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1、第八章 债券定价与风险管理,1,主要内容,利率风险 久期 凸性 消极的债券组合管理,2,这里所谓的风险管理，是针对债券的利率风险控制，而债券本身的风险（例如，违约风险）不在讨论范围之内。,3,积极策略（Active strategy）： attempts to achieve returns greater than to those commensurate with the risk borne. Trade on interest rate predictions Trade on market inefficiencies 消极策略（Passive strategy）：takes ma
2、rket prices of securities as fairly set. Control risk Balance risk and return,管理固定收益证券的基本策略：,4,1、利率风险,5,利率风险,当利率上涨和下降时，债券持有者就会面临资金损失和收益。这些损失或者收益使得在债券投资中，即使利息和本金支付能够保证得到（例如国债），投资者也面临风险。,6,利率风险,为什么利率变动时，债券价格会变动？ 在一个完全竞争市场中，所有的证券提供的都是公平合理的期望回报率（fair expected rates of return）。,7,利率风险,例子：一种债券，息率为8% 。如果市场
3、的竞争收益率为8% ，则它的价格为面值。 如果市场竞争收益率上升为9%，则债券价格将下降，以使得总期望回报率为9%。 如果市场的竞争收益率下降为7%，则债券价格将上升，以使得总期望回报率为9%。,8,利率风险：折价债券,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 below-market coupon rate just sufficient
4、ly to provide a fair total rate of return.,9,利率风险：溢价债券,If the coupon rate exceeds the market interest rate, the interest income 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
5、the investor receive only a fair rate of return.,10,利率风险：公平合理的期望回报率,Each bond offers investors the fair total rate of return. Although the capital gain versus income components differ, the price of each bond is set to provide competitive rates, as we should expect in well-functioning capital markets
6、.,11,利率风险,债券价格受市场的影响，市场利率波动是固定收入证券市场的主要风险根源。 价格和收益率之间的反向关系：The inverse relationship between price and yield is a central feature of fixed-income securities. 决定价格对利率波动敏感度一个关键因素是到期日。Interest rate fluctuations represent the main source of risk in the fixed-income market, and one key factor that determi
7、nes 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 short-term Treasury securities such
8、as T-bills 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. 到期日是唯一因素吗？,12,债券定价定理：定性描述利率风险,债券定价定理：说明市场收益变化和价格变动之间的关系（定性描述）。假设每年支付一次利息，以到期收益为研究对象：,13,债券定价定理：定性描述利率风险,1. 如果债券的市场价格上升，则收益下降；反过来，如果债券价格下降，
9、则收益上升。,14,债券定价定理：定性描述利率风险,2. 如果债券的收益在到期日之前不变，则它的折价或者酬金的规模将随着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,15,债券定价定理：定性描述利率风险,3. 如果债券的收益在到期日之前不变，则它的折价或者酬金的规模变化速度随着到期日的靠近加快。 4. 当债券的收益上升和下降相同的数量时，收益上升导致价格下降的规模，小于收益下降导致价格上升的规模。（凸性）,16,Change i
10、n Bond Price as a Function of Change in Yield to Maturity,17,债券定价定理：定性描述利率风险,5.长期债券的价格对利率变化的敏感度大于短期债券的敏感度。即，长期债券有更大的利率风险。 6.债券的息率越高，由收益变化导致的价格变化的百分比越小。,18,例子,Bond G: coupon rate=7%, yield=7%, P=1000 Bond H: coupon rate=9%, yield=7%, P=1082 when yield change to be 8% bond G: price 1000 960.03, 3.993%
11、 bond H: price 1082 1039.93 3.889%,19,债券定价定理：定性描述利率风险,7. 债券发行时的初始到期收益越低，则它对收益变化的敏感度越大。 债券价格对市场利率变化的敏感度受三个关键因素的影响：到期日，息率，到期收益,20,2、Duration,21,仅仅只用到期日描述利率风险是不够的,债券定价定理说明，到期日是决定利率风险的主要因素，但是，仅仅只有到期日不能完全度量债券价格对利率的敏感度。例如债券B、C,22,例子：息率8%的债券（每年支付两次）与零息债券,23,例子说明,这里的到期日并不是债券长期或者短期的完美度量。 有效到期日：Because we kno
12、w 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 longer-term bond than an equal-time-maturity coupon bond. This is the insight about effective maturity.,24,例子说明:有效到期日,比较20年到期的零息债券和带息债券(8% coupon rate)。 The 2
13、0-year 8% bond makes many coupon payments, most of which come years before the bonds 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 t
14、he bond. The zero-coupon bond, by contrast, makes only one payment at maturity. Its time to maturity is a well defined concept.,25,例子说明:有效到期日,To deal with the ambiguity of the maturity of a bond making many payments, we need a measure of the average maturity of the bonds promised cash flows to serve
15、 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.,26,Duration,这里 表示在时间 接受的现金流的现值，利用债券的到期收益作为折现率得到。 表示债券现在的市场价格。 表示债券剩下的距到期日的时间。,27,Cash flows paid by 9% coupon, annual payment
16、bond with 8-year maturity and 10 y-t-m,28,8%,Bond,Time,years,Payment,PV of CF,(5% per period),Weight,C1 X,C4,0.5,40,38.095,.0395,.0197,1,40,36.281,.0376,.0376,1.5,2.0,40,1040,sum,34.553,855.611,964.540,.0358,.,8871,1.000,.0537,1.7742,1.8852,Duration Calculation: Example,29,Duration,当到期收益保持不变时，证券组合duration 是单个债券duration的加权和,30,Duration,Duration 在固定收益投资组合管理中的作用 测量证券组合有效平均到期日的统计量 度量证券组合对利率的敏感度（定量刻画） an essential tool in
