Compound interest: the most powerful force in the universe

Fixed income markets have enjoyed a relatively uninterrupted bull market over the past 30 years. With interest rates generally low and economic growth appearing to be picking up, investors are understandably concerned about rising rates. However, some investors may take this concern too far, abandoning bonds to hold cash or other assets for fear of large losses when the rate environment changes.

There’s a reason bonds are generally considered the “safe” asset class, and it’s not because bonds have benefited from such a long bull market. This is because bonds have several inherent elements that mitigate potential losses from interest rate fluctuations. Therefore, readers may be surprised by the low yields on bonds, even given a significant bear bond market.

The key part to recognize is that bonds are always drawn to par. This is not an accounting trick; this is how bonds actually trade. As an example, let’s say we take a bond with a maturity of five years and a yield of 3% at a price of $100. Now suppose that interest rates suddenly increase by 230 basis points, so that this bond goes from yielding 3% to 5.30%. This decision would lead to a loss of 10 points in the price of the bond. Over time, holding that 5.30% yield constant, the dollar price of the bond will naturally rise. This is because a bond priced below par has a capital appreciation assumed in the yield calculation. In other words, the 5.30% return can be broken down into 3.33% coupon income (i.e. 3% divided by the new lower price of $90) and 2% value updated main. Thus, the bond can be expected to appreciate by approximately 2.30% each year as the bond approaches maturity. If you did a yield calculation on a 5-year bond with a 3% coupon and a 5.30% yield, the dollar price would be $90. If you did the same calculation on a bond with only four years to maturity (that is, the same bond one year later), the price would be around $91.84, or 2% more than the original price of $90.

This first point emphasizes that time is always on your side when you are in a bond. This is true in more ways than one. Consider that the market generally demands more yield to compensate investors who hold bonds with longer maturities. This is why a graph of yields by maturity is almost always upward sloping: 5-year bonds tend to yield more than 4-year bonds which tend to yield more than 3-year bonds. The yield curve can benefit investors as a bond ages. On April 12, the 5-year Treasury bond yielded 2.25%; 4-year Treasury bonds returned 1.77%. If all conditions are equal, one year from now, today’s 5-year bond yield would decline to the 4-year rate. We would also expect a commensurate increase in the price of the bond. This effect is called “unrolling the curve”.

Lowering the curve can lessen the impact of rising yields. Suppose that over the course of a year, all interest rates increase by 100 basis points, moving from the orange line in Figure 1 to the blue line. The 5-year Treasury note starts at 2.25% (or point A on the chart). The 100 basis point change moves the 5-year securities from point A to point B. However, as a year has passed and the 5-year bond has changed to a 4-year bond, the “endpoint is actually point C. An investor holding a 5-year Treasury note in this example would not have experienced the price deterioration implied by the move from 2.25% to 3.25%, but rather 2 .25% to 2.77%, or about half the yield increase.

Keep in mind the simple fact that bonds always produce cash, which in a rising rate environment allows investors to take advantage of higher rates by reinvesting cash flows in higher yielding bonds. As Albert Einstein once said, “The most powerful force in the universe is compound interest”. The power of compounding is amplified, not reduced, by rising rates. Thus, while an investor holding a bond portfolio initially experiences price declines when rates rise, they simultaneously benefit from better opportunities to reinvest the interest generated by the portfolio.

Figure 1. Example of curve unwinding

Source: Bloomberg, Brown Advisory Calculations

(Click on graphics to expand)

By bringing together the reinvestment of income, the rolling of the curve and the increase in haircuts, we can estimate the change in the equilibrium rate necessary for a particular bond to show a loss over a given period. Of course, there are many moving parts that can affect the actual performance of a portfolio, including the alpha-generating activities (ie, returns independent of market fluctuations) of the portfolio manager. To illustrate the behavior of bonds, we have taken the yield of a generic A-rate industrial corporate bond for each of several maturities. We then calculated how much interest rates would have to rise, given the effects of income, increasing discounting, and curve rolldown, for each maturity to produce exactly zero one-year return.

Figure 2. Interest rate changes towards breakeven – one-year horizon

Source: Bloomberg, Brown Advisory Calculations

Figure 2 can be read as follows: if an investor buys a generic 2-year corporate bond today and all interest rates increase by exactly 172 basis points over one year, maintaining all other Constant factors, this bond will produce exactly zero total return.

Figure 3 is the same analysis with an extended horizon of two years.

Figure 3. Interest rate changes towards breakeven – two-year horizon

Source: Bloomberg, Brown Advisory Calculations

There are a few things to note about both graphs. First, time is on your side as a bond investor. Over two years, even 10-year rates need to rise about 200 basis points to produce real losses. In the current environment, this would translate to 10-year Treasury yields roughly equal to the 1990-2008 average of 5.78%. Second, note that an intermediate portfolio of 1-10 year maturities, similar to the bond strategies managed by Brown Advisory, has a substantial “cushion” for rates to rise before producing losses for long-term holders. . This is especially true when considering that in a portfolio setting, interest and maturities will be reinvested at the highest rates. It also suggests that holding cash while hoping for interest rates to rise is a tough proposition. Also note that the changes shown in the graph are the equilibrium rate; thus, any change less than indicated will produce a profit. Short-term interest rates will rise once the Federal Reserve begins to tighten monetary policy, but there is no indication that such a change is imminent. On the other hand, holding a conservative bond portfolio of short to mid-term maturities produces a much higher current yield than cash, while providing a considerably larger interest rate cushion than investors may assume. Certainly, if one manages to time the rate change at the right time, holding cash can work, but timing the market is a high-risk exercise.

Brown Advisory is doing several things to help mitigate the impact of rising rates. First, we favor fixed income sectors that tend to perform well in rising rate environments, including inflation-protected treasury bills, floating rate notes and short-term mortgage securities. Some ETFs, which follow similar strategies to those Brown employs, include iShares Barclays TIPS Bond Fund (TIP), SPDR Nuveen S&P VRDO ETF (VRD), and SPDR Barclays Mortgage Backed ETF (MBG).


Many investors lament the current low bond yields. It’s fair to say that low yields imply limited upside opportunities for investment grade bond investors. However, some investors may overestimate the possibility of large losses in bond portfolios. The reality is that since investors need a high-liquidity, low-variability part of their portfolio, a conservative bond portfolio still fits that bill.

Disclosure: I have no positions in the stocks mentioned and do not plan to initiate any positions in the next 72 hours.

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