Buffett: Maturity and the Mathematics of Bonds

Many people, in buying bonds, select maturities based on how long they think they are going to want to hold bonds, how long they sire going to live, etc. While this is not a silly approach, it is not necessarily the most logical. The primary determinants in selection of maturity should probably be (1) the shape of the yield curve; (2) your expectations regarding future levels of interest rates and (3) the degree of quotational fluctuation you are willing to endure or hope to possibly profit from. Of course, (2) is the most important but by far the most difficult upon which to comment intelligently.

Let’s tackle the yield curve first. When other aspects of quality are identical, there will be a difference in interest rates paid based upon the length of the bond being offered. For example, a top grade bond being offered now might have a yield of 4. 75% if it came due in six or nine months, 5. 00% in two years, 5. 25% in five years, 5. 50% in ten years and 6.25% in twenty years. When long rates are substantially higher than short rates, the curve is said to be strongly positive. In the U. S. Government bond market, rates recently have tended to produce a negative yield curve; that is, a long term Government bond over the last year or so has consistently yielded less than a short term one. Sometimes the yield curve has been very flat, and sometimes it is positive out to a given point, such as ten years, and then flattens out. What you should understand is that it varies, often very substantially, and that on an historical basis the present slope tends to be in the high positive range. This doesn’t mean that long bonds are going to be worth more but it does mean that you are being paid more to extend maturity than in many periods. If yields remained constant for several years, you would do better with longer bonds than shorter bonds, regardless of how long you intended to hold them.

The second factor in determining maturity selection is expectations regarding future rate levels. Anyone who has done much predicting in this field has tended to look very foolish very fast. I did not regard rates as unattractive one year ago, and I was proved very wrong almost immediately. I believe present rates are not unattractive and I may look foolish again. Nevertheless, a decision has to be made and you can make just as great a mistake if you buy short term securities now and rates available on reinvestment in a few years are much lower.

The final factor involves your tolerance for quotational fluctuation. This involves the mathematics of bond investment and may be a little difficult for you to understand. Nevertheless, it is important that you get a general grasp of the principles. Let’s assume for the moment a perfectly flat yield curve and a non-callable bond. Further assume present rates are 5% and that you buy two bonds, one due in two years and one due in twenty years. Now assume one year later that yields on new issues have gone to 3% and that you wish to sell your bonds. Forgetting about market spreads, commissions, etc. , you will receive $1,019.60 for the original two year $1, 000 bond (now with one year to run) and$1,288. 10 for the nineteen year bond (originally twenty years). At these prices, a purchaser will get exactly 3% on his money after amortizing the premium he has paid and cashing the stream of 5% coupons attached to each bond. It is a matter of indifference to him whether to buy your nineteen year 5% bond at $1,288. 10 or a new 3% bond (which we have assumed is the rate current – one year later) at $1, 000. 00. On the other hand, let’s assume rates went to 7%. Again we will ignore commissions, capital gains taxes on the discount, etc. Now the buyer will only pay $981. 00 for the bond with one year remaining until maturity and’ $791. 00 for the bond with nineteen years left. Since he can get 7% on new issues, he is only willing to buy your bond at a discount sufficient so that accrual of this discount will give him the same economic benefits from your 5% coupon that a 7% coupon at $1, 000. 00 would give him.

The principle is simple. The wider the swings in interest rates and the longer the bond, the more the value of a bond can go up or down on an interim basis before maturity. It should be pointed out in the first example where rates went to 3%, our long term bond would only have appreciated to about $1, 070. 00 if it had been callable in five years at par, although it would have gone down just as much if 7% rates had occurred. This just illustrates the inherent unfairness of call provisions.

For over two decades, interest rates on tax-free bonds have almost continuously gone higher and buyers of long term bonds have continuously suffered. This does not mean it is bad now to buy long term bonds – it simply means that the illustration in the above paragraph has worked in only one direction for a long period of time and people are much more conscious of the downside risks from higher rates than the upside potential from lower ones.

If it is a 50-50 chance as to the future general level of interest rates and the yield curve is substantially positive, then the odds are better in buying long term non-callable bonds than shorter term ones. This reflects my current conclusion and, therefore, I intend to buy bonds within the ten to twenty-five year range. If you have any preferences within that range, we will try to select bonds reflecting such preferences, but if you are interested in shorter term bonds, we will not be able to help you as we are not searching out bonds in this area.

Before you decide to buy a twenty year bond, go back and read the paragraph showing how prices change based upon changes in interest rates. Of course, if you hold the bond straight through, you are going to get the contracted rate of interest, but if you sell earlier, you are going to be subject to the mathematical forces described in that paragraph, for better or for worse. Bond prices also change because of changes in quality over the years but, in the tax-free area, this has tended to be – and probably will continue to be – a relatively minor factor compared to the impact of changes in the general structure of interest rates.

This article is an excerpt of Buffett Partnership Letter, February 25th, 1970

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