the yield curve would have to become very flat before a Libor floater with a +50 basis point spread would become callable, a floater with a 300 basis point spread over Libor might be called if the curve is still fairly positively sloped. Why would we want a floater which is more likely to be called away from us? Price stability. If the goal of a floater is to provide a cushion versus interest rates (duration risk) then one would want a security which is more likely to be called, just as one would want a high-coupon fixed-rate callable bond or preferred to reduce duration.

In recent years, floaters have been sold as way to cushion against rising rates with little regard paid to the actual floating rate features.

However, investors and advisors are beginning to take notice as floaters and fixed-to-float securities with tight Libor spreads tend to trade at discounts while such securities with wide Libor coupon spreads tend to trade at premiums to par at the present time. This is the market’s way of telling investors and advisors which floaters/fixed-to-floats are more valuable in its opinion.

Change the State of Play

Readers need to understand than most options found within fixed income securities are designed to benefit the issuer. It is for this reason that fixed income market participants will demand extra yield in return for giving issuers such optionality. If one understands this, one can use this to one’s advantage. For instance: An investor who truly wants a long- dated bond might be able to pick up extra yield to maturity by purchasing a bond with a fairly low coupon. Although a callable bond with a low coupon is unlikely to be called, there is always the possibility that it is retired early. For this reason, such a bond might offer a somewhat higher yield than a non-callable bond with similar maturity. It should be understood that a low-coupon long-dated callable bond carries with it the potential much duration-related volatility. For investors seeking attractive returns without wanting to extend far out on the yield curve, they might consider investing in a high-coupon bond with a long maturity and a short or medium term call date. The high coupon makes a call more likely to occur, but it is not a certainty. It is possible that the bond is not called and remains outstanding until maturity. For this reason, investors again wish to be compensated for the uncertainty. This is represented in terms of a yield to call which might be higher than the yield to maturity of a non-callable bond with a maturity similar to the callable bond’s worst call date. In essence, an issuer purchases optionality from investors. Understanding this can make fixed income investing less daunting.

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We hope that you have found this discussion of bond theory helpful. Please keep in mind that this is a discussion of bond theory fundamentals. We do not expect anyone who reads this report to become a fixed income expert. That is what Bond Squad is for. We live and breathe fixed income every day and offer professional fixed income portfolio management on an SMA basis using individual securities. All portfolios are custom-built for the needs of specific investors (households or institutions). Please contact us for more information or to ask questions regarding fixed income. As always, share with your colleagues what you have learned from this report and spread the word about Bond Squad.

By Thomas Byrne – Director of Fixed Income – Investment Consultant

thomas bryneThomas Byrne brings 26 years of financial services experience to Wealth Strategies & Management LLC. He spent the last 23 years as Director of Taxable Fixed Income for Citigroup, Inc. and predecessor firms in New York, NY. During the course of his long fixed income career, Mr. Byrne was responsible for trading preferred stock, corporate bonds, mortgage backed securities, government debt, international debt and convertible bonds. Mr. Byrne was also responsible for marketing, sales, strategy and market commentary within the taxable fixed income markets.


  • November 2012 – Present, Wealth Strategies & Management LLC, Stroudsburg PA
  • December 2011 – November 2012 – Bond Squad, Kunkletown, PA
  • April 1988 – December 2011, Citigroup and predecessor firms, New York, NY
  • June 1986 – March 1988 – E.F. Hutton, New York, NY

Thomas Byrne
Director of Fixed Income
Wealth Strategies & Management LLC
570-424-1555 Office
570-234-6350 Cell

Twitter: @Bond_Squad




All trading carries risk. Views expressed are those of the writers only. Past performance is no guarantee of future results. The opinions expressed in this Site do not constitute investment advice and independent financial advice should be sought where appropriate. This website is free for you to use but we may receive commission from the companies we feature on this site.

Thomas Byrne

Thomas Byrne serves ad the Director of Fixed Income for Wealth Strategies Management LLC. Thomas brings 26 years of financial services experience to Wealth Strategies & Management LLC. He spent the last 23 years as Director of Taxable Fixed Income for Citigroup, Inc. and predecessor firms in New York, NY. During the course of his long fixed income career, Mr. Byrne was responsible for trading preferred stock, corporate bonds, mortgage backed securities, government debt, international debt and convertible bonds. Mr. Byrne was also responsible for marketing, sales, strategy and market commentary within the taxable fixed income markets. High yield/junk bonds (grade BB or below) are not investment grade securities, and are subject to higher interest rate, credit, and liquidity risks than those graded BBB and above. They generally should be part of a diversified portfolio for sophisticated investors. The opinions voiced in this material are for general information only and are not intended to provide specific advice or recommendations for any individual. To determine which investment(s) may be appropriate for you, consult your financial advisor prior to investing. All performance referenced is historical and is no guarantee of future results. All indices are unmanaged and may not be invested into directly.
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