Legend has it that Frederick Macaulay faced a very difficult math problem in 1938.
He was tasked with determining how long a 50-year bond issued to finance a railroad locomotive would effectively last. You may recall that the milestone “Golden Spike” had been driven in Promontory Point, Utah, in 1869, thus connecting the two coasts via the transcontinental railroad and dramatically accelerating commerce in the United States.
There were uneven monthly principal and interest payments in the 50-year bond, instead of a standard monthly principal and interest payback plan. This made the bond’s useful life calculation very complicated. The 50-year term of the bond was not uncommon at the time as locomotives were very durable and thus were a low risk for a bond of that term. How could one calculate the true useful life (average maturity) of such a long-term, varying principal and interest bond?
Macaulay’s solution was a mathematical concept called duration. By using present value, he discounted each individual principal and interest payment over the 50-year term back to today’s value. Think of this process as reverse compounding, like with interest on a bank CD.
Macaulay’s Duration, as it is known today, is a valuable tool for more accurately measuring the price volatility of a bond (or a portfolio of bonds) and I highly recommend it for your portfolio management process. Duration is almost always shorter than a bond or a portfolio’s average maturity, and actually provides much better information. If and when interest rates return to normal, you will certainly want to know your portfolio’s duration, usually expressed in years. Most bond accounting systems now calculate duration for you each month.
Over the years, I have found that a bond portfolio duration between three and four years has been the sweet spot on the yield curve for banks. You are generally not too short or too long for the highs or lows of interest rate cycles that have occurred over the past 30 years.
There are actually several forms of duration. Modified duration is the most widely used type of duration as it ties directly to the price volatility of a bond or entire portfolio. If interest rates rise 1 percent, you will lose the percentage in market value indicated by your portfolio’s or bond’s duration. This is good information.
For example, the UMB Peer Group’s duration is currently 3.64, so you would lose 3.64 percent of market value. If rates rise 2 percent, you would double the duration to determine the percentage loss in the bond, or 7.28 percent. In theory, if rates rise 3 percent, you would triple the loss to 10.92 percent. I have found that immediate and parallel interest rate shocks that you model may sometimes project more dramatic swings in market value than duration might indicate.
Using duration, you can quickly determine if a paper loss in your portfolio caused by rising interest rates could ever threaten your bank’s capital position. Although falling interest rates recently have created record bond gains, it makes sense to think ahead about the economic effects of higher interest rates some day.
Another type of duration is called effective duration. This calculation uses mathematical models (option adjusted spread) to calculate whether call features or mortgage-backed security prepayments will be triggered, thus altering the cash flows and average life of the portfolio. If you have lots of mortgage backed securities and callable bonds in your portfolio, you may wish to use effective duration to be more precise.
Hopefully, the concept of duration helps you make better investment decisions for your bond portfolio and also better understand the inherent interest rate risk. A simple solution to reduce surprises and create more predictable returns is to keep your portfolio’s average maturity and duration within 12-15 months of each other.
Jeff Goble is executive vice president and managing director, investment banking, at UMB Bank, n.a., Kansas City.
Copyright (c) July 2014. BankNews Media.