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It’s absolutely amazing what you can find on the web once you start looking for info. The following long post is from something called the Bogleheads Forum.

Frankly, on a first quick reading, I don’t understand all of it. I’ve ground my way through books on “bond immunization” before, but concluded –-maybe wrongly— that I could bypass the topic in my own investing.

Cuss. I do NOT want to deal with “Duration”, “Convexity”, etc. Just going through the process of finding bonds to buy is work enough. But I’ve been running numbers on my own holding, trying to figure out CAGR vs. YTM vs. Inflation-Discounted Returns, etc. It occurred to me, as soon as I started reading this article, that it is absolutely relevant to the now-lengthy NC muni thread.

It’s a mind-stretcher, but give it a try.

There have been a dozen or more threads in which advocates of individual bonds spread fear that, were rates to drop at exactly the wrong time, you would not get your money back out of the bond fund when you needed it, and therefore buying individual bonds must be safer. In response, others (at least some of whom I would consider experts in the bond market) have responded that as long as your duration is greater than your need for the funds, you will not lose money, and that comparing a non-rolling bond ladder to a fund--equivalent to a rolling bond ladder--is not a valid comparison.

More recently, the final twist on this endless circle has been a claim by anti-bond-fund posters that since at some point you will need the money, even if you are investing for the long-term, at some point you will need the money and your principal will not be safe.

In response to this, I will excerpt and summarize one of the major academic books elucidating how bonds respond to price changes, Fabozzi's Fixed Income Mathematics (1993), pp175-190 or so, the chapter called "Price Volatility Measures: Duration," sub-chapter "Role of Duration in Immunization Strategies." Note that Fabozzi uses the term "immunize" to mean ensuring that the amount that you get out of a "bond portfolio" (the term here can mean either a ladder of individual bonds, a bond fund, or a grouping of bond funds, as long as the duration is the same across types).

"Because the interest rate risk and reinvestment risk offset each other, however, is it possible to select a bond or bond portfolio that will lock in the yield at the time of purchase, regardless of interest rate changes in the future? That is, is it possible to immunize the bond or bond portfolio against interest rate changes? Fortunately, under certain circumstances, it is. This can be accomplished by constructing a portfolio so that its Macaulay duration is equal to the length of the investment horizon."

You'll note that Fabozzi uses bond and bond portfolio interchangeably because there is no difference in how they respond to market conditions. Indeed, the examples he goes on to provide make it clear that the optimal way to meet a future obligation is NOT to purchase a bond or group of bonds which matures when the obligation is due, but rather a bond or group of bonds whose duration is the length of time remaining until the obligation comes due. Since for any bond which pays a coupon, the duration is shorter than the maturity, this means you will wind up selling the supposedly safe bond on the open market, and be subject to the same market pricing that people worry about with bond funds. The reason to invest even an individual bond towards a fixed future obligation based on duration rather than maturity is that you face reinvestment risk on the coupon payments. If interest rates drop, you will not be able to meet your obligation, because you will be making less on the reinvested coupon payments than you expected to. Therefore to ensure meeting your obligation, you will need to invest more than you would otherwise.

"To immunize a portfolio's target accumulated value (target yield) against a change in the market yield, a portfolio manager must invest in a bond (or a bond portfolio) such that (1) the Macaulay duration is equal to the investment horizon*, and (2) the present value of the cash flow from the bond (or bond portfolio) equals the present value of the liability."
The footnote: "* This is equivalent to equating the modified duration of the portfolio to the modified duration of the investment horizon."

Point (1) is what has been advocated here. Point (2) simply means that you should invest enough money to reach your goal!

In his examples, he assumes the market yield changes immediately after the bond is purchased, as a one-time event. This point has been raised in discussions here as well, that if yields constantly increase, you could fail to make up the lost NAV by the time you need the fund's principal. The response in other posts was to suggest that the duration should be lowered smoothly as the fixed need for the money approaches, so that the duration always equals the remaining time. This can be accomplished by moving money from e.g. an intermediate-term fund to a short-term fund over time, in the same way that one rebalances from stocks to bonds over time. The duration of the bond portfolio is simply the dollar-weighted average of the durations of the funds or bonds within the portfolio.

Fabozzi has the following to say on this topic:
"In the face of changing market yields, a manager can still immunize a portfolio by rebalancing it so that the Macaulay duration of the portfolio is equal to the remainder of the investment horizon."

Finally, there is a caveat, which is that if the shape of the yield curve changes (that is, if bonds of different duration do not all change by the same amount), the immunization will be imperfect. This will result in a loss (practically speaking, a pretty small one) if short-term yields fall (reducing interest on reinvested coupon payments) but long-term yields rise (causing NAV loss which is not compensated completely for by the higher interest rates due to low short-term rates). He suggests a strategy elucidated by Fong and Vasicek in the Journal of Finance, December 1984, to minimize this risk. I would guess that this strategy is likely too complicated for individual investors, and the need is quite small, since this risk is minimal.

Indeed it should be possible to "insure" against this risk by overestimating your actual need by a small amount. This is almost certainly an amount smaller than that needed to "insure" a coupon-paying individual bond in case the interest rate changes on the reinvestment of the coupons. Indeed, in practice what most advocates of the individual-bonds-are-safe philosophy seem to do--quite reasonably so--is use the maturity value of the bond to meet their obligation, and the coupon payments become income or get reinvested into the general portfolio. This is in effect over-"insuring" by the value of the coupon payments plus their reinvested interest.

If even this miniscule amount of risk is too much to bear, and building in a small cushion as insurance against the small loss if the yield curve shifts the wrong way (applicable to either individual bonds or funds, as was discussed) is not possible, then a zero-coupon bond is appropriate.

Finally, I want to thank everyone for the discussions of the past several months about bond funds. As frustrating as the discussions have been, in the end they have forced me to read further and further (and even run the numbers myself) to understand why the experts were in fact correct. As a result I have gone from only the most basic understanding of bond funds to feeling considerably more comfortable with how they will respond to a variety of market conditions. I strongly recommend looking up Fabozzi's book, either at the library or the latest revision.

Thanks everyone, and I look forward to more discussion which will inevitably follow.
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