【正文】 ，則定價過低 (underpriced)。 ? 如果 ，則定價過高 (overpriced)。 ? ??? ??ntttyCV1*1?V? 為了利用 Capitalization of Ine Method of Value，必須決定 ， ， 的值。 ? 期限結(jié)構(gòu) (different maturities)：不同到期日 ? 風(fēng)險結(jié)構(gòu) (different default risk)：不同違約風(fēng)險 ? yield spread：兩種債券之間的收益差。 ? 例子：前面例子里的債券與下面的國庫券比較：面值 1000元，息率 5%，價格 。 5年后，類似的5年期的債券的收益為 8%。 ? Put provisions ? putable bonds ? 當(dāng)利率上漲時，投資者采用該策略 ? Tax status ? 因為稅收的延遲性，低息債券比高息債券有更高的內(nèi)在價值。投資者并不真正期望獲得 26%的回報率，他們預(yù)期不可能得到所有承諾支付，以期望現(xiàn)金流為基礎(chǔ)的收益遠遠小于以承諾現(xiàn)金流為基礎(chǔ)的收益。 dp??1ddppyy???1?yyyppyyyddd ??????????????1?? 例子： ?dp ??? ?y ??? ???d? One particular manner in which yield spreads seem to very over time is related to the business cycle. Yield spreads tend to be wider when the economy is in a recession. Apparently, investors perceive a higher probability of bankruptcy when the economy is faltering, even holding bond ratings constant. They require a mensurately higher default premium. ? Risk premium ? 對風(fēng)險債券而言，它的期望到期收益和具有同樣到期日、息率的無風(fēng)險債券到期收益之間的差稱為風(fēng)險酬金。每種債券的風(fēng)險酬金為 0，但違約酬金顯然大于 0。 ? 例子： ? Default premium ? yield ? spread Risk premium Defaultfree yieldtoMaturity 12% promised yieldtomaturity 9% expected yieldtomaturity 8% yieldtomaturity on a defaultfree bond of similar and coupon rate 0% ? 債券的違約性越大，它對市場潛在的敏感度越大。 . Yield spread 的確定 ? 評估 yield spread 的四種測度： ? The extent to which the firm?s ine had varied over the preceding nine years(measured by the coefficient of variation of earningsthat is, the ratio of standard deviation of earnings to average earnings) ? The length of time that the firm had operated without forcing any of its creditors to take a loss. ? The ratio of the market value of the firm?s equity to the par value of its debt. ? The market value of the firm?s outstanding debt. ? Yield spread= ? +(earnings variability) ? (time without default) ? (equity/debt ratio) ? (market value of debt) ? This form of the relationship accounted for roughly 75% of the variation in the bond?s yield spread . 債券定價 ? 給定合理的利率，給債券公平定價 ? 何為合理利率？ ? 合理的利率（或者折現(xiàn)率）是由市場唯一確定的，包括： ? 實利率 ? 通貨膨脹率 ? yield spread ? 一級市場：以面值發(fā)行息率近似為市場收益率 ? 二級市場：債券價格受市場的影響，市場利率波動是固定收入證券市場的主要風(fēng)險根源。 ? 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。 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。 ? 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. ? The zerocoupon bond, by contrast, makes only one payment at maturity. Its time to maturity is a well defined concept. ? To deal with the ambiguity of the ?maturity? of a bond making many payments, we need a measure of the average maturity of the bond?s promised cash flows to serve as a useful summary statistic of the effective maturity of the bond. We would like also to use the measure as a guide to the sensitivity of a bond to interest rate changes. Duration ? 這里 表示在時間 接受的現(xiàn)金流的現(xiàn)值，利用債券的到期收益作為折現(xiàn)率得到。對等價或者溢價發(fā)行的債券，上述關(guān)系總是成立 ? 別的因素不變，到期收益越低，帶息債券的duration越高。通過準確預(yù)測利率來辨別誤定價的債券或者制定交易時間，從而能夠獲得超額收益。 ? 價格風(fēng)險 ? 重投資風(fēng)險 ? ? 4 6 9 0 0 0 05 ??? Terminal value of a bond portfolio after 5 years (all proceeds reinvested) ? A. rates remain at 8% 1 4 8 0 0 ? ?4? = 1 0 8 8 . 3 92 3 8 0 0 ? ?3? 1 0 0 7 . 7 73 2 8 0 0 ? ?2? 9 3 3 . 1 24 1 8 0 0 ? ?1? 8 6 45 0 8 0 0 8 0 0S a l e o f b o n d 0 1 0 8 0 0 / 1 . 0 8 1 0 0 0 01 4 6 9 3 . 2 8? Terminal value of a bond portfolio after 5 years (all proceeds reinvested) ? B. rates fall to 7% 1 4 8 0 0 ? ?4?2 3 8 0 0 ? ?3?3 2 8 0 0 ? ?2?4 1 8 0 0 ? ?1?5 0 8 0 0S a l e o f b o n d 0 1 0 8 0 0 / 1 . 0 71 4 6 9 4 . 0 5? Terminal value of a bond portfolio after 5 years (all proceeds reinvested) ? C. rates increase to 9% 1 4 8 0 0 ? ?4?2 3 8 0 0 ? ?3?3 2 8 0 0 ? ?2?4 1 8 0 0 ? ?1?5 0 8 0 0S a l e o f b o n d 0 1 0 8 0 0 / 1 . 0 91 4 6 9 6 . 0 2? For a horizon equal to the portfolio?s duration, price ri