# Estimating Bond Losses If Interest Rates Change

If I own bonds and am concerned about rates changing, can I estimate how much the price of my bond will change for a given interest rate change?

Yes, you can. The key to the estimate is the Macaulay Bond Duration.  It is not hard to calculate but a little tedious.

The idea behind it is that a bond is actually a collection of promises.  There are as many little promises as there are interest payments left and there is one bigger promise at maturity being the return of the face value of the bond. The predent value of each payment is different because it must be time adjusted.  For example, a \$100 payment a year from now with a required interest return of 5% is worth \$95.24 today.  The 2-year out payment is worth \$90.70.  The \$1,000 principle 30 years from now is worth just \$231 today.

The present value, given the bond’s interest rate, its maturity, its face value and my required yield, is the total of all the individual promises.

I suppose you could calculate all of them for the required rate today and then calculate them all again for some different rate, but that is difficult.  Montreal economist Frederick Macaulay provided a short cut in the 1930s.  The Macaulay Bond Duration is a way to calculate how long it takes to get your money back using weighted present value.

If market rates go up,  the present value of an existing bond will go down.  People want more return and the bond’s promises are fixed, so people will pay less for them.  The Macaulay duration will give you an estimate of how much the value of your bond will change.  The estimated change is the duration times the rate change.

The Macaulay duration for \$1,000 bond with a 30 year maturity issued at 4% and trading at \$1,000 is 18.  The estimate then is that if required rates change 1% higher, the principle value of the bond will change by 18% (duration times change.)  The estimate is usually a little high with large rate changes.  Actual is about 15.5%.

This is a case where precision adds little real value.  If the estimate is I will lose 18% and actual can be proven to be 15.5% my reaction will be the same.  John Hatishita’s law.  “In time of danger the best defense is to be somewhere else.” Small differences in comparative danger is irrelevant.

The summary is simple.

1. Long maturity bonds have a higher duration so they will change more for a given rate change.  Compared to the 30 year bond above, a 5 year bond’s duration is 4.6.  A 1% rate change would have just a quarter the effect on your portfolio.  Long bonds are riskier in terms of their market value.
2. A bond with a higher interest rate has a lower duration for any given maturity time.  In our 30 year bond example, if the interest rate on the bond was 10% its duration would drop from 18 to about 15.

It is reasonable to assume that rates will not stay low forever, so your bond holdings are exposed to loss, we just don’t know when.  How much depends on the configuration of your portfolio.

If you consider the market value of your bonds in your portfolio to be important, (if you intend to hold them to maturity you might not,) it is time to asses your exposure.  Be a little aware of tax consequences.  Capital losses on your bonds may take a long time to become deductible. Talk to your tax advisors.

Simple rule of thumb. Be the first to panic, then be somewhere else.

Don Shaughnessy arranges life insurance for people who understand the value of a life insured estate. He can be reached at The Protectors Group, a large insurance, employee benefits, and investment agency in Peterborough, Ontario.  In previous careers, he has been a partner in a large international public accounting firm, CEO of a software start-up, a partner in an energy management system importer, and briefly in the restaurant business.