【正文】 ? 對(duì)永久性現(xiàn)金流，在利率 10%之下的久期是11年。 ? 即使利率不變，當(dāng)時(shí)間變化時(shí)，久期也會(huì)發(fā)生變化 ? Rebalancing immunized portfolio ? Even if an obligation is immunized at the outset, as time passes the durations of the asset and liability will fall at different rates. Without portfolio rebalancing, durations will bee unmatched and the goals of immunization will not be realized. ? Immunization is a passive strategy only in the sense that it does not involve attempts to identify undervalued securities. Immunization mangers still actively update and monitor their positions. ? 例子：假設(shè)證券組合經(jīng)理在 7年后有一筆19487元的債務(wù)，以現(xiàn)在 10%的市場(chǎng)利率計(jì)算現(xiàn)值為 10000元。 ? 價(jià)格風(fēng)險(xiǎn) ? 重投資風(fēng)險(xiǎn) ? ? 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 risk and reinvestment risk exactly cancel out. ? Accumulated value of invested funds ? funds ? 0 t* D t ? value ? 10000 ? 6000 ? 8% interest rate Coupon bond Single payment obligation ? 在 8%，資產(chǎn)和債務(wù)的現(xiàn)值相等；當(dāng)利率變化幅度不大時(shí)，資產(chǎn)和債務(wù)的值的變化量相等；當(dāng)利率變化幅度很大時(shí)，資產(chǎn)和債務(wù)值的變化量不再相等。 ? Bondindex funds ? Create a portfolio that mirrors the position of an index that measures the broad market. ? 債券市場(chǎng)指標(biāo) ? Lehman Brothers, Merrill Lynch, Salomon Brothers ? Number of issues ? maturity of included bonds ? excluded issues ? weighting ? reinvestment ? Daily availability ? 構(gòu)造反映債券市場(chǎng)指標(biāo)的證券組合 ? 問(wèn)題： ? 債券種類過(guò)多，難以一一購(gòu)買 ? 交易少，很難以公平市價(jià)買到指標(biāo)中包含的所有債券 ? 指標(biāo)不斷更換到期日少于 1年的債券 ? 不斷調(diào)整，利息收入重投資 ? 方法：精確復(fù)制債券指標(biāo)不可行，采用 cellular方法 ? 把債券市場(chǎng)分成幾類 ? 指標(biāo)中債券在各類中占的比例 ? 按這一比例構(gòu)造債券組合 ? In these way, the characteristics of the portfolio in terms of maturity, coupon rate, credit risk, industrial representation, and so on, will match the characteristics of the index, and the performance of the portfolio likewise should match the index. Sector TtM Treasury Agency MortgageBacked Industrial Finance Utility Yankee 1 year % 13 years % 35 years % 57 years 710 years % 1015 years 1530 years % % 30+ years Immunization ? 兩種不同的看待利率風(fēng)險(xiǎn)的方式 ? 銀行，使得資產(chǎn)凈現(xiàn)值不受利率波動(dòng)的影響 ? 養(yǎng)老金，使得資產(chǎn)將來(lái)的值不受風(fēng)險(xiǎn)的影響 ? What is mon to the bank and the pension fund is interest rate risk. The worth of the firm or the ability to meet future obligations fluctuates with interest rates. ? 通過(guò)適當(dāng)調(diào)整證券組合的到期日結(jié)構(gòu)，規(guī)避利率風(fēng)險(xiǎn) ? Immunization techniques refer to strategies used by such investors to shed their overall financial status from exposure to interest rate fluctuations. ? Net worth immunization ? 例子：承諾在兩年后支付 1000000元，有兩種債券可供選擇： ? 債券 1年 2年 3年 yield ? 1 80 80 1080 10% ? 2 1070 10% ? 121 ??ww 21 ???? ww? 例子：保險(xiǎn)公司以價(jià)格 10000元發(fā)行一種guaranteed investment contract(GIC)， 5年到期，保證利率為 8%。通過(guò)準(zhǔn)確預(yù)測(cè)利率來(lái)辨別誤定價(jià)的債券或者制定交易時(shí)間，從而能夠獲得超額收益。證券選擇(security selection)和決定交易時(shí)間 (market timing)都是無(wú)用的，不會(huì)帶來(lái)超平均的收益。對(duì)等價(jià)或者溢價(jià)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。 ? 表示債券剩下的距到期日的時(shí)間。 ? 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