证券投资学之债券定价与风险管理(PPT 75页).ppt

1、第八章 债券定价与风险管理,2,主要内容,利率风险 久期 凸性 消极的债券组合管理,3,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。,4,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：,1、利率风险,6,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。,7,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）。,8,利率风险,例子：一种债券，息率为8% 。如果市场的竞

3、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%。,9,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 sufficiently

4、 to provide a fair total rate of return.,10,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 t

5、he investor receive only a fair rate of return.,11,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、,12,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 determin

7、es 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 a

8、s 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？,13,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：,14,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，则

9、收益上升。,15,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,16,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）,17,Change in

10、 Bond Price as a Function of Change in Yield to Maturity,18,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。,19,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%,20,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,2、Duration,22,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,23,例子：息率8%的债券（每年支付两次）与零息债券,24,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 know th

12、at 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.,25,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 20-ye

13、ar 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 the b

14、ond. The zero-coupon bond, by contrast, makes only one payment at maturity. Its time to maturity is a well defined concept.,26,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 as

15、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.,27,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。,28,Cash flows paid by 9% coupon, annual payment bond

16、 with 8-year maturity and 10 y-t-m,29,8%,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,30,Duration,当到期收益保持不变时，证券组合durati

17、on 是单个债券duration的加权和,31,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 immunizing portfolios from interest rate risk,32,Duration 和股票价格变化之间的关系,这里 表示债券价格的变化 是债券的初始价格 是到期收益的变化 是初始的到期收益,33,例子,Bond : coupon rate 8%, yield to maturity 8%, par value 1000, price

18、 1000, duration 10 when yield to maturity 8% 9%,34,What determines duration?,35,Rule for duration,1.零息债券的duration等于其到期日 2.到期日保持不变，息率越低， duration越高 3.息率不变，到期日越大， duration一般越大。对等价或者溢价发行的债券，上述关系总是成立 4.别的因素不变，到期收益越低，带息债券的duration越高。,36,Rules for Duration (contd),5.永久性现金流的duration为 到期日与duration的差别 当到期日越来

19、越大时， duration接近于相应永久性现金流的duration 注意支付时间单位与利率之间的一致性,37,Rules for Duration (contd),Rule 6 The duration of a level annuity is equal to:,38,The modified duration,3、Convexity,40,仅仅只需Duration就够了吗？,As a measure of interest rate sensitivity, duration clearly is a key tool in fixed income portfolio manageme

20、nt. The duration rule for the impact of interest rates on bond prices is only an approximation.,41,Yield,Price,Duration,Pricing Error from convexity,Duration and Convexity,42,The duration rule is a good approximation for small changes in bond yield, but it is less accurate for larger changes. The du

21、ration 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.,43,As a practical rule, we ca

22、n 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.,44,Correction for Convexity,Correction for Convexity:,45,The convexity is more important as a practical matter when pot

23、ential interest rate changes are large.,46,例子：,A 30-year 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 11.26years. If the bonds yield increase from 8% to 10%, the bond price will fall to $811.46, a decline of 18.

24、85%. The duration rule would predict The duration-with-convexity rule,47,If the change in yield were smaller ,0.1%, convexity would matter less.the price of the bond actually would fall to 988.85, a decline 1.115% .,48,Why do investors like convexity?,Bond A,Bond B,49,Bond A has greater price increa

25、ses and smaller price decreases when interest rates fluctuate by larger amounts.,4、Passive bond management,51,Passive methods 假设债券市场时半强有效的。证券选择(security selection)和决定交易时间(market timing)都是无用的，不会带来超平均的收益。 Active methods 假设债券市场不是非常有效的。通过准确预测利率来辨别误定价的债券或者制定交易时间，从而能够获得超额收益。,52,Passive methods,消极债券管理认为债券的

26、价格是公平的，只能控制固定收入证券组合的风险 主要策略： 指标化策略:复制给定债券指标的行为 Immunization 策略：shield the overall financial status of the institution from exposure to interest rate fluctuations.,53,两者认为市场价是公平的 两者的区别 债券-指标证券组合和债券市场指标具有相同的风险-收益回报 Immunization建立了零风险的证券组合，利率的波动对公司的价值没有影响。,54,Bond-index funds Create a portfolio that mi

27、rrors the composition of an index that measures the broad market. 债券市场指标 Lehman Brothers, Merrill Lynch, Salomon Brothers Number of issues maturity of included bonds excluded issues weighting reinvestment Daily availability,55,构造反映债券市场指标的证券组合 问题： 债券种类过多，难以一一购买 交易少，很难以公平市价买到指标中包含的所有债券 指标不断更换到期日少于1年的债

28、券 不断调整，利息收入重投资 方法：精确复制债券指标不可行，采用cellular方法 把债券市场分成几类 指标中债券在各类中占的比例 按这一比例构造债券组合,56,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

29、 likewise should match the index.,57,58,Immunization,两种不同的看待利率风险的方式 银行，使得资产净现值不受利率波动的影响 养老金，使得资产将来的值不受利率风险的影响 What is common to the bank and the pension fund is interest rate risk. The net worth of the firm or the ability to meet future obligations fluctuates with interest rates. 通过适当调整证券组合的到期日结构，规避

30、利率风险 Immunization techniques refer to strategies used by such investors to shed their overall financial status from exposure to interest rate fluctuations.,59,Net worth immunization F. M. Redington,60,例子：,承诺在两年后支付1000000元，有两种债券可供选择： 债券 1年 2年 3年 yield 1 80 80 1080 10% 2 1070 10%,61,例子：,保险公司以价格10000元发

31、行一种guaranteed investment contract(GIC)，5年到期，保证利率为8%。 假设公司选择息率8%，6年到期、价格为10000元的带息债券为债务提供基金。 价格风险 重投资风险,62,Terminal value of a bond portfolio after 5 years (all proceeds reinvested) A. rates remain at 8%,63,Terminal value of a bond portfolio after 5 years (all proceeds reinvested) B. rates fall to 7%

32、,64,Terminal value of a bond portfolio after 5 years (all proceeds reinvested) C. rates increase to 9%,65,For a horizon equal to the portfolios duration, price risk and reinvestment risk exactly cancel out.,66,Accumulated value of invested funds funds 0 t* D t,67,Figure Immunization,68,在8%，资产和债务的现值相

33、等；当利率变化幅度不大时，资产和债务的值的变化量相等；当利率变化幅度很大时，资产和债务值的变化量不再相等。,69,Rebalancing immunized portfolio,当资产的收益变化时，其久期也发生了变化，这时，资产和债务的久期不再相匹配。 即使利率不变，当时间变化时，久期也会发生变化,70,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 por