Reading 57 债券估值介绍-CFA-东方华尔
东方华尔CFA 一级培训课程
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Asset Valuation
Fixed Income Investment:Enhance and Practice.东方华尔
A.“Features of Debt Securities,”
B. “Risks Associated with Investing in Bonds,”
11 types: Interest rate risk 、Call risk 、Prepayment risk 、Yield curve risk 、Reinvestment risk 、Credit risk 、Liquidity risk 、Exchange-rate risk 、Volatility risk 、Inflation risk 、Event risk
C. “Overview of Bond Sectors and Instruments,”
D. “Understanding Yield Spreads,”
E. “Money Policy in an Environment of Globle Financial Markets”东方华尔
?Fundamental principles of bond valuation ?Types of bonds with uncertain cash flows ?Price-yield curve and how a bond changes as approaches its maturity ?
Compute the value of a zero-coupon bond ?
Appropriate single or multiple discount rates ?Arbitrage-free valuation approach IP#东方华尔
?学习要点57. a: 解释债券估值过程的步骤。（Explain the steps inthe bond valuation process.）
?学习要点57. b: 说明难以估计现金流的债券类型。（Describe types of bonds for which estimating the expected cash flows is difficult. ）?学习要点57. c: 计算债券的价值（息票和零息）。（Calculate the value of a bond （coupon and zero-coupon ）.）东方华尔
?学习要点57.e:已知贴现率的变化时，计算债券价值的变化。（Calculate the change in value of a bond given a change in its discount rate.）?学习要点57.f:解释和阐述无套利估值法的应用，并解释当债券出现定价偏误时，交易员如何进行套利。（Explain and demonstrate the use of the arbitrage-free valuation approach and describe how a dealer could generate an arbitrage profit if a bond is mispriced.）?学习要点57.d:解释贴现率变化时以及债券接近到期日的情况下，债券价格如何变化（Explain how the price of a bond changes if the discount rate changes and the bond approaches its maturity date.）
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?The general procedure for valuing bonds or any security is to take the present values of all expected cash flows and add them up,why PV?
?Step1estimate the cash flows over the life of the security.for a bond ,it is coupon payments and return of principal.
?Step2determine the appropriate discount rate based on the risk
?Step3calculate the present value of the expected cash flows by multiplying the bond’s expected cash flows by the appropriate discount
factors ?P=?Delete I 东
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aside from credit risk ,three situation cause additional difficulties on estimating cash flows ：
1.The principal repayment stream is not known with certainty. ( callable putable accelerated sinking fund provision prepayment options)
2.The coupon payment are not known with certainty ( floating rate ).
3.The bond is convertible into another security (convertible bonds).东方华尔
Coupon rate = market yield,bond trade at par value Coupon rate > market yield, bond trade at premium Coupon rate < market yield, bond trade at discount Bond price Maturity date Premium bond
Discount bond
Example on P90东方华
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Given the yield to maturity, the calculation is
Alternatively,using calculator , we enter:
PMT=0;FV=par;N=# years *2;I/Y=YTM/2=semiannual
discount rate; CPT->PV 东方华尔
Compute the value of a 10-years, $1,000 face value zero-coupon bond with a yield to maturity of 8%.Or , N=10*2=20;FV=1,000;I/Y=8/2=4;PMT=0;CPT->PV=-$456.39The difference between 456.39 and par value(1,000) is the amount of compound interest that will be earned over the 10-year life of the issue.
In the exam, pls write down FV , N, PMT , I/Y 东方华尔
Single discount rate=real risk-free +inflation rate +risk premium (credit risk,liquidity risk,option risk)
real risk-free +inflation rate=nominal risk-free rate(time value )Example consider a security that will pay $100per year for 10years and make a single $1,000payment at maturity (in 10years).if the appropriate discount rate is 8%for all cash flows,the value is :
N=10;PMT=100;FV=1,000;I/Y=8;CPT →PV=-$1,134.20
YTM is really an average of the required rates for the individual cash flows of a bond.(single discount rate)东方华尔
Discount each cash flow using a discount rate that is specific to the maturity of each cash flow ,also are called spot rates and can be thought of as the required rates of return on zero-bonds maturing at various times in the future.
If the value is not equal to the market price,there is an arbitrage profit to be earned by buying the lower-priced alternative (either the bond or the individual cash flows)and selling the higher-priced alternative,thus will force the bond price toward equality with their arbitrage-free values,eliminating further arbitrage opportunities,specially using STPIPS ,Two Examples P93(coupon bond overvalued)and slide 21What is arbitrage?Practice of taking advantage of a price differential between two or more markets 东方华尔
calculating bond value using discount factors
Discount factor:the t-period discount factor is the PV of $1to be received at the end of period,so the FV of $1to be invested today is 1/d(t).example d(0.5)=0.9939;d(1)=0.9880;d(1.5)=0.9825
DF(n)=1/(1+r/2)2n 0.9939=1/(1+r/2),r=1.2275%;0.9825=1/(1+r/2)3,r=1.1805%1/0.9825=(1+r/2)3,LN(1/0.9825)=3LN(1+r/2),
1+r/2=e Ln(1/0.9825)/3Suppose that the discount factor for the first 180-day coupon period is as follows:D(0.5)=0.92432calculate the price of a bond that pay $108six months from today.
Sine $1to be received in six months is worth $0.92432today,$108received in six month is worth 0.92432*$108=$99.83today.东方华尔
Suppose you observe the annual coupon bonds shown as follows:
maturity YTM Coupon rate (annual pay)Price (% of par)1 years 4%0%
96.1542 years 8%0%
85.7342 years 8%8%100
The 2-year spot rate is 8.167%.Is there an arbitrage opportunity?If so,describe the trades necessary to exploit the arbitrage opportunity.Check 2year discount factor 85.734东方
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Decide which bonds are overvalued,Sell high buy low
Short 2Zeros,one year with par of 8,two years with par of 108
Buy two year coupon bond 8%,100par
Initial cash flows
Short Zeros 8*0.96154+108*0.85734=+100.28504Buy coupon bond –100
Net cash flow =100.28504-100=0.28504
At year one you receive 8coupon to pay zero of 8
At year two,you receive 8coupon and 100principal to pay zero of 108东方华尔
A newly issued 10-year option-free bond is valued at par on June 1,2000.The bond has an annual-pay coupon of 8percent.On June 1,2003,the bond will have a yield to maturity of 7.1percent.The first coupon is reinvested at 8percent and the second coupon is reinvested at 7percent.The future price of the bond on June 1,2003is closest to :
A 100%of par
B 102.5%of par
C 104.8%of par
D 105.4%of par
Whether we should consider the FV of coupon
FV=1000,PMT=80,N=7,I/Y=7.1东
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Consider a five-year bond with a 10percent coupon bond that has a present YTM of 8percent.if interest rates remain constant,one year from now the price of this bond will be:A higher B lower C the same D cannot be determined
The bond is treading at premium 东方
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THANK YOU
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