Rolling ladders versus bond funds

The major factors  in deciding between owning a bond fund versus individual bonds are:  diversification,  convenience,  costs, and  control over maturity. There is a common belief (promoted by Suze Orman, among others) that owning individual bonds is less risky than a bond fund, but this is not necessarily true if an appropriate bond fund or collection of funds is chosen. Duration is an essential concept for understanding the riskiness of a fund or ladder over time. There's also an important distinction between owning individual bonds (declining duration) and holding a rolling bond ladder. Rolling bond ladders are a constant duration investment, whereas an individual bond's duration decreases as it approaches maturity.

Methods of achieving declining versus constant duration
What kinds of financial instruments produce a declining duration?
 * An individual bond, with coupons reinvested in some form that is liquid on the bond's date of maturity (e.g. a bank account, bonds with shorter and shorter maturities as described above, or CDs with put options)
 * A Zero-coupon bond, which doesn't pay out a coupon so that no reinvesting of coupons is required.
 * A portfolio of individual bonds, purchased with shorter and shorter maturities. A.k.a. a non-rolling bond ladder
 * A target-date bond fund. These are rare funds and tend to have very high expense ratios.  We will therefore not consider them further.

What kinds of financial instruments produce a constant duration?
 * A portfolio of individual bonds, set up such that when one bond matures another bond of equal maturity is purchased. A.k.a. a  rolling bond ladder.
 * A bond fund, where a manager maintains the portfolio to have a fairly constant duration.

Reasons for choosing declining or constant duration
Assuming the complexities and expenses associated with each were about the same...

Why would you choose a declining duration portfolio/fund?
 * You have a known expense at a future date that you want to set money aside for. Examples include saving for a car, or for some investors, college.

Why would you choose a constant duration portfolio/fund?
 * You are saving for expenses with unknown amounts and/or unknown time horizons. Examples include retirement, saving for a house down payment, or for some investors, college.

A framework for comparing portfolios of individual bonds to bond funds

 * Many, if not most, Bogleheads and other investors use bonds as part of a larger portfolio because of their stabilizing properties on the whole portfolio (in this context, the proper framework for analysis is its historical long-term returns as an asset class, its risks, and its relation to the rest of the portfolio).
 * What matters is total return, not the return of any one component such as the principal which is often focused on in isolation. Total return has three components:
 * Principal
 * Interest (coupon payments)
 * Interest-on-interest (reinvested coupon payments)
 * We will discuss what happens to the fund or bond after a single interest-rate change. However, as long as the duration of the portfolio is kept approximately equal to the remaining time horizon, then this single interest rate change generalizes to all interest rate changes.  For instance, suppose a portfolio of bonds or funds is purchased with 5-year duration to meet a goal 5 years in the future, and is properly rebalanced to keep the duration equal to the investment horizon.  With 4 years remaining, a parallel shift of the yield curve occurs .  The investor would be indifferent to that interest rate change because of duration matching.  If six months later interest rates change again, the investor similarly does not care, because their duration is now 3.5 years and so they are similarly indifferent.
 * This makes clear a key fact often omitted in the financial advice literature. The recommendation to "keep your duration equal to your need for the money" cannot be applied once and forgotten, but must be updated continuously (or more realistically, by rebalancing every 3-12 months into shorter-term funds).  The only way to achieve duration matching automatically is to purchase a zero-coupon bond.  Neither individual bonds nor funds will do this perfectly, although individual bonds come closer (particularly in low-interest rate environments).
 * Note that the scenario of rebalancing bond funds or portfolios of individual bonds to meet a known, fixed, future obligation is a bit silly. If you have such an obligation, the safest course of action is to purchase neither a fund nor an individual coupon-paying bond, but instead to purchase a zero-coupon bond maturing on the date needed.  Nevertheless, it illustrates the point that your money is safe, as will be elaborated in the rest of this page.

Rolling versus non-rolling bond ladders
If you need to satisfy date-certain future liabilities, a non-rolling ladder of individual bonds is superior to a bond fund. For example, if you commit to make a $10,000 a year payment to a charity for five years, the most effective way to invest for that is to buy 5 zero-coupon bonds, one maturing each year. A non-rolling bond ladder matches cash flows to liabilities, which immunizes a portfolio against interest rate shifts.

However, most bond ladders are "rolling", because they are not designed to deal with date-certain future liabilities. They are created with a specific average duration, and when the oldest bond comes due, a new long-dated bond is purchased to replace it. A rolling ladder of this kind can and should be directly compared with a bond fund using the criteria below. According to Vanguard in their paper Taxable bond investing: Bond funds or individual bonds?, "The total return of a laddered account with characteristics identical to those of an open-end bond fund will deviate from the fund’s return only by the transaction and operational cost differentials."

As advocated by Zvi Bodie, some people aim to fund their retirement by purchasing a ladder of individual TIPS with durations of 1 to 30 years. The idea is to avoid the volatility of the underlying bonds by always holding them to maturity, so as to avoid having to sell the fund at moments when high yields have caused the NAV to drop.

If you are planning to reinvest (i.e, rollover) some of the annual redemption into new individual TIPS bonds, then you have gained nothing by using a rolling ladder over a fund. Because not rolling over the whole bond at the (hypothetically) very high yield has an identical opportunity cost to selling a portion of your fund at the (hypothetically) very low NAV. Another issue with this approach is how to deal with the longevity risk if you outlive your ladder.

Thus, the distinction between a non-rolling ladder (designed to meet date-certain future liabilities) and a rolling ladder (which essentially represents a personal bond fund) is much more important than the difference between a rolling ladder and a bond fund.

Rolling ladders and funds are similar
It has been regularly argued on the Bogleheads forum that a bond fund is risky because of NAV fluctuations. For example, the NAV for Vanguard Inflation Protected Securities fell 20.4% from peak to trough in 2008. Instead, it is said, investors should hold individual bonds, which can always be redeemed at face value by holding until maturity. However, the value of individual bonds held in a personal portfolio fluctuates just as the NAV of a bond fund fluctuates. You can see this by looking at the daily price changes of individual bonds online at Fidelity's fixed income site. Bond prices can also be obtained online through Vanguard's Bond Desk. The daily fluctuation of the price of an individual bond will be similar to a bond fund if their duration is the same.

Non-rolling ladders versus funds
A non-rolling ladder (or a single bond) will behave differently than a bond fund over time. This is because a bond fund (usually) maintains a relatively constant duration. On the other hand, a non-rolling ladder has a duration that decreases over time. If you want to obtain the behavior of a non-rolling ladder using bond funds you must decrease the duration of the bond fund over time. This is done by mixing two funds so that their weighted average duration is the same as the ladder which you are trying to mimic. In some cases it may not be possible to find a fund with the duration that you desire. For example, Vanguard only offers one TIPS fund so you will need to buy individual TIPS to achieve the duration that you desire.

Duration
It's useful to focus on the duration of your bond fund, such as the Vanguard TIPS Fund, which currently has a duration of 5.0 years. William Bernstein provides an insightful definition of duration as the "point of indifference" for the owner of a bond fund in dealing with interest rate changes. If interest rates rise after purchasing a bond fund, the NAV of the fund falls, which hurts the investor. However, the dividends that the bond fund throws off can now be reinvested at a higher rate. The duration is the length of time that an investor needs to hold the fund for the increased yields to compensate for the decrease in NAV. In that sense, duration represents the length of time it would take for the total value of the fund, with dividends reinvested, to be worth exactly what it would have been worth had interest rates not risen. So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall).

Of course, as discussed above, this definition of duration applies equally to bond funds and to an individual portfolio of bonds. The relationship does not exactly hold if the yield curve shifts in a non-parallel fashion, but the difference is expected to be small.

Interest rates change continuously, not just at a single point in time. Therefore, as the time when you will need the money approaches, you must reduce your duration accordingly, to protect you against any further increases in prevailing rates. The ways in which this can be done are discussed below.

Why thinking of a rolling ladder's return as "safe" is misleading
The common argument for individual bonds over a fund is that at maturity you are guaranteed to get your principal back. While this is true, the principal is only one of the three sources of return for a bond:
 * 1) Principal
 * 2) Interest (coupon payments)
 * 3) Interest-on-interest (reinvested coupon payments)

According to Fabozzi in the Handbook of Fixed Income Securities, 1991, p97: "In high interest rate environments, the interest-on-interest component for long-term bonds may be as high as 70 percent of the bond's potential total dollar return."

Therefore, focusing on the principal as "safe" misses the point, since it is in many circumstances the smallest component of a bond's return. If you are saving for a large goal, you therefore have to invest considerably more into the bond than you want guaranteed to ensure the need is met by the principal.

To make sure the total value (all three components listed above) winds up being what you expected it to be, you should maintain a portfolio duration equal to your investment horizon and continually reduce the duration as your investment horizon nears (or more realistically, rebalance every 3-12 months, which Michael Granito in Bond Portfolio Immunization claims didn't cause any substantial deviations from target return vs. continuous rebalancing in a variety of simulated market conditions). A zero-coupon bond does this automatically. A coupon-paying bond does not (duration declines very slowly at first and then more rapidly once the bond nears its maturity; this is more pronounced in high-rate environments and less important in low-rate periods), nor does a bond fund (duration is relatively constant). Stated differently, since the duration of a coupon-paying bond is less than its maturity, if you invest such that the bond matures when you need the money, you are by definition not investing such that the duration is equal to your investment horizon, leaving you vulnerable to interest rate declines.

In another text (Fixed Income Mathematics, 1993, p175), Fabozzi summarizes, "Therefore, investing in a coupon bond with a yield to maturity equal to the target yield and a maturity equal to the investment horizon does not assure that the target accumulated value will be achieved."

Zero-coupon example
If you have a sudden need to extract the principal from a bond fund (or portfolio of individually-held bonds, for that matter), you can do so as rapidly as possible by selling the fund and buying a zero-coupon bond with the face value of your principal. Such a bond will always be available, because if the fund's NAV is down, yields will have gone up a commensurate amount. On average (with a typical yield curve), the bond will have a maturity equal to the duration of the TIPS fund. (A regular TIPS bond would also serve the same purpose, but a zero coupon bond makes the calculation simpler, because the duration equals the maturity.)

The strategy of buying a zero-coupon bond works because the duration of a zero equals the maturity, and therefore declines steadily as time passes. No other commonly-available type of bond instrument has this property (although it can be replicated with bond funds or with individual bonds, provided you rebalance regularly). Therefore, if you have a fixed, known obligation at some future point in time, a zero-coupon bond is the obvious choice to satisfy it.

For example: Fred buys a bond fund while Larry buys bond ladder, each with equal duration. Interest rates skyrocket just afterward. At that moment, Fred and Larry have an equal loss. Fred can log into Vanguard and see that his fund balance is, say, 70% of what he invested. Larry can log into Vanguard Brokerage Services and see that the total value of all of the bonds in his ladder are 70% of what he invested. Whether either decides to realize the loss or not, the loss has in fact occurred.

Now, the only difference between Fred and Larry is that Larry has two options for getting his money back and Fred has one. Fred can sell his bond fund and buy a zero coupon bond with a maturity value equal to his initial capital investment. Larry can likewise sell his bond ladder and buy a zero coupon bond. Larry's additional option is to hold all of his bonds until maturity. However, this second option is unambiguously worse for Larry. He would need to hold his longest bonds twice as long as the zero coupon bond to get his money back. Due to the opportunity cost of having his money unnecessarily locked up, this means he would actually be losing money versus the zero coupon option. In addition, for taxable accounts, selling their holdings to buy zero coupon bonds would let Larry and Fred take advantage of tax loss harvesting.

Please note that this whole example is artificial, because it is extremely rare for a bond holder to decide that he needs to immediately liquidate all of his principal. Instead, bond holders are generally interested in steady growth over the long term. Some people suffered 15 or 20% losses in their bond holdings (both fund and ladders) in late 2008. Very few sold their holdings to buy zero coupon bonds. Instead, they continued making periodic contributions like they always do, ignoring the balance of the fund. And this was certainly the right choice, as the funds have regained their previous value.

The whole argument for individual bonds being less risky is based on this completely artificial concept that you will one day decide you need all of your money back, and then happily wait 20 years to get it back (all in nominal terms, meaning the money has been eaten away by inflation in the meantime). The point of using zero coupon bonds is that they are an equally arbitrary option. But they show that Fred is never worse off than Larry: a bond fund is no riskier than a bond ladder.

In real life, people should hold bond funds (high grade, short or intermediate term, and a mix of nominal and inflation-adjusted), and just ignore the NAV. All that matters is total return, and if you hold the fund longer than the duration, your total return will be just fine. The zero coupon example is just an academic way of making that point.

These ideas were discussed on these threads:

Convexity
Positive convexity, a characteristic possessed by bonds without options, is ignored in the above discussion but only strengthens the argument, since positive convexity lengthens duration when rates fall and shortens duration when rates rise. The Advanced Bonds section contains more detail.

Yield curve changes
Changes in the shape of the yield curve may make a difference in the above comparison, but the effect is expected to be minor for a long term investment.

Diversification
Diversification is important for bonds, as it is for all asset classes. The argument against an investor ever owning individual corporate or municipal bonds (even in a ladder) is that the effect of a single default (such as a corporation or city brought down by fraud), even if unlikely, could be devastating to the investor's portfolio. By contrast, bond funds allow extremely broad diversification at a very low cost.

A ladder of individual bonds generally includes between 10 and a couple dozen bonds. That means that each bond represents 2.5% to 10% of a portfolio. By contrast Total Bond owns 3855 different bonds, and Intermediate Term Tax Exempt owns 1971. So, the failure (default) of any one bond has a minuscule effect on the fund.

The only exceptions are Treasury bonds (including TIPS). Because all Treasury bonds are explicitly backed by the US government, they have the highest possible credit rating. They also all have the same issuer. There is no diversification benefit from owning a Treasury bond fund instead of individual Treasury bonds.

Convenience
Investors in a bond fund can buy or sell additional shares at any time in any quantity. There is usually no transaction fee for buying or selling additional shares. With individual bonds, purchases on the primary market may only be made on the pre-set issuer schedule (e.g., every few months for TIPS). Purchases on the secondary market are generally subject to a commission and one always pays a bid/ask spread, which can be substantial. Also, individual bond purchases are only available in increments of $1,000 (and more often $5,000 or $10,000).

Bond funds offer automatic dividend reinvestment. While you are in your accumulation phase, it is far more convenient to have dividends automatically reinvested. Even after beginning to spend your holdings, it is generally simpler to have bond funds automatically reinvest dividends and then just sell a fixed amount of the fund monthly or quarterly. By contrast, there is no simple way to reinvest small amounts into individual bonds. It is also far more convenient to rebalance between a bond fund and other assets in your portfolio.

Taxes are simpler for bond funds. If you invest in a bond fund in a taxable account, you receive tax forms from the bond fund company. If you have a portfolio of individual bonds, you receive tax forms from TreasuryDirect or your brokerage account listing the tax-related items for each bond. It's easier to figure out the tax reporting for one bond fund versus many individual bonds. Also, owners of individual TIPS owe a tax on phantom income that they do not receive. This is not an issue with TIPS funds.

On the other hand, for investors who are accustomed to managing a portfolio of individual bonds, a rolling bond ladder can be fairly simple to manage and can be simpler to understand conceptually. This is made somewhat more complicated when individual issues are discontinued, leaving a hole in the bond ladder. For instance, there were no 20-year Treasuries issued from 1986-1993. The solution is either to find equivalent combinations of bonds which keep the overall duration the same (in a 6% interest rate environment, to replace the 20-year you could use 36% 10-year and 64% 30-year bonds), or to buy a longer issue from which some time has elapsed on the secondary market (e.g. buy a 30-year bond issued 10 years ago) and bear the cost of the poor spread individuals receive when buying bonds in small lots.

Costs
The costs associated with owning bonds are commissions, bid/ask spreads, and management fees. Primary purchases of bonds (such as at a TIPS auction) generally do not incur commissions or bid/ask spreads. Purchases and sales on a secondary market can have substantial commissions and bid/ask spreads, particularly on less liquid bonds like municipals and corporates. Spreads also tend to be wider for the smaller value transactions that individual investors make. With the exception of primary purchases of Treasury bonds and TIPS, bond funds pay much lower bid/ask spreads on their bond transactions, giving them a significant cost advantage over regular investors purchasing individual bonds. Even for Treasuries bought at auction, the cost discrepancy is not clear-cut; off-the-run Treasuries generally pay higher yields than new issues of the same effective maturity, mitigating much of the advantage of buying new issues with no spread. Swedroe points out (see comment 20) that the same phenomenon exists in the municipal bond market as well.

There is no management fee for holding a portfolio of individual bonds. However, there is an opportunity cost associated with the time to do so. If you enjoy purchasing TIPS in auction, than this time is really a consumption item rather than an expense. If tracking auction dates and the shape of the yield curve doesn't seem like fun, than it should be treated as a real cost. For example, holding $100,000 of VAIPX (Vanguard Inflation-Protected Securities Fund Admiral) costs $110 per year (with an expense ratio of 0.11%). If you value your time at $55 an hour, it is more cost effective to use this fund than hold your own portfolio of bonds if it takes you more than 2 hours a year to manage your portfolio.

Control over maturity
By managing your own portfolio of bonds, you can either pick the average duration you want or "ride" the yield curve to pick up bonds that are "cheap" compared to the  ladder overall, and allow your duration to fluctuate with your purchases. In either case, you are in control. With a bond fund, the duration is designed not to move more than a year or two and is managed by the fund.

However, investors need to consider who is in the best position to find bonds that are slightly under-priced, you or a dozen expert bond analysts at a fund company whose only job it is to follow the bond market?

Also, if you'd like a shorter duration than offered by a bond fund, it is easy to shorten it by putting a portion of the money in a money market fund. For example, the Vanguard municipal bond fund for New York has an average maturity of 11.1 years. You can approximately halve that by holding half of your money in that fund and half in the New York Tax Exempt Money Market. Depending on the shape of the yield curve (concave vs. convex), this may cost you return.

Control over convexity
While it is relatively easy to calculate the convexity of a portfolio of individual bonds, most bond funds (including Vanguard) do not make the convexity of their funds available. This opens the door for manager risk (where unscrupulous managers can "juice" their yield by buying bonds with lower convexity--investors will never know until it is too late). However, while investors in a portfolio of individual bonds can calculate the convexity, few do, in part because taking advantage of this generally requires purchasing on the secondary market, which is expensive for small portfolios. Therefore the real-world application of this difference may be limited.

Control over inflation factor
There is an additional factor to consider for TIPS, in that buying individual issues gives you control over the "inflation factor" (also known as the "index ratio"). This allows you to manage deflation risk (generally at some premium which reflects the market's expectation of deflation).

Control over tax-efficient characteristics
Some managers may choose to purchase AMT bonds to increase yield, which disadvantages investors subject to this tax. This is easily avoided by researching the fund's holdings.

Control over call risk
Managers may also choose to purchase bonds with higher call risk to boost the fund's yield, which disadvantages investors if the risk shows up at the wrong time or if they are not planning for this risk in their overall portfolio. Careful research into long-term track records and holdings of funds will mitigate this problem.

Control over liquidity
Bond funds have to meet redemptions at any time. They may handle this in at least two ways: by holding cash reserves or by investing in more liquid bonds (e.g. on-the-run Treasuries vs. off-the-run Treasuries). Both approaches earn lower yields on the proportion of the fund held as liquidity reserves.

Availability of other fixed income types
CDs are not available in a bond fund. Often, CDs yield more than the equivalently risk-free Treasury of similar duration.

Manager risk and opacity
Bond funds should be selected carefully. The experience of Schwab YieldPlus Investor (SWYPX) demonstrates this risk--an UltraShort bond fund that was billed as a safe alternative to money market funds lost over 50% of its NAV. Read the prospectus carefully for indications such as the use of complicated derivatives (options, futures, options on futures, swaps), leverage, short sales, junk bonds, foreign and emerging market bonds, convertible securities, mortgage dollar rolls, etc. YieldPlus used all of these. While it is possible to use these tools to reduce risk, it is also possible to greatly magnify the risk in exchange for only small gains in yield. The rise of bond index funds holds the possibility of eliminating manager risk entirely, leaving only the much smaller risk of tracking error.

Tax-loss harvesting
Larry Swedroe makes the interesting point that holding a portfolio of individual bonds lets you tax-loss harvest at the single-bond level; with a fund you can only TLH when a whole fund incurs a loss. The magnitude of this benefit is unclear and will depend on the investor's tax bracket. Since bid-ask spreads tend to be large on the secondary market (particularly for non-Treasuries), this strategy is not viable for most individual investors. Moreover, since Boglehead strategy is to place bonds in tax-advantaged spaces whenever possible, the ability to TLH is likely quite limited for most smaller investors (as he himself points out, "For typical smaller investor bond funds are the ONLY way to go."). For larger portfolios involving Treasuries in taxable accounts, Mr. Swedroe's insight may tip the balance in favor of holding individual bonds.

When to hold a rolling ladder or fund
As explained earlier, the value of a rolling bond ladder reacts the same to market changes as the NAV of a bond fund if their holdings are the same so daily price fluctuations should not be a consideration. However, there are other factors to consider when choosing between a bond fund and a rolling ladder of individual issues, as detailed below. The principal tradeoff for a long-term investor is the diversification of bond funds and the low trading costs vs. the expense ratio of the fund.

For bond categories with high credit risk such as corporate bonds, high yield bonds, or emerging market bonds, bond funds are the clear choice because the diversification benefit clearly exceeds the expense ratio. For municipal bonds the picture is less clear, as default rates are quite low; nevertheless for small-to-medium-sized portfolios (Swedroe suggests $500k minimum portfolio size whereas Alan Roth suggests $50m) the diversification benefit still argues for a fund, as does the liquidity premium (bid/ask spreads are quite high for munis).

For treasury bonds (including  TIPS), which are assumed to lack any credit risk, the diversification of a fund adds little benefit over a rolling bond ladder. Therefore the expense ratio is merely a convenience fee (or perhaps a small liquidity premium). For a low-cost Treasury fund, however, that fee may be reasonable and is a matter of personal preference. If the greater liquidity and lower demands on investor time of a fund are not desired, the preferred method of investing in Treasuries is to purchase individual bonds at auction (which is generally free), assuming the spread over equivalent off-the-run issues is not too large. This is particularly true if the investor is considering CDs as a substitute for treasuries, as they often yield more and are unavailable in fund form.

Whitepapers and Articles

 * Taxable Bond Funds and Individual Bonds by Vanguard Investment Counseling and Research
 * Municipal Bond Funds and Individual Bonds by Vanguard Investment Counseling and Research
 * Bonds vs. Bond Funds? An Easy Choice by Allan Roth
 * Taxable bond investing: Bond funds or individual bonds? by Vanguard Investment Counseling & Research