債券定價(jià)和風(fēng)險(xiǎn)管理概述-免費(fèi)閱讀
【正文】 ? 當(dāng)資產(chǎn)的收益變化時(shí)，其久期也發(fā)生了變化，這時(shí)，資產(chǎn)和債務(wù)的久期不再相匹配。 ? 永久性現(xiàn)金流的 duration為 ? 到期日與 duration的差別 ? 當(dāng)?shù)狡谌赵絹碓酱髸r(shí)， duration接近于相應(yīng)永久性現(xiàn)金流的 duration ? 注意支付時(shí)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(shí)半強(qiáng)有效的。即，長期債券有更大的利率風(fēng)險(xiǎn)。 ? The inverse relationship between price and yield is a central feature of fixedine securities. Interest rate fluctuations represent the main source of risk in the fixedine market, and one key factor that determines that sensitivity is the maturity of the bond. A general rule in evaluating bond price risk is that, keeping all other factors the same, the longer the maturity of the bond, the greater the sensitivity of price to fluctuations in the interest rate. This is why shortterm Treasury securities such as Tbills are considered to be the safest. They are free not only of default risk, but also largely free of price risk attributable to interest rate volatility. ? 當(dāng)息率等于市場利率時(shí)，價(jià)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(shí)，價(jià)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(jià)格 =70（） +1000（） = ? 一年后公平價(jià)格為 =70（） +1000（） = ? 過去的一年的回報(bào)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 p
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