Duration is a measure that reflects how a bond acts in response to changes in prevailing interest rates. Frederick Macaulay first introduced the concept of bond price volatility by measuring the length to maturity and fixed cash flows to be received over time. Here is his formula:
Mr. Patrilack, my high school calculus teacher, would put a formula like this up on the chalkboard and say “It’s cake, c’mon it’s cake!” Once I picked my jaw up from my desk, I would settle in and try to learn the formula components. You can forget Macaulay’s formula and just remember this:
The most volatile bonds are long-term, low-rated zero coupon bonds.
If you buy a bond and hold it to maturity, the yield to maturity is locked-in. That aside, it is important to know that there is an inverse relationship between the price of bonds and prevailing interest rates. If rates rise, the market price of outstanding bonds drops, and if rates fall, the market price of outstanding bonds rise. It makes sense intuitively, because if you buy a new bond today and then rates plummet, your bond becomes more valuable because investors can no longer get the higher rate that you locked in. Conversely, if you buy a bond and rate rise, the value of your bond drops because now investors can find higher rates. I use the image of a see-saw to remember this concept with interest rates on one side and bond prices on the other:
Interest rate have been hovering at very low levels for the past few years, and investors want to know what affect rising rates will have on bond holdings. Let’s look at two examples that will show you a bond that will have a very low duration or price volatility, versus one that will fluctuate more dramatically as interest rates change:
CITY OF GREENVILLE, SOUTH CAROLINA GENERAL OBLIGATION BOND 3% DUE 04/01/2014 AAA RATED CURRENT PRICE 103.00 0R $1,030 PER $1,000 FACE VALUE
VIRGINIA TOBACCO SETTLEMENT FINANCING CORP ASSET BACKED 0% DUE 06/01/2047 CCC+ RATED CURRENT PRICE 9.586 OR $95.86 PER $1,000 FACE VALUE
The City of Greenville rating was upgraded to AAA in 2011, the highest attainable level. This bond is very short-term, has a high rating, and pays coupon interest. Any changes in interest rates would have little affect on the price of this issue because is a short-term, high quality bond.
In the late 1990’s, some of the major tobacco companies and most U.S. states signed a settlement agreement to resolve ongoing lawsuits and disputes over costs associated with illnesses caused by smoking. As one part of the settlement, the tobacco companies agreed to make payments to help the states cover Medicaid costs for patients with smoking related illnesses. Virginia is one of many states that issued bonds securitized by the future payments to be received from the tobacco companies. These bonds have faced trouble for some time now, because the payment calculations are based on a per unit sold formula, and smoking rates have decreased steadily since the settlement. The payments have been shrinking, and now many states do not have money coming in to pay back the holders of the tobacco municipal bonds. Unlike the City of Greenville SC bond, the Virginia tobacco bond has a very long maturity date, only pays interest at maturity, and has a low credit rating of CCC+. This value of this bond will fluctuate wildly in a changing interest rate environment.
In summary, please feel free to solve for Macaulay’s formula on your bonds, and if you do I would love to see the math and will even post it to the site! For the rest of us, we will stick to common sense and know that the least volatile bonds have high credit ratings, good coupon rates and short-term maturities.
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