The Duration Station - Coupon Matters

Duration is a term thrown about quite carelessly by investment professionals when discussing fixed income investing. Duration is thought of as a measure of interest rate risk, but it is more involved than many investors realize. There are several components which go into determining the duration of a bond, maturity is only one factor. Cash flows play a major role in determining the duration of a bond. In fact, Macaulay’s Duration is defined as being the weighted average maturity of a bond’s cash flows. Modified Duration measures price sensitivity. However, when the duration of a bond is calculated using both Macaulay’s Duration and Modified Duration, the results are very similar. As an example, we will use the current 10-year U.S. Treasury Note (1.625% due 8/15/22). At a closing price of 99-6/32s (YTM: 1.716%) the Modified Duration of the 1.625% due 8/15/22 Treasury note is 8.97. The Macaulay’s Duration calculation gives us a duration calculation of 9.04. The results are fairly close. Now let’s compare this to the 7.25% due 8/15/22 government bond. The 7.25% due 8/15/22 government bond was issued in 1992 as a 30-year Government bond, but since it only has 10-years remaining and, other than its coupon, is identical to the current 10-year note, one would expect its duration to be similar to that of the current 10-year. However, when we run the duration calculations the results are quite different. At a closing price of 151-5/32s (YTM: 1.582%) the Modified Duration calculation gives us a result of 7.57. The Macaulay’s Duration calculation gives us a similar answer of 7.57. Why the big difference in the duration (almost 1.5 years) between two U.S. government securities of with the exact same maturities? The answer is simple: Cash flows. More money is being returned on a timely basis. The lower the coupon, the more a bond’s total return is paid at maturity. Some teachers of bond concepts use a fulcrum to describe this. With a zero coupon bond, the fulcrum is placed at maturity. The higher the coupon, the closer the fulcrum moves to the center of the hypothetical beam carrying the total return of principal and interest. A zero-coupon bond has a duration equal (or almost equal) to its maturity, therefore it is the most sensitive to interest rate moves than bonds which pay investors on a timely basis. A case in point is the U.S. Treasury Strip due 8/15/22. At a closing price of 83-26/32s (YTM: 1.814%), its Modified Duration is 9.77. Macaulay’s Duration gives us a result of 9.69. How does this translate into price movement? Let’s run the numbers. If let’s assume a 100 basis point rise in 10-year rates. The yield of the 1.625% due 8/15/22 Treasury note would rise to 2.716%. The price will have fallen to 90.685 from 99-6/32s. This is a drop of more than nine points. The price decline for the 7.25% due 8/15/22 is going to surprise you at first, but it will soon make sense. Moving its yield to 2.582% from 1.582% results in a price decline to 140.102 from 151-5/32s, by now you must be saying to yourself: “I thought the higher coupon was supposed to make a bond less volatile, but the price dropped more than 11 points versus just over nine points for the current 10-year. What investors must keep in mind is that fixed income investing is all about percentages. The 1.625% due 8/15/22 Treasury note experiences a price drop of about 8.6%. However, the 7.25% due 8/15/22 experienced a price decline of 7.4%. Do these numbers look familiar? They should as they are similar to the Modified Duration calculations of 8.97 and 7.57, respectively. This is where the percentage move in price comes into play when considering duration. What about our zero-coupon Treasury Strip due 8/15/22? Moving its yield up 100 basis points from 1.814% to 2.814% results in a price decline from 83-26/32s to 76.093, a decline of 9.3%, again similar to Modified Duration (9.69). The response to our analysis might be: I (or my client) only care about the price drop in dollar terms, not in terms of percentages. Alright, let’s discuss dollars. For this exercise, we will give or fictitious investor $100,000. Let’s see what happens in dollar terms. For $100,000 our investor can buy the following: 100m of the 1.625% due 8/15/22 65m of the 7.25% due 8/15/22 119m of the strips 0.00% due 8/15/22. Now let’s apply the price declines: T 1.625% due 8/15/22 = -9 points. 9 x 100m = $9,000. T 7.25% due 8/15/22 = -11 points. 11 x 65m = $7,150. S 0.00% due 8/15/22 = -7.75 points. 7.75 x 119m = $9,225.50. In dollar terms, the bonds with the lowest coupons and highest durations experienced the biggest dollar losses. One can make the case for the lower coupon bonds if one is willing to hold it until maturity. One will earn a higher rate of return for the lower coupon bonds 1.814% for the strips, 1.716% for the 1.625% due 8/15/22 and only 1.582% for the 7.25% due 8/15/22. However, the investors who own the 7.25% due 8/15/22 bonds will be able to reinvest cash flows on a timely basis. In a rising rate environment this can be most beneficial. This is why investors are willing to accept a lower yield for high-coupon bonds and/or demand higher yields for instruments with inferior timely cash flows. Interestingly, in retail-oriented securities, such as preferred stocks, often times we find the opposite to be true. In the preferred market, high-coupon preferreds often trade at higher yields as retail investors are often averse to paying premiums. This is the exact opposite of what happens in the institutionally-driven Treasury market, especially when the mostly likely path of interest rates is higher. Other factors can come into play in determining a security’s duration. Optionality is one. A call feature can lower the duration of a bond if a call becomes “in the money” (I.E. the security is likely to be called for economic reasons advantageous for the issuer). If a callable bond is likely to be called, its duration calculation would take that into account and its volatility would be less. However, if a call was out of the money (rates, at which the issuer could refinance, were equal to or higher than the coupon on the bond), the duration of the bond in question would be similar to that of a non-callable bond of a similar maturity from the same issuer. This leads us to the topic of convexity. As we are risking making this report too wordy and risk losing the attention of our readers, we will give a simple laymen’s explanation of convexity. Convexity compares the price movement of a bond when rates move up to when rates move down the same amount. A bond that experiences a greater downward price move when rates rise than it does upward price movement when rates decline is said to be “negatively convexed.” Callable bonds tend to be negatively convexed, especially as its first call date approaches, as the upward price movement due to falling rates is limited by its call price. If rates fall sufficiently for the issuer to call in the bond and refinance at a lower rate, it is likely to do so. Rather than the price of a callable bond rallying to where its similar non-callable brethren are trading, it will stop rising when it approaches its call price. However when rates rise and the call is “out of the money,” its price decline should be similar to similar non-callable bonds. Remember, call features on a bond are an embedded option designed to favor the issuer. This is not dissimilar to the advantage many home mortgage borrowers gain when they have the ability to refinance without penalty. We will leave off here for this week. Next week we will discuss how duration is works and is assessed within a portfolio. This discussion of duration and convexity and next week’s discussion of duration within a portfolio, as well as portfolio construction, was due intelligent questions asked by a Bond Squad subscriber. Whether building your own portfolios or having an outside manager doing that work for you, it is important that both investors and advisors understand how bonds work and how portfolios can and should be constructed (portfolio duration and bond fund duration must be looked upon differently than bond duration). The questions asked by our subscriber come at a fortuitous time for Bond Squad as we are in the final stages of negotiations to enter the fixed income portfolio management business. We will keep subscribers updated as to what is happening to that end. We do not foresee very many changes to how we serve or loyal customers. Tom Byrne tom@bond-squad.com. www.bond-squad.com www.mksense.blogspot.com 347-927-7823 Twitter: @Bond_Squad Disclaimer: The opinions expressed in this publication are those of the author. They are not, nor should they be considered solicitations to purchase or sell securities.