Bonds Versus Bond Funds: A Different Perspective
Plus October Market Report

This month our focus is on bonds, specifically the question of whether it’s smarter to invest in individual bonds or in bond mutual funds. Many financial journalists, advisors, and investors question the wisdom of investing in bond mutual funds, especially when interest rates are expected to rise. They gain emotional security in knowing investors can buy and hold an individual bond to maturity and get their money back. What some fail to recognize is that bond mutual funds are merely diversified portfolios of individual bonds, and both are equally exposed to the same market pricing mechanism. The day interest rates go up, individual bonds will fall in value just like bond mutual funds. Truth is, interest rate risk can be immunized with either individual bonds or bond mutual funds as long as the duration of the bond portfolio is appropriately matched to the desired investment horizon. The fact that an investor is able to get principal back at a specific maturity date adds no economic value compared to a bond mutual fund that does not have a specific maturity date. To unpack this story, we cite directly from research, noting sources along the way. This article is long, so we’ve tried to highlight key conclusions. Before we jump in, a quick look at October market performance.

Let’s start by addressing head-on the primary reason some investors prefer individual bonds to bond funds. It comes down to a sense of control. You know what you’re getting, you know when the bond will mature, and the redemption amount. A specific maturity date is comforting to many investors, and bond funds don’t have that. One hears these arguments most often when investors fear that rising interest rates will hammer bond prices. 

Yet these same investors fail to recognize that bond portfolios are diversified containers of individual bonds, and as such, both bonds and bond funds are exposed to the same market pricing mechanisms. When interest rates rise, both bonds and bond funds decline in value. The idea that holding a bond to maturity somehow provides more economic protection than a bond mutual fund ignores marketplace reality. Market forces work equally in favor (or against) against both instruments.  

Most bond portfolio management models can be characterized as either some form of Buy and Hold (B&H) to maturity or Duration Targeting (DT), which is a rebalancing process prevalent in bond mutual funds where a relatively stable duration is maintained over time.  

For example, if a five-year zero-coupon bond is held to maturity under the Buy and Hold model, the duration (a measure of interest rate sensitivity) simply “ages down” year by year until the maturity and the annualized return equals the initial yield.

In contrast to Buy and Hold, Duration Targeting attempts to maintain a stable duration over the entire investment horizon. At the end of the first year, the five-year bond ages to a four-year bond. The four-year bond is then sold and replaced with a new five-year bond. A Duration Targeting approach is central to the rebalancing procedures of most active and passive bond mutual funds. Figure 1 below contrasts the time evolutions of the durations of Buy and Hold and Duration Targeting for a five-year zero-coupon bond.

Let’s continue with our five year zero-coupon where the bond duration equals its maturity and explore the following example. (Charts and text from Northern Trust, Mladina and Moore, March 2014).

To simplify the illustration, a five-year bond held for one year serves as a proxy for a stable maturity bond fund. At the end of the first year, the bond is sold and then immediately replaced with a new five-year bond. This sell/buy pattern is repeated each year to replicate the relatively stable maturity profile of a typical intermediate-term bond fund. 

In the chart below, the yield curve (blue line) depicts a sample historical yield curve for one- to five-year maturities. Forward rates (black line) are the period-to-period returns. Assuming no change in interest rates, the five-year bond that yields 3.35% to maturity would return 4.00% in the first year, 3.68% in the second year, 3.35% in the third year, 3.03% in the fourth year and 2.71% in the final year before maturing.  

Scenario 1 under exhibit 2 below shows that at inception, the five-year individual bond and the bond fund proxy have the same value and offer the same yield to maturity because they are identical. Assuming no change in the yield curve, both the individual bond and the bond fund proxy earn the 4.00% forward rate in year one. After year one, the individual bond becomes a four-year bond and earns the 3.68% forward rate in year two. 

In contrast, the Bond Fund proxy sells the aged bond which is now a 4-year bond after the first year and repurchases the five-year bond, thereby earning 4.00% again in the second year. In each subsequent year, the individual bond continues to roll down the upward sloping yield curve, earning consecutively lower forward rates (lower returns) until it matures at $50,000 par. The bond fund proxy, however, maintains its constant maturity of five years and earns 4.00% each year. This is represented in scenario one in exhibit 2 below (stable interest rates). The bond fund proxy generates more economic value over time because it earns the higher forward rate.

Scenario 2 under exhibit 2 shows what happens to values after a 1% unexpected rise in interest rates across maturities at the end of year one (i.e., each yield and forward rate in the Historical Curve increases 1%). Thereafter, a stable yield curve is assumed. Both the individual bond and the bond fund proxy experience the same initial loss in value at the end of year one. This scenario shows that both are worth $42,428 at the end of year one instead of $44,097, losing $1,669 in value due to the unexpected rise in interest rates. Whether or not the investor holds the individual bond to maturity, it is worth $42,428 at the end of year one, and that is what the investor would receive if he or she were to sell it. The individual bond continues to roll down the new yield curve, earning the new forward rate each period, until it matures at $50,000 par. 

In contrast, the bond fund proxy sells the four-year bond right after the unexpected rise in interest rates at the end of year one and repurchases the five-year bond to maintain its constant maturity profile. It now earns the higher 5% forward rate each year. The bond fund proxy generates more economic value over time because it earns the higher forward rate. 

The point is not necessarily to show that the bond fund proxy delivers more economic value than the individual bond, although it does in this case. Rather, the main point is that both the individual bond and the bond fund proxy are subject to the identical term structure of interest rates, which determines their prices. The only reason the bond fund proxy delivered more economic value is that it offered forward rates associated with a longer average maturity. There is no unique interest-rate protection over bond funds by holding individual bonds to maturity, other than capturing shrinking duration (and return) as maturity approaches. But this same interest-rate protection is easily achieved by simply owning lower-duration bond funds.

Now, for more general insight into how changes in yield affect bond fund returns, we offer two additional examples: First, a trendline path of interest rate changes, and second, an implied random walk of interest rate changes. 

To illustrate how upward sloping changes in yield affect bond fund returns, the study begins with a simple nine-year horizon that proceeds from an initial yield of 3% to a final yield of 7%. Table 1 is based on yields that rise at a constant 50 bps a year.

To simulate the bond mutual fund, the study utilizes the same five-year zero-coupon bond. At the end of each one-year holding period, the aged bond is sold and the proceeds are re-invested in a new five-year bond to maintain a targeted five-year duration. 

Two types of price movements are considered: (1) price effects derived from changes in yield and (2) “accruals” that result from changes in yield over the passage of time.

The first-year-yield accrual is derived from the 3% initial yield, and so the excess yield accrual over the 3% initial yield is just 0%. Over the year, the bond fund ages and the initial five-year bond duration is reduced to four. Because the year-end trendline yield is 0.5% higher than the initial yield, the rebalancing bond sale results in a price loss of approximately negative 2%, or –4 duration × 0.5% change in rates.

The sale proceeds are then reinvested in a new five-year bond with a 3.5% yield, which becomes the basis for the second-year accrual. The trendline yield increases by another 0.5% at the end of the second year, resulting in another negative -2% price loss. This 2% loss combines with the second-year excess yield accrual of 0.5% to provide an excess return of negative -1.5%, a cumulative excess return of negative -3.5%, and an annualized excess return of negative -1.75% after two years. With each subsequent year, the excess accrual rate increases by another 50 bps, while the price loss remains constant at negative -2%. At the end of four years, the cumulative excess return is negative -5%.

By the fifth year, yields and accruals have risen by 2% (from 3% to 5%). The excess accrual of 2% precisely offsets the negative -2% price loss, and so the cumulative excess return remains unchanged at negative -5%. In later years, the excess accruals continue to grow such that, after nine years, the cumulative excess yield accrual of 18% completely offsets the cumulative price loss of negative -18%. The cumulative excess return is 0% and the annualized return equals the 3% starting yield. 

The key to understanding the behavior of bond fund returns lies in recognizing the offsetting relationship between price effects and incremental accruals. At the outset, annual price losses dominate the incremental accruals. But because the annual price losses remain constant along a trendline whereas the annual accrual rate rises with each year’s higher level of yields, the cumulative accrual is sufficiently above the starting yield to fully offset the cumulative price loss. The incremental return is thereby reduced to zero, and the annualized return just equals the starting yield.

To better illustrate how the relationship between accruals and price changes develops over time see Figure 4. At the outset, the price loss far exceeds the nominal excess yield accrual. However, the new accruals build on the preceding yields, and the net effect is that the cumulative accrual grows rapidly and ultimately overcomes the cumulative price loss formulaically at “two times duration minus one" or in this example, in the ninth year.

Duration Targeting and Random Walk

Of course, a trendline is only one of countless paths that interest rates can follow over time. Each non-trendline path to a particular terminal yield can be framed in terms of positive or negative yield deviations from the trendline path. Under duration-targeting, a non-trendline path and a trendline path with the same overall yield change incur about the same capital gain or loss. In contrast, the accruals in Duration Targeting are highly sensitive to the actual rate path, and deviations from the non-trendline path can lead to significantly different accruals. 

To simulate the effects of a random walk of interest rate fluctuations on actual multi-year returns, Leibowitz and Bova studied the returns of the Barclay’s US Aggregate Government Credit Index and the Barclay’s Credit Index dating back to 1981. These indexes have had fairly stable durations (5.4 years since 1985 and 6.1 years since 1981, respectively) and can be viewed as implicitly following a Duration Targeting approach. In both cases, the average returns over almost all six-year holding periods were within approximately one hundred basis points plus or minus of the initial yield. Researchers found that even though returns along a trendline may vary widely, the accumulation of accrual and price offsets exerts a kind of “gravitational force” that drives duration-targeted yield back towards the starting yield. 

There are a few important parallels between the returns of a Buy and Hold approach and the returns of a Duration Targeting approach, which is generally what bond funds are doing. 

To summarize, despite the widespread presence of Duration Targeting bond mutual funds, there’s an underappreciation for the behavior of their returns. Most of the concern about Duration Targeting bond mutual fund investing is focused on short-term price sensitivity in the context of near-term liability management and interest rate price risk. At the outset, when interest rates rise unexpectedly, the "price" loss in a duration targeting strategy exceeds the excess "yield" accrual. The new accruals, however, build on preceding yields and the net effect is that the cumulative accruals grow rapidly and ultimately overcome the risk of cumulative price losses completely. Over an appropriate timeframe, the final yield equals the starting yield to maturity.

The objective of bond portfolio management is to immunize investors against interest rate risk by matching bond portfolio duration with investor liabilities. A portfolio of bonds, whether implemented with individual bonds or bond mutual funds, is immunized from interest rate risk if the duration of the portfolio is appropriately matched to the desired investment horizon.

As summed up by Cliff Asness (Financial Analysts Journal, 2014), by buying and holding an individual bond to maturity, an investor will indeed get their principal back, but in a climate of higher interest rates and inflation, the purchasing power of those dollars will be less. The fact that an investor is able to get principal back at a specific maturity date adds no economic value compared to an appropriately targeted bond mutual fund that does not have a specific maturity date.

Individual bonds can provide certain benefits over funds, and these advantages mostly have to do with a preference for control and satisfying near-term liabilities. One could think of this preference for individual bonds as a “control premium” that is reflected in generally higher (or additional) transaction costs, lower liquidity, more limited return opportunities and higher bond portfolio risk. 

Given the generally higher risks and costs associated with portfolios of individual bonds, the vast majority of investors are better served by low cost bond mutual funds.