# Be Aware and Beware of Interest Rate Risk

April 11, 2013
by
Judy Cox

Category:
Financial Management

In an article[1] in

*The Wall Street Journal*, Federal Reserve (Fed) officials are reported saying that they plan to use monetary policy to keep short-term interest rates low until the rate of unemployment falls to below 6.5%—something they don’t expect to happen until the end of 2015. In the same article,

*The Wall Street Journal*reported on the results of a poll it took in mid-March of 50 private economists showing that they expect more than two more years of “rock bottom” short-term interest rates. So, this seems like a good time to introduce the topic of

*interest rate risk*to those who do not know about it or to reintroduce it to people who do.

*Interest rate risk is the possibility that interest rates will increase, which will result in a decrease in the price of bonds you currently own.*[2]

*How much*

*the decrease will be depends on (a) the coupon rates of the bonds and (b) the length of time until the bonds mature.*

We will look at three examples that illustrate these statements.

**1. An increase in interest rates will cause prices of existing bonds to fall.**

Assume you own a bond worth $1000, and it bears a coupon paying 4%, or ($1000 x .04) = $40 a year.[3] Now, at some later date, you want to sell this bond. Since you have purchased yours, however, interest rates have risen. New issues of $1000 bonds are paying 5%, or $50 a year. No one will be willing to pay you $1000 for your bond which is paying 4% or $40. You can sell it, but you will have to take a price lower than $1000. How much lower? Well, you can use trial and error to find out. If you offered your bond at $900, what would the current yield be? You divide the dollar amount of the coupon by the bond price to get the current yield.

Current yield (CY) = (coupon/current bond price) x 100 = ($40/$900) x 100 = 4.44%

At a price of $900 for the bond, the current yield would be 4.44%. That is still not good enough to make a sale when other bonds are yielding 5%. It turns out that you will have to lower your price all the way to $800.[4] At that price, the current yield will be ($40/$800) x 100 = 5% and if you sell, you will have a loss of $1000 – 800 = $200. Not a good investment outcome! [5]

For practice, let’s look at the

*. If new bonds are issued at an interest rate of 3%, the coupon will be $30 a year, and you will be able to sell your bond for more than the $1000 you paid for it. When the price of your bond is $1000, the $40 coupon makes your bond more attractive and people will offer you more than $1000 to get the higher coupon. So, how high does the price of your bond have to rise in order for a $40 payment to produce a current yield of 3%? Whoever yelled “$1333.33” from the back of the room is correct.*

**opposite situation—a decrease in interest rates will cause bond prices to increase**CY = ($40/$1333.33) x 100 = 3%

Lower interest rates will produce gains if you sell your bonds. Here the gain would be $1333.33 – 1000 = $333.33.

*How does this relationship between a change in interest rates and a change in bond prices apply to the current economic situation?*

Currently rates are incredibly low and have been for the last couple years. During that time, many people have been saying: “Interest rates can’t go any lower,” but they have. On April 9, 2013, the yield on a government bond with two years to maturity was 0.24%, and the yield on a government bond with 20 years to maturitiy was 2.57%. A year ago, the yield on a bond "due" (for payment) in two years was 0.32%, and the yield on a bond due in 20 years was 2.82%. However, at some point, interest rates will start to go up. That may not happen until 2015, if you believe that the Federal Reserve will be able to keep rates low with its monetary policy.

At that point, the value of the bonds you are holding will fall.

**2. A given change in the interest rate has a bigger effect on the price of a bond with a lower coupon rate than one with a higher rate.**

Let’s take your $1000 bond with a coupon of $40 (4% current yield) and see how the price changes if interest rates increase to 4.2%. New $1000 bonds will have a coupon of $42 when the rate increases to 4.2%, and that is more attractive than the $40 coupon on your bond. To sell the bond with the $40 coupon, the price will have to fall until the current yield is 4.2%.

Current yield (CY) = (coupon/current bond price) x 100 = ($40/$952.38) x 100 = 4.2%

The bond price will have to fall to $952.38, producing a loss of $1000 – 952.38 = $47.62

But what if you are living in a world of low interest rates, as we have now, and the bond for which you paid $1000 has a coupon of $10 for a current yield of 1%? How much would its price have to change if the interest rate increased by 0.2% to 1.2%? In order for this bond to attract buyers, its price will have to fall until the $10 coupon produces a yield of 1.2%. The price of the bond will have to fall to $833.33.

CY = ($10/$833.33) x 100 = 1.2%

In this case, the loss, if you sell the bond, is $1000 – 833.33 = $166.67 compared to a $47.62 loss from the same 0.2% increase when the rate went from 4% to 4.2%. The loss from an equal increase in rates (0.2% in this example) will be greater for the bond with the lower coupon rate.

*How does this relationship between a change in interest rates and a change in bond prices apply to the current economic situation?*

Because interest rates are currently low, a small change (0.2% in our example) can have a surprising big effect on the price of bonds. As we saw in the first example, an increase in interest rates will always cause the price of bonds to decrease. But, five or six years ago, when interest rates were in the range of 3% to 5%, such a small change had a relatively small negative effect on bond prices. Now, when interest rates are so low, the decrease in price (your loss) is much larger—$166.67 in this example, compared to $47.62.

**3. The fall in the price of a bond with a longer maturity (the time the bondholder has to wait to get back the principal of $1000 that was originally invested) will (almost always) be greater than the fall in the price of a bond with a shorter maturity and the same coupon rate.**

The slickest way to explain this point is to use present value or “time value of money” analysis. However, since I doubt that all the readers have taken introductory microeconomics, let me try the following approach. [6]

Except for a brief mention in footnote 5, I haven’t talked about the fact that bonds “mature.” At some date (you know what that date is when you purchase the bond), the borrower pays back the amount borrowed, $1000 in this case, to the owner of the bond on the date of maturity. So, even though that bond may have previously decreased in value because interest rates increased, eventually this “loss” is recouped.

Let’s say that the interest rate has risen to 3% from 1%. A $1000 bond with a coupon of $10 that matures in one year will have to drop in price to $980.58, or let's say $980, to provide a "yield to maturity" of 3%. A bond of $1000 with a coupon of $10 that matures in 20 years will have to sell for $702 to provide the same 3% yield to maturity. The reasoning is that, in the first example, the $20 discount ($1000 – 980) over one year is sufficient, along with the coupon of $10, to bring the yield to maturity up to 3%. On the bond that does not mature for 20 years, however, a much bigger drop in price, $298 ($1000 – 702), is required because the $298 gain is recouped over a much longer time period.

**Putting It All Together**

ANY increase in interest rates is going to cause the price of bonds to fall. The amount of the decrease in price for a given increase in interest rates will be greater when the coupon rate on the bonds is lower. The amount of the decrease in the price of bonds will also be greater the longer the time until the bond matures.

*In the future, although maybe not for two years or so, we expect interest rates to increase and bond prices to fall. The amount of the fall will be “relatively large” because current interest rates are so low. If you hold longer term bonds, perhaps because you are looking for a higher yield, the fall will be larger than if you hold short term bonds.*

[1] “Easy Money Era a Long Game for Fed,” by Jon Hilsenrath,

*The Wall Street Journal*, March 7, 2013.

[2] The discussion will apply to any kind of bond: corporate, municipal, or U.S. government and its agencies. Remember, however, that you can only invest in bonds for your local government that are on the list of Eligible Investments for Public Funds in the State of Washington.

[3] We use the term “coupon” to denote the interest payment, even though there are no longer any coupons. Back in the “olden days,” when bonds were paper rather than electronic documents, they had coupons attached to them, each one of which was worth a certain number of dollars on a particular payment date (usually twice a year rather that once a year as shown in these examples). One cut the coupon off the bond and presented it to the bank for payment.

[4] Those who remember their algebra will realize that there is a formula that works better than trial and error.

Rearranging the terms in the above equation to solve for “bond price,” one gets:

Bond price = coupon/current yield = $40/.05 = $800.

[5] Note that the current yield does not take into account the fact that, at some date in the future, your bond will “mature,” and the borrower will pay back to you (or whoever owns the bond at the time) the “par” value (also called “principal” or “face value”) of $1000. The rate that takes that factor into account, in addition to the interest payments, is called the “yield to maturity.” But “current yield” is a good concept to use for these examples because the calculations are simpler.

[6] This explanation is based on that given in O’Hara, Neil.

*The Fundamentals of Municipal Bonds.*6

^{th}ed. Hoboken NJ: John Wiley and Sons, 2012. 140.

If you are familiar with the concept of

*present value*or the “time value of money” and want a little “proof” of this statement, just email me at jcox@mrsc.org.

*MRSC is a private nonprofit organization serving local governments in Washington State. Eligible government agencies in Washington State may use our free, one-on-one Ask MRSC service to get answers to legal, policy, or financial questions.*