巴菲特致合伙人的信（1970年2月25日）⑥债券的期限和计算

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 are 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.

债券的期限和计算

许多买债券的人在选择期限时的依据是，他们觉得要持有债券多长时间，或者他们觉得自己能活多长时间。这种做法没什么大错，但不是最符合逻辑的。选择债券期限的主要决定因素有三点：(1)收益率曲线的形状；(2)你对将来利率的预期；(3)报价波动有多大，你是否承受得了，是否想从中获利。这里面的第二点最重要，也是最不好说的。

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.

我们先讲收益率曲线。在各方面的质地都相同的情况下，债券的期限不同，利率也不一样。以当前评级最高的债券为例，期限为6到9个月的，收益率是4.75%；2年的，5.00%；5年的，5.25%；10年的，5.50%；20年的，6.25%。当长期利率远高于短期利率时，我们说收益率曲线向上倾斜。在美国政府债券市场，最近的收益率曲线是向下倾斜的，在过去一年里，长期政府债券的收益率始终低于短期债券。有时候收益率曲线是非常平坦的，有时候是向上倾斜，然后趋于平坦（例如，向上倾斜十年，之后趋于平坦）。各位需要知道的是，收益率曲线会经常出现显著变化。从历史情况来看，当前的收益率曲线可能会出现向上倾斜的情况。在这种情况下，长期债券不会更值钱，只是和其他时期相比，购买期限更长的债券，获得的利息更高。如果收益率在几年内保持不变，则无论你打算持有多长时间，期限较长的债券都会比期限较短的债券给你带来更多的收益。

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.

在选择债券期限时，第二个要考虑的因素是将来的利率水平。经常预测利率的人总是被打脸。一年前，我觉得利率不低，没过多长时间，事实就表明我完全错了。现在我也觉得利率不低，事实可能还会证明我不对。不管怎么样，判断是必须做的。你要是决定现在买短期品种，结果过几年再投资时利率大跌，你也一样是犯了大错。

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 $791.60 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.

最后要考虑的是，你能否承受得起市场报价的波动。这里面涉及债券投资的数学计算，理解起来可能有难度，但是你必须要知道是怎么算的。现在假设收益率曲线完全是平的，债券是不可赎回的。再假设当前的利率是5%，你买了两只债券，一只是2年后到期，一只是20年后到期。假设一年后，新发行债券的收益率变成了3%，你想把自己的债券卖了。完全忽略市场差价、手续费等因素，原来买的2年期债券（现在剩一年了）能卖1,019.60美元，原来的20年期债券（现在剩19年了）能卖1,288.10美元。按这些价格，对于买家来说，将支付的溢价摊销并将每只债券5%的现金流兑现后，获得的恰好是3%的收益率。对于买家来说，是支付1,288.10美元买你的票面利率为5%的19年期债券，还是支付1,000.00美元买新发行的票面利率为3%的债券（我们假设一年后的现行利率是3%），没任何区别。再假设利率变成了7%，还是不考虑手续费、资本利得税等因素。现在那只还有一年到期的债券，买家只会出981.00美元，那只还有19年到期的，只会出791.60美元。因为他能买到利率为7%的新发行的债券，所以只有你的债券有折价，折价购买你票面利率为5%的债券和以1,000.00美元购买票面利率为7%的债券收益相同时，他才会买你的。

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.

道理很简单。利率的波动越大、债券的期限越长，在到期之前，债券价值越容易出现暂时性的大起大落。有一点要指出的是，在第一个例子中，我们假设利率变成3%，如果我们购买的长期债券可以在五年后以面值赎回，那么它只能升到1,070.00美元，但是如果利率上涨到7%，这只债券跌的一样多。这说明了赎回条款是不合理的。

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.

在过去二十年里，免税债券的利率一直在上涨，购买长期债券的投资者一直很吃亏。虽然如此，不是说买长期债券就不好。我们在上面的例子中讲了利率的上下波动，但在过去很长一段时间里，利率一直只朝一个方向波动。和以前相比，现在人们越来越觉得利率比较高，可能要下调了，而不是觉得利率太低，还有上升空间。

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.

将来的普遍利率水平可能高，也可能低，概率是对半开，而且当前的收益率曲线是显著向上倾斜的，与买入短期债券相比，还是买长期不可赎回的债券赢面比较大。这是我现在得出的结论，所以我打算买入期限为10到20年的债券。如果你也看好这个期限范围内的债券，我们可以帮你挑选。如果你想买期限较短的，我们就帮不上忙了，因为我们没研究期限较短的。

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.

请先回头阅读债券价格如何因利率变化而变动的部分，然后再决定是否购买20年期的债券。如果你一直持有到期，你会获得合约规定的利率，如果你提前卖出，会受到我们已经计算过的情形的影响，可能赚，也可能赔。在很长时间内，债券质地会逐渐发生变化，债券价格也因此产生变动。但是对于免税债券来说，无论在现在还是将来，引起价格变动的主要因素还是利率的变化。