【文章內(nèi)容簡介】 ate volatility. ? 當(dāng)息率等于市場利率時，價格等于面值 ? In these circumstances, the investor receives fair pensation for the time value of money in the form of the recurring interest payments. No further capital gain is necessary to provide fair pensation. ? 當(dāng)息率小于市場利率時，價格小于面值 ? The coupon payments alone will not provide investors as high a return as they could earn elsewhere in the market. To receive a fair return on such an investment, investors also need to earn price appreciation on their bonds. The bond would have to sell below par value to provide a “builtin” capital gain on the investment. ? 例子：面值 1000元，息率 7%，公平利率 8%，三年到期 ? 現(xiàn)在公平價格 =70（） +1000（） = ? 一年后公平價格為 =70（） +1000（） = ? 過去的一年的回報率為 70+ ? When bond prices are set according to the present value formula, any discount from par value provides an anticipated capital gain that will augment a belowmarket coupon rate just sufficiently to provide a fair total rate of return. ? If the coupon rate exceeds the market interest rate, the interest ine by itself is greater than available elsewhere in the market. The price is greater than the par value, the resulting capital losses offset the large coupon payments so that the investor receive only a fair rate of return. ? Each bond offers investors the fair total rate of return. Although the capital gain versus ine ponents differ, the price of each bond is set to provide petitive rates, as we should expect in wellfunctioning capital markets. ? Security returns all should be parable on an aftertax riskadjusted basis. If they are not, investors will try to sell lowreturn securities, thereby deriving down the prices until the total return at the now lower price is petitive with other securities. Prices should continue to adjust until all securities are fairly priced in that expected returns are appropriate(given necessary risk and tax adjustments) 2. Fixedine portfolio management ? 這里所謂的風(fēng)險管理，是針對債券的利率風(fēng)險控制，而債券本身的風(fēng)險（例如，違約風(fēng)險）不在討論范圍之內(nèi)。 利率風(fēng)險 ? As interest rates rise and fall, bondholders experience capital losses and gains. These gains or losses make fixedine investments risky, even if the coupon and principal payments are guaranteed, as in the case of Treasury obligations. ? Why do bond prices respond to interest rate fluctuations? ? In a petitive market all securities must offer investors fair expected rates of return. ? The sensitivity of bond prices to changes in market interest rates is obviously of great concern to investors. ? 債券定價定理：說明市場收益變化和價格變動之間的關(guān)系（定性描述）。假設(shè)每年支付一次利息，以到期收益為研究對象： ? 1. 如果債券的市場價格上升，則收益下降；反過來，如果債券價格下降，則收益上升。 ? 2. 如果債券的收益在到期日之前不變，則它的折價或者酬金的規(guī)模將隨著到期日的接近而下降。 Today Maturity Date Par Value Price of a premium bond Price of a discount bond premium discount ? 3. 如果債券的收益在到期日之前不變，則它的折價或者酬金的規(guī)模變化速度隨著到期日的靠近加快。 ? 4. 當(dāng)債券的收益上升和下降相同的數(shù)量時，收益上升導(dǎo)致價格下降的規(guī)模，小于收益下降導(dǎo)致價格上升的規(guī)模。 ? 5. 債券的息率越高，由收益變化導(dǎo)致的價格變化的百分比越小。 例子 ? Bond C: coupon rate=7%, yield=7%, P=1000 ? Bond D: coupon rate=9%, yield=7%, P=1082 ? when yield change to be 8% ? bond C: price 1000 , % ? bond D: price 1082 % ? 6. 長期債券的價格對利率變化的敏感度大于短期債券的敏感度。即，長期債券有更大的利率風(fēng)險。 ? 7. 債券發(fā)行時的初始到期收益越低，則它對收益變化的敏感度越大。 ? 債券價格對市場利率變化的敏感度受三個關(guān)鍵因素的影響： 到期日，息率，到期收益 Duration ? The propositions confirm that maturity is a major determinant of interest rate risk. However, the also show that maturity alone is not sufficient to measure interest rate sensitivity. 例子：息率 8%的債券 Y i e l d t om a t u r i t yT = 1 y e a r T = 1 0 y e a r s T = 2 0 y e a r s8% 1000 1000 10009 9 9 0 . 6 4 9 3 4 . 9 6 9 0 7 . 9 9C h a n g e i np r i c e0 . 9 4 % 6 . 5 % 9 . 2 0 %Y i e l d t om a t u r i t yT = 1 y e a r T = 1 0 y e a r s T = 2 0 y e a r s8% 9 2 4 .5 6 4 5 6 .3 9 2 0 8 .2 99 9 1 5 .7 3 4 1 4 .6 4 1 7 1 .9 3C h a n g e i np r i c e0 .9 6 % 9 .1 5 % 1 7 .4 6 %? Because we know that long term bonds are more sensitive to interest rate movements than are short term bonds, in some sense a zero coupon bond represents a longerterm bond than an equaltimematurity coupon bond. This is the insight about effective maturity. ? 比較 20年到期的零息債券和帶息債券 (8% coupon rate)。 ? The 20year 8% bond makes many coupon payments, most of which e years before the bond?s maturity date. Each of these payments may be considered to have its own “maturity date”, and the effective maturity of the bond is therefore some sort of average of the maturities of all the cash flows paid out by the bond. ?