【正文】 oupon 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)。 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。即，長期債券有更大的利率風(fēng)險。 ? 表示債券現(xiàn)在的市場價格。 ? 永久性現(xiàn)金流的 duration為 ? 到期日與 duration的差別 ? 當?shù)狡谌赵絹碓酱髸r， duration接近于相應(yīng)永久性現(xiàn)金流的 duration ? 注意支付時間單位與利率之間的一致性 yy?1 Convexity ? As a measure of interest rate sensitivity, duration clearly is a key tool in fixed ine portfolio management. ? The duration rule for the impact of interest rates on bond prices is only an approximation. Yield Price Duration Pricing Error from convexity Duration and Convexity ? The duration rule is a good approximation for small changes in bond yield, but it is less accurate for larger changes. ? The duration approximation always understates the value of the bond, it underestimates the increase in bond price when the yield falls, and it over estimates the decline in price when the yield rises. ? The curvature of the price yield curve is called the convexity of the bond. ? As a practical rule, we can view bonds with higher convexity as exhibiting higher curvature in the price yield relationship. ? Convexity allows us to improve the duration approximation for bond price changes. Correction for Convexity ???????? ?????nttt ttyCFyPC o n v e x ity122 )()1()1(1Correction for Convexity: ])([21 2yC o n v e i x it yyDPP ????????? Ex. A 30year maturity, an 8% coupon, and sells at an initial yield to maturity of 8%. The bond sells at par value, $1000. The modified duration is . If the bond?s yield increase from 8% to 10%, the bond price will fall to $, a decline of %. ? The duration rule would predict ? The durationwithconvexity rule ? y %* ????????? yDPP%])([2122???????????????? yC o n v e i x i t yyDPPWhy do investors like convexity? y_y ?y? Bond A Bond B ? Bond A has greater price increases and smaller price decreases when interest rates fluctuate by larger amounts. Passive bond management ? Passive methods ? 假設(shè)債券市場時半強有效的。 Passive methods ? 消極債券管理認為債券的價格是公平的，只能控制固定收入證券組合的風(fēng)險 ? 主要策略： ? 指標化策略 :復(fù)制給定債券指標的行為 ? Immunization 策略： shield the overall financial status of the institution from exposure to interest rate fluctuations. ? 兩者認為市場價是公平的 ? 兩者的區(qū)別 ? 債券 指標證券組合和債券市場指標具有相同的風(fēng)險 收益回報 ? Immunization建立了零風(fēng)險的證券組合，利率的波動對公司的價值沒有影響。 ? 當資產(chǎn)的收益變化時，其久期也發(fā)生了變化，這時，資產(chǎn)和債務(wù)的久期不再相匹配。設(shè) 為零息債券的權(quán) ?711)1(3 ????? ????? 第二年，債務(wù)的現(xiàn)值為 11000元，資金也變?yōu)?11000元：零息債券 5500元，永久性500+5000元 ? 第 2年，即使利率不變，經(jīng)理也需要調(diào)整策略 611)1(2 ????? ??95??? An appropriate promise must be established between the desire for perfect immunization and the need to control trading costs. ? Immunization 在實際中 的問題 ? The notion of duration is strictly valid only for a flat yield curve. ? multiple nonparallel shifts in a nonhorizontal yield curve ? 通貨膨脹 ? On this note, it is worth pointing out that immunization is a goal that may well be inappropriate for many investors who would find a zerorisk portfolio strategy unduly conservative. Full immunization is a fairly extreme position for a portfolio manager to pursue. Active bond management ? Interest rate forecasting ? identification of relative mispricing 演講完畢，謝謝觀看！