證券投資學之債券定價與風險管理(PPT 75頁).ppt

1、第八章 債券定價與風險管理,2,主要內容,利率風險 久期 凸性 消極的債券組合管理,3,這里所謂的風險管理，是針對債券的利率風險控制，而債券本身的風險（例如，違約風險）不在討論范圍之內。,4,積極策略（Active strategy）： attempts to achieve returns greater than to those commensurate with the risk borne. Trade on interest rate predictions Trade on market inefficiencies 消極策略（Passive strategy）：takes ma

2、rket prices of securities as fairly set. Control risk Balance risk and return,管理固定收益證券的基本策略：,1、利率風險,6,利率風險,當利率上漲和下降時，債券持有者就會面臨資金損失和收益。這些損失或者收益使得在債券投資中，即使利息和本金支付能夠保證得到（例如國債），投資者也面臨風險。,7,利率風險,為什么利率變動時，債券價格會變動？ 在一個完全競爭市場中，所有的證券提供的都是公平合理的期望回報率（fair expected rates of return）。,8,利率風險,例子：一種債券，息率為8% 。如果市場的競

3、爭收益率為8% ，則它的價格為面值。 如果市場競爭收益率上升為9%，則債券價格將下降，以使得總期望回報率為9%。 如果市場的競爭收益率下降為7%，則債券價格將上升，以使得總期望回報率為9%。,9,利率風險：折價債券,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,利率風險：溢價債券,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,利率風險：公平合理的期望回報率,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,利率風險,債券價格受市場的影響，市場利率波動是固定收入證券市場的主要風險根源。 價格和收益率之間的反向關系：The inverse relationship between price and yield is a central feature of fixed-income securities. 決定價格對利率波動敏感度一個關鍵因素是到期日。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. 到期日是唯一因素嗎？,13,債券定價定理：定性描述利率風險,債券定價定理：說明市場收益變化和價格變動之間的關系（定性描述）。假設每年支付一次利息，以到期收益為研究對象：,14,債券定價定理：定性描述利率風險,1. 如果債券的市場價格上升，則收益下降；反過來，如果債券價格下降，則

9、收益上升。,15,債券定價定理：定性描述利率風險,2. 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)模將隨著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,債券定價定理：定性描述利率風險,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。 4. 當債券的收益上升和下降相同的數量時，收益上升導致價格下降的規(guī)模，小于收益下降導致價格上升的規(guī)模。（凸性）,17,Change in

10、 Bond Price as a Function of Change in Yield to Maturity,18,債券定價定理：定性描述利率風險,5.長期債券的價格對利率變化的敏感度大于短期債券的敏感度。即，長期債券有更大的利率風險。 6.債券的息率越高，由收益變化導致的價格變化的百分比越小。,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,債券定價定理：定性描述利率風險,7. 債券發(fā)行時的初始到期收益越低，則它對收益變化的敏感度越大。 債券價格對市場利率變化的敏感度受三個關鍵因素的影響：到期日，息率，到期收益,2、Duration,22,僅僅只用到期日描述利率風險是不夠的,債券定價定理說明，到期日是決定利率風險的主要因素，但是，僅僅只有到期日不能完全度量債券價格對利率的敏感度。例如債券B、C,23,例子：息率8%的債券（每年支付兩次）與零息債券,24,例子說明,這里的到期日并不是債券長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,例子說明:有效到期日,比較20年到期的零息債券和帶息債券(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,例子說明: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,這里 表示在時間 接受的現金流的現值，利用債券的到期收益作為折現率得到。 表示債券現在的市場價格。 表示債券剩下的距到期日的時間。,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,當到期收益保持不變時，證券組合durati

17、on 是單個債券duration的加權和,31,Duration,Duration 在固定收益投資組合管理中的作用 測量證券組合有效平均到期日的統(tǒng)計量 度量證券組合對利率的敏感度（定量刻畫） an essential tool in immunizing portfolios from interest rate risk,32,Duration 和股票價格變化之間的關系,這里 表示債券價格的變化 是債券的初始價格 是到期收益的變化 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,1.零息債券的duration等于其到期日 2.到期日保持不變，息率越低， duration越高 3.息率不變，到期日越大， duration一般越大。對等價或者溢價發(fā)行的債券，上述關系總是成立 4.別的因素不變，到期收益越低，帶息債券的duration越高。,36,Rules for Duration (contd),5.永久性現金流的duration為 到期日與duration的差別 當到期日越來

19、越大時， duration接近于相應永久性現金流的duration 注意支付時間單位與利率之間的一致性,37,Rules for Duration (contd),Rule 6 The duration of a level annuity is equal to:,38,The modified duration,3、Convexity,40,僅僅只需Duration就夠了嗎？,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 假設債券市場時半強有效的。證券選擇(security selection)和決定交易時間(market timing)都是無用的，不會帶來超平均的收益。 Active methods 假設債券市場不是非常有效的。通過準確預測利率來辨別誤定價的債券或者制定交易時間，從而能夠獲得超額收益。,52,Passive methods,消極債券管理認為債券的

26、價格是公平的，只能控制固定收入證券組合的風險 主要策略： 指標化策略:復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.,53,兩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險-收益回報 Immunization建立了零風險的證券組合，利率的波動對公司的價值沒有影響。,54,Bond-index funds Create a portfolio that mi

27、rrors the composition of an index that measures the broad market. 債券市場指標 Lehman Brothers, Merrill Lynch, Salomon Brothers Number of issues maturity of included bonds excluded issues weighting reinvestment Daily availability,55,構造反映債券市場指標的證券組合 問題： 債券種類過多，難以一一購買 交易少，很難以公平市價買到指標中包含的所有債券 指標不斷更換到期日少于1年的債

28、券 不斷調整，利息收入重投資 方法：精確復制債券指標不可行，采用cellular方法 把債券市場分成幾類 指標中債券在各類中占的比例 按這一比例構造債券組合,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,兩種不同的看待利率風險的方式 銀行，使得資產凈現值不受利率波動的影響 養(yǎng)老金，使得資產將來的值不受利率風險的影響 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. 通過適當調整證券組合的到期日結構，規(guī)避

30、利率風險 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%,61,例子：,保險公司以價格10000元發(fā)

31、行一種guaranteed investment contract(GIC)，5年到期，保證利率為8%。 假設公司選擇息率8%，6年到期、價格為10000元的帶息債券為債務提供基金。 價格風險 重投資風險,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%，資產和債務的現值相

33、等；當利率變化幅度不大時，資產和債務的值的變化量相等；當利率變化幅度很大時，資產和債務值的變化量不再相等。,69,Rebalancing immunized portfolio,當資產的收益變化時，其久期也發(fā)生了變化，這時，資產和債務的久期不再相匹配。 即使利率不變，當時間變化時，久期也會發(fā)生變化,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