债券定价ppt课件

PV
24.375 1.006003
24.375
1.0060032
24.375
1.0060033
24.375
1.0060034
24.375
1.0060035
1024.375
1.0060036
$1,107.95
Valuing a Bond
Example continued - USA
➢ Take the same 3 year US Government bond. If investors demand a 4.0% semiannual return, what is the new price of the bond?
Maturity
2009年2月的长期利率超过3,5%，而短期利 率为1%或更低。为什么人们不都去购买长 期债券？
• 可能的原因： • （1）相信未来短期利率会上升 • （2）担心长期债券受到利率变化的影响 • （3）担心未来通货膨胀带来的风险
Yield to Maturity
Example • A $1000 treasury bond expires in 5
.711
3.555
1019.70
1.00
Duration= 4.249
• 修正久期（波动率）计算的是到期收益率 变化一个百分点的时候，债券价格变化的 比例。
• 修正久期越大，债券价格受到利率变化的 影响更大。
• 久期（或修正久期）是一种方便的风险度 量指标。
Bond Price, percent
Yield To Maturity (YTM) - The IRR on an interest bearing instrument
Spot rates (%)
Yield Curve
利率期限结构呈上升趋势
U.S. Treasury Strip Spot Rates as of February 2009
Law of One Price
• 一价律： 同样的商品在功能完善的市场 中应按同样的价格销售。
• 支付数额相同，到期日相同的现金流量 应用同样的即期利率贴现
• PV=1/(1+r1)+1/(1+r2)+1/(1+r3)+… • 即期利率系列r1，r2（两年后的即期利率）， r3，… 给出
了利率的期限结构
investorsdemand40semiannualreturnwhatnewprice1024042404240424042404二利率如何影响债券价格interestrate10yrtreasuriesinterestrate10yrtreasuries波动性波动性yearbondpricesyieldsbondpricesyields债券价格和利率水平的变化方向相反债券价格和利率水平的变化方向相反interestrates800085009000950010000105001100011500pricesmaturityprices债券价格随利率变化的轨迹债券价格随利率变化的轨迹interestrates30yrbondyrbondwheninterestrateequals5couponbothbondssellfacevalue三三久期和波动率久期和波动率久期
Forward Rate - The interest rate, fixed today, on a loan made in the future at a fixed time.
Future Rate - The spot rate that is expected in the future
Duration & Bond Prices
Interest rate, percent
四、利率的期限结构 term structure of interest rates
• 利率期限结构：短期利率和长期利率的关 系
Interest Rates
• Short- and long-term interest rates do not always move in parallel. Between September 1992 and April 2000 U.S. shortterm rates rose sharply while long term rates declined.
0 1 2 3 4 5 6 7 8 9 10
Bond Prices and Yields
债券价格和利率水平的变化方向相反
115.00 110.00 105.00 100.00
95.00 90.00 85.00 80.00
Interest Rates, %
Maturity and Prices
债券价格随利率变化的轨迹
PV
115 1.075
115
1.0752
115
1.0753
115
1.0754
1,115
1.0755
$1,161.84
Valuing a Bond
Example - France
➢ In December 2008 you purchase 100 Euros of bonds in France which pay a 8.5% coupon every year. If the bond matures in 2012 and the YTM is 3.0%, what is the value of the bond?
PV
24.375 1.04
24.375
1.042
24.375
1.043
24.375
1.044
24.375
1.045
1024.375
1.046
$918.09
• 二、利率如何影响债券价格
Yield , %
Interest Rate on 10yr Treasuries
波动性
Year
Bond Price, %
PV
8.5 1.03
8.5
1.032
8.5
1.033
108.5
1.034
120.44 Euros
Valuing a Bond
Another Example - Japan
➢ In July 2010 you purchase 200 Yen of bonds in Japan which pay a 8% coupon every year. If the bond matures in 2015 and the YTM is 4.5%, what is the value of the bond?
100 100 1100
PV(Ct) at 5.0%
95.24 90.7 950.22 V = 1136.16
Proportion of Total Value [PV(Ct)/V]
0.084 0.08 0.836
1
Proportion of Total Value Time
0.084 0.16 2.509 Duration= 2.753 years
Duration 1 PV (C1) 2 PV (C2 ) 3 PV (C3) ... T PV (CT )
PV
PV
PV
PV
Modified Duration volatility (%) duration 1 yield
Duration Calculation
Year
1 2 3
Ct
Cash Flows
Sept 11 12 13 14 15
115
115 115 115 1115
Valuing a Bond
Example continued
➢ If today is October 1, 2010, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
Duration
Example (Bond 1)
Calculate the duration of our bond @ 4.9 %
YeYaTr MCF PV@YTM % of Total PV
% x Year
1 68.75 65.54
.060
0.060
2 68.75 62.48
.058
0.115
what is this bond’s duration? Year CF PV@YTM % of Total PV
% x Year
1
90 82.95
.081
0.081
2
90 76.45
.075
0.150
3
90 70.46
.069
0.207
4
90 64.94
.064
0.256
5 1090 724.90
• PV=1/(1+y)+1/(1+y)2 • y是到期收益率
• 先有即期利率，确定债券价格PV后才有到期收益 率
Term Structure of Interest Rates
YTM (r)
1981 1987 & Normal
1 5 10 20
30
1976 Year
Spot Rate - The actual interest rate today (t=0)
3 68.75 59.56
.055
0.165
4 68.75 56.78
.052
0.209
Hale Waihona Puke 5 68.75 841.39
.775
3.875
1085.74
1.00
Duration 4.424
Duration
Example (Bond 2)
Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM,
C0
C1 C2 C3 C4 C5
-1078.80 105 105 105 105 1105
Calculate IRR = 8.5%
Term Structure
What Determines the Shape of the Term Structure?
Expectations Theory 期限结构呈现上升趋势的唯一原因是投资者预期将来的
30 yr bond
When the interest rate equals the 5% coupon, both bonds sell for face value
3 yr bond
Bond Price, ($)
Interest Rates, %
三 久期和波动率
• 久期：债券的平均到期日
Duration Formula
短期利率将会上升； 期限结构呈现下降趋势的唯一原因是投资者预期将来的
短期利率将会下降
Debt & Interest Rates
Classical Theory of Interest Rates (Economics) • developed by Irving Fisher
Nominal Interest Rate = The rate you actually pay when you borrow money
years. It pays a coupon rate of 10.5%. If the market price of this bond is 107.88, what is the YTM?
Yield to Maturity
Example
• A $1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is 107.88, what is the YTM?
Real Interest Rate = The theoretical rate you pay when you borrow morney, as determSuinpepldy by supply and demand
Valuing Bonds
一债券估值Valuing a Bond
PV C1 C2 ... 1,000 CN
(1 r)1 (1 r)2
(1 r) N
Valuing a Bond
Example
➢ If today is October 1, 2010, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
PV
16 1.045
16
1.0452
16
1.0453
16
1.0454
216
1.0455
243.57 Yen
Valuing a Bond
Example - USA
➢ In February 2009 you purchase a 3 year US Government bond. The bond has an annual coupon rate of 4.875%, paid semi-annually. If investors demand a 0.6003% semiannual return, what is the price of the bond?