Compound Interest: The Most Powerful Force in the Universe

Includes: MBG, TIP, VRD
by: Tom Graff, CFA

Fixed Income markets have enjoyed a relatively uninterrupted bull market for the last 30 years. With interest rates generally low and economic growth appearing to pick up, investors are logically concerned with rising rates. However, some investors may be taking this concern too far, abandoning bonds to hold cash or other assets for fear of large losses when the rate environment shifts.

There is a reason why bonds are generally considered the “safe” asset class, and it isn’t that bonds have enjoyed such a long bull market. It is because bonds have several inherent elements that mitigate potential losses stemming from interest rate shifts. As a result, readers may be surprised by how benign returns for bonds are likely to be – even given a significant bond bear market.

The critical part to recognize is that bonds are always being pulled toward par. This isn’t some trick of accounting; it is how bonds actually trade. As an example, say we take a bond with five years to maturity and a 3% yield priced at $100. Now let’s say interest rates suddenly rise 230 basis points such that this bond goes from a 3% yield to 5.30% yield. This move would produce a 10-point loss in the price of the bond. As time passes, holding that 5.30% yield constant, the dollar price of the bond will naturally rise. That is because a bond priced at a discount to par has capital accretion assumed in the yield calculation. Put another way, the 5.30% yield can be broken down into 3.33% in coupon income (i.e., 3% divided by the new, lower $90 price) and 2% in discounted principal value. Thus the bond can be expected to appreciate 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 (i.e., the same bond just one year later), the price would be approximately $91.84, or 2% higher than the initial $90 price.

This first point underscores that time is always on your side when you are a bond holder. This is true in more ways than one. Consider that the market usually demands more yield to compensate investors for owning bonds with longer maturities. This is why a plot 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 work to investors’ advantage as a bond ages. On April 12, the 5-year Treasury yielded 2.25%; 4-year Treasury bonds yielded 1.77%. If all conditions are equal, in one year’s time, today’s 5-year bond would decline in yield to the 4-year rate. We would also expect a commensurate increase in the price of the bond. This effect is called “rolling down the curve.”

Curve roll down can mitigate the impact of rising yields. Say that over the course of a year, all interest rates rise by 100 basis points, thus shifting from the orange line in figure 1, to the blue line. The 5-year Treasury starts at 2.25% (or point A on the chart). The 100 basis points shift moves 5-year securities from point A to point B. However, because one year has passed, and the 5-year bond has “rolled” to a 4-year bond, the “end point” is actually point C. An investor who held a 5-year Treasury in this example wouldn’t have suffered the price deterioration implied by the shift from 2.25% to 3.25%, but instead from 2.25% to 2.77%, roughly half of the yield increase.

One should not forget the simple fact that bonds are always producing cash, which in a rising rate environment allows investors to take advantage of higher rates by re-investing the cash flow into 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. So while an investor holding a bond portfolio initially suffers price declines when rates rise, he simultaneously enjoys better opportunities to reinvest the interest generated by the portfolio.

Figure 1. Curve Roll down Example

Source: Bloomberg, Brown Advisory Calculations

(Click charts to expand)

Putting the reinvestment of income, curve roll down and accretion of discounts together, we can estimate the break-even rate shift needed to result in a particular bond posting a loss over any particular period of time. Of course, there are many moving parts that can impact an actual portfolio’s return, not the least of which are alpha-generating (i.e., returns that are independent of market movement) activities by the portfolio manager. To illustrate how bonds behave, 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 income, discount accretion and curve rolldown effects, to make each maturity produce exactly zero return over one year.

Figure 2. Break-Even Interest Rate Shifts – 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 rise by exactly 172 basis points over one year, holding all other factors constant, that bond will produce exactly zero total return.

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

Figure 3. Break-Even Interest Rate Shifts – Two-Year Horizon

Source: Bloomberg, Brown Advisory Calculations

There are a few things to notice about both charts. First, time is on your side as a bond investor. Given two years, even 10-year rates need to rise by about 200 basis points to produce actual losses. In today’s environment, that would result in 10-year Treasury yields approximately equal to the 1990-2008 average of 5.78%. Second, notice that an intermediate portfolio of 1- to 10-year maturities, similar to the fixed income 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 one considers that in a portfolio setting, interest and maturities will be reinvested at the higher rates. It also suggests that holding cash while hoping for interest rates to rise is a difficult proposition. Note also that the shifts shown in the graph are the break-even rate; thus, any shift that is smaller than what is shown will produce a profit. Short-term interest rates will rise once the Federal Reserve starts tightening monetary policy, but there is no indication that such a shift is imminent. On the other hand, owning a conservative bond portfolio of short to intermediate maturities produces much more current yield compared to cash, while at the same time it has considerably more interest rate cushion than investors may be assuming. Granted, if one manages to time the rate shift just right, holding cash can work, but market timing is a high-risk exercise.

Brown Advisory is doing several things to help mitigate the impact of rising rates. First, we are favoring bond sectors that tend to perform well in rising rate environments, including Treasury Inflation Protected Notes, floating-rate notes and short amortization mortgage securities. Some ETFs, which follow similar strategies to what Brown is employing include iShares Barclays TIPS Bond Fund (NYSEARCA:TIP), SPDR Nuveen S&P VRDO ETF (NYSEARCA:VRD), and SPDR Barclays Mortgage Backed ETF (NYSEARCA:MBG).


Many investors lament how low bond yields are currently. It is fair to say that the low yields imply limited upside opportunity for investment-grade bond investors. However some investors may be over-estimating the possibility of severe losses in bond portfolios. The reality is that, to the extent that investors have a need for a high-liquidity, low-variability portion of their portfolio, a conservative bond portfolio still fits that bill.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.