# A Look at Total Return: Bonds

### October 2013

A while back we took a look at the concept of total return as it applies to stock returns (see April 2013). We can apply a similar analysis to the fixed income market and the total return of bonds.

To review, the total return of any asset is the income it generates plus its change in price, or:

Total Return = Income +/– Change in Price

For a bond, the income component consists of the interest, or coupon, payments received. So for bonds, the above expression becomes:

Total Return = Interest Payments +/– Change in Price

#### Bonds, You’re So Sensitive

While a change in interest rates generally influences the pricing of all stock and bonds, for a fixed rate bond, it is the most important factor. One key reason for this is that while a stock can in theory, last forever, a bond has a limited life. The fact that a bond matures has meaningful impact on its price throughout the course of its life. For this reason, analysts use a factor called *duration* to measure the sensitivity of a bond’s price to changes in interest rates.

Duration, stated in years, takes into account the periodic interest payments received on a bond and the return of principal at maturity. The relationship between the change in price, duration, and the change in interest rate can be expressed as:

% Change in Price = [Duration x (–Change in Interest Rate)]

Note the negative sign applied to the change in rate in the above expression. This reflects the *inverse relationship* between changes in interest rates and the change in bond price. That is, if interest rates rise, a bond’s price falls and conversely if rates fall a bond’s price rises. Given this relationship we can recast our total return expression as:

Total Return = Interest Payments + [Duration x (–Change in Rate)]

#### An Example

A simple example may help illustrate the implication of these relationships on total return for a bond investor in today’s environment.

Perhaps the most “vanilla” and widely held bonds in the fixed income investment world are U.S. Treasury Notes. The ten-year note is widely used as a benchmark for other securities such as corporate bonds and mortgage-backed bonds. The current ten-year note carries an interest rate of 2.5 % and has a duration of 8.7. Using these parameters in our total return expression results in the following:

Total Return = 2.5% + [8.7 x (–Change in Rate)]

Using this formula, we can assess the total return of this note given different changes in interest rates. The table below shows the total return of this ten-year Treasury note under various interest rate changes.

##### Even a relatively small increase in rate results in a negative total return!

The figures above show the inverse relationship between changes in interest rate and the total return.

The current ten-year Treasury rate of 2.50% is near historic lows and is arguably artificially held down by the extraordinary monetary policy employed by the Federal Reserve. With nominal GDP running at around 4%, many models suggest that in a “normalized” monetary policy environment the ten-year Treasury rate should be at or above that level. From 2.50%, an increase in rate to 4.0%, or a change of 1.50%, would result in a *negative* total return of nearly 10% on the bond in the example. (See circled figures in the table.)

Unlike the favorable market potential for stocks that we outlined in April, the risk/reward potential for bonds in the current environment seems to us skewed to the downside. This environment requires careful selectivity and caution when investing in the fixed income market.

We remain focused on understanding the current trends in fundamentals because it gives us the best probability for success.