英文早读第165篇，选自巴菲特年度信，友才翻译。

Maturity and the Mathematics of Bonds
债券期限和算法

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.
很多人在购买债券时，基于他们认为他们想持有债券多久或者他们还能活多久等等来选择期限。尽管这不是一个愚蠢的方式，但也不是最符合逻辑的。在选择期限时首要考量点或许应该是（1）利率走向；（2）你对未来利率水平的预期和（3）你愿意对报价浮动程度的忍耐程度和希望可能获得的利润。当然，第（2）点是最重要的但是到目前是最困难的能够明智的预测。

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.
首先让我们处理下利率走向。当其它质量方面是一致的，支付的利息基于债券期限有所区别。例如，一个优质债券如果六到九个月到期或许可以提供4.75%的利率，2年期5.00%，5年期5.25%，10年期5.50%和20年期6.25%。当长期利率远高于短期利率时，这个曲线是所谓的强正向。在美国政府债券市场，利率最近倾向于产生负相关利率曲线；也就是说，一个长期政府债过去超过一年持续利率低于短期债券。有时这个利率曲线很平，有时他在指定点前正相关，例如十年期，然后变平。你应该理解他有所区别，经常很大，从历史来看当前的利率倾向于是历史正相关高点。这并不意味着长期债券将会更值钱但他确实意味着你将会比很多时期收到更多延长期限的费用。如果利息保持稳定很多年，长期债券将会比短期债券对你更好，不管你希望持有他们多久。

The second factor in determining maturity is expectations regarding future rate levels. Anyone who has done much predicting in this fields 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.
第二个决定期限的因素是你对未来利息的预期。任何在这个领域更有预测性的人都很快倾向于显得很傻。在一年我不会想到利息是没吸引力的，几乎立刻我就被证明是非常错的。我相信现在的利率也不是没有吸引力，但我或许再一次看起来愚蠢。然而，决定必须要做，你可以犯很大的错误如果你现在以可获得利息购买短期债券然后几年后再投资是利息低很多。

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.
最后一个因素包括你对报价浮动的容忍。这包括债券投资的算法，对你们来说理解起来或许有些困难。然而，你能够对这个规则大体有了解是很重要的。让我们假设此刻一个完美的稳定的利息曲线和不可赎回的债券。进一步假设当前利息是5%然后你购买两个债券，一个是两年期一个是二十年期。现在假设一年后新发行债券利息降到了3%，你希望出售你的债券。不管市场波动、手续费等，你将从两年期（现在只剩一年运营）债券原始1000美金投资中收到1019.60美金，而你将从19年期债券（原始20年）收到1288.10美金。以这个价格，购买者在将他的钱摊还了他支付的溢价和从每个债券中5%息票收到的现金后折算也正好是以1000美金计的3%。另一方面，让我们假设利息涨到了7%。我们再一次忽视市场波动、手续费、折扣所得的本金获利税等等。现在购买者将会支付给只剩1年到期的债券981美金和给剩19年到期的债券791.60美金。既然它可以在新发行上得到7%，他只会愿意你充分的折扣价购买你的债券这样累计的折扣将会给他从你5%息票上获得的经济利益相比于1000美金购买7%息票同等收益。

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.
原理是简单的。利率浮动越大，债券越长期，债券价值就越能够在到期之前中间上上下下。需要指出在第一个例子中当利率降到3%，如果它可以按5年期赎回，我们的长期债券将仅仅涨到大约1070美金，尽管当利率为7%时他还会下降那么多。这仅仅说明赎回条款内在的不公平性。

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.
对于超过20年，免税债券利率机会持续上涨而长期债券购买者也持续受损。这并不意味着现在购买长期债券是糟糕的——他仅仅意味着上面段落里的解释很长一段时间仅仅在一个方向上起作用，而人们更加担心利率从高位下降而不是从潜在低位上涨。

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.
如果有50对50的概率在未来利率水平上且利率曲线是正相关的，更大概率购买长期不可赎回债券要比短期债券要好。这反映了我现在的结论，因此，我倾向于购买10年到25年期的债券。如果你有在这个范围的喜好，我们将会试图选择一些反应你喜好的债券，但如果你对短期债券感兴趣，我们将无法帮助到你，因为我们没有在这个领域搜寻过债券。

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.
在你决定购买20年期债券之前，回过头看看表明价格将会如何基于利率变化而改变的这一段。当然，如果你一直持有这个债券，你将继续得到约定利率，但是如果你提前出售，你将收到那段描述的计算作用的影响，更好或更糟。债券价格同样会因为质量变化而改变，但是，在免税债券领域，倾向于——或许将继续倾向于——相比于在利率结构变化的影响是相对微小的因素。

71.maturity：成熟；到期
72.mathematics：计算；运算
73.silly：愚蠢的；傻的；荒唐的
74.endure：忍耐；容忍；持久；持续
75.intelligently：明智地；聪明地
76.tackle：解决；处理；应付；交涉
77.flatten：把…弄平
78.slope：斜坡，斜率；斜面
79.commission：佣金；手续费；委员会
80.amortize：分期偿还；摊还
81.accrual：（投资的）累加；（利息的）自然累积