Ccra session 9_new

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Certified Credit Research Analyst Program
Module 3: Understanding on Bonds
Session 9
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Module 3 – Understanding on Bonds
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Session 7
Chapter 1 – Understanding Covenants, Types & Indenture Analysis
Chapter 2 – Types of FIS, Spreads & Valuation Curves

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Session 8
Chapter 3 – CDS Types and RBI Guidelines on CDS in Indian Market
Chapter 4 – Seniority Ranking of Bonds
Chapter 5 – Introduction to Rich Cheap Analysis

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Session 9
Chapter 6 – Bond Valuation Measures – OAS, YTM, Duration, PVBP
6.1 Valuation of Bonds, Clean & Dirty Price, YTM
6.2 Term Structure and its Theories
6.3 Duration and Modified Duration
6.4 PVBP

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Bond Valuation
It is a simple three step process:
1. Estimate all the cash flows expected on a security
2. Determine the appropriate discount rate
3. Calculate the present value of the estimated cash flows
Formula for finding value of a bond:
where,
CN = coupon payment for year N,
YTM = yield to maturity (interest rate)
PAR = Face Value of the bond
5
N
N
3
3
2
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YTM)(1
PARC
......
YTM)(1
C
YTM)(1
C
YTM)(1
C
bondaofValue









In case the coupon payment is semi annually, the coupon rate in the
numerator should be halved and the time period used for compounding
in the denominator should be doubled

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Bond Valuation (Cont‘d...)
1. The value of a bond is obtained by discounting the bond's expected cash flows to the present using an
appropriate discount rate.
2. If the coupon rate of the security is equal to the market yield then the bond will sell at par
1. Coupon Rate = Market Yield => Price = Par Value
3. If the coupon rate of the security is more than the market yield then the bond will sell at premium
1. Coupon Rate > Market Yield => Price > Par Value
4. If the coupon rate of the security is less than the market yield then the bond will sell at discount
1. Coupon Rate < Market Yield => Price < Par Value
5. If Interest Rates Increase, Price of a Bond Decreases
6. If Interest Rates Decrease, Price of a Bond Increases
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Bond Valuation – Important Points
1. When interest rates rise, market prices of bonds fall (and vice versa)
2. The longer the time until maturity, the more sensitive the bond price is to changes in interest rates
3. In practice most bonds pay interest semi-annually, so we have to ﬁnd the appropriate semi-annual rate and adjust
coupon payments
4. The yield to maturity (YTM)of a bond is the discount rate which equates the price of a bond with the PV of its expected
future cash ﬂow
5. Bond valuation is the determination of the fair price of a bond. As with any security or capital investment,
6. The theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.
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Bond Valuation Process
Example :
Par Bond
Bond value 1000, Interest Rate 10%, Coupon Rate : 10% Term 5 year.
Calculate the PV by discounting method…. (100)
Premium Bond
Bond value 1000, Interest Rate 9 %, Coupon Rate : 10% Term 5 year.
Present Value : 1038.89
Discount Bond
Bond value 1000, Interest Rate 11 %, Coupon Rate : 10% Term 5 year.
Present Value : 963.04
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Example: Bond Prices
Consider a 5 year vanilla bond with a face value of $1000 and 10% annually paid coupon. Calculate its price if the interest
rates are 9%, 10%, and 11%.
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Time Cash flow PV @11% PV @ 10% PV @ 9%
T=1 100 90.09 90.91 91.74
T=2 100 81.16 82.64 84.17
T=3 100 73.12 75.13 77.22
T=4 100 65.87 68.30 70.84
T=5 1100 652.80 683.01 714.92
Total 963.04 1,000.00 1,038.90
Comment Bond trading at
a Discount
Bond trading
at Par
Bond trading at
a Premium

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Computing The Value Of A Zero Coupon Bond
Value of a Zero Coupon Bond
It is the present value of the face value of the bond.
Value = Maturity Value / (1+i) ^ (Number of years *2)
In the above formula we are using the semi-annual discount rate to value the bond. The annual rate can also be used.
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How Discount Rates And Maturity Date Affect Price
1. Interest rates and Bond Values are inversly related
2. A decrease in the interest rate will result in an increase in the bond price as the bond is giving a higher coupon rate
compared to the reduced market interest rate
3. As a result, the price yield curve is a downward sloping curve
4. Changes in Value with Passage of Time: Whether the bond is trading at a premium or at a discount, as a bond
approaches maturity, its value converges to the par value.
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Bond Valuation – Pull to Par
1. Pull to Par is the effect in which the
price of a bond converges to par
value as time passes. At maturity the
price of a debt instrument in good
standing should equal its par or face
value.
2. Pull to Par is the phenomenon that as
time passes, the price of a credit
instrument in good standing moves
towards its par value. The nearer to
maturity the greater the influence
because the security will only pay out
the stated principal amount
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Pull To Par
Consider two bonds. One trading at a discount and the other trading at a premium:
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Bond-Discount
Coupon 5%
Tenure 10
YTM 10%
Face Value 100
Bond-Premium
Coupon 10%
Tenure 10
YTM 5%
Face Value 100
FY 0 FY 1 FY 2 FY 3 FY 4 FY 5 FY 6 FY 7 FY 8 FY 9 FY 10
Price Bond-
Discount $69.28 $71.20 $73.33 $75.66 $78.22 $81.05 $84.15 $87.57 $91.32 $95.45 $100.00
Price Bond-
Premium $138.61 $135.54 $132.32 $128.93 $125.38 $121.65 $117.73 $113.62 $109.30 $104.76 $100.00

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Arbitrage-free Valuation Approach
1. Discounting all cash flows of a bond with the same discount rate is a flaw in the traditional approach.
2. In the arbitrage free valuation approach, each cash flow is discounted by the discount rate that pertains to the maturity
of that cash flows. This discount rate is nothing but the Spot Rate
3. We had studied earlier about STRIPS. As per this approach, the value of the Treasury Bond as a whole should be equal to
the value of its individual parts
1. Each part =
4. If this is not the case, a person can achieve arbitrage-free profits by buying the whole and selling the parts or vice-versa
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 periods
rate/2Spot1
flowCash
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Questions
1. If the current yield is 8%, what is the value of a security carrying a annual coupon of 7%, maturing in 8 years, redeemable at par value of $1,000?
A. $942.53
B. $1,000
C. $1,059.71
D. I know the security is valuable. It can’t be valueless. But I can’t quantify this value. As beauty lies in the eyes of beholder, similarly value of this security lies in the
eyes of lender. Hence, it’s difficult to quantify.
2. If the current value of a bond is $1,065, what is the YTM of the bond carrying a annual coupon of 7%, maturing in 6 years, redeemable at par value of $1,000?
A. 5.69%
B. 7%
C. 6.69%
D. It’s finite, definitely finite and not infinite. I think you should be happy with this answer.
3. The current price of a bond is $985. An increase in the yield by 50 basis points will most likely result in the price becoming:
A. $1,000
B. $1,015
C. $970
D. I remember you told price changes when yield changes but how much is too much to ask.
4. The value of a $10,000 face value zero-coupon bond with 10 years to maturity and a semi-annual pay yield of 8% is:
A. $2,145.48
B. $4,563.95
C. $4,635.67
D. We are students. I think you should ask us simple questions. You are after our lives...just not letting us live in peace
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Solutions
1. A. $942.53
2. A. 5.69%
3. C. $970. This is a trick question requiring no calculations as the value of a bond will decrease as yields increase.
4. B. $4,563.95 [ = 10000/(1 + 0.08/2)] ^ (10*2)
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Practise Questions
1. Fall in interest rate causes the bond prices also to fall.
A. False
B. True
C. Difficult to say
D. Look man! I have a very busy day ahead. I have to rush for a mug of bear. Then my friends will join me. We will have few rounds of
Vodka. I need to be inside a movie theatre immediately after that. Then I will like to eat something … you know some fast food type.
After that I am expecting some calls…the important ones…then I have to catch up with sleep. You know I haven’t slept since last so
many days. Once I get up I will immediately go online to check mails, update my status on Facebook, Twitter. I plan to return some of
the important calls I would have missed while watching movie….; I really appreciate your question…really appreciate, but just that I
don’t have time to look into this right now…but I promise I will get back to you, I promise…you can take my words
2. When interest rates go up, prices of fixed interest bonds –
A. Go up
B. Go down
C. Remain unchanged
D. Why do you keep asking such questions? You are the teacher, you should know the answer…for every small thing you ask a question. Dude, go
and find out yourself. I don’t want to spoil your habits by answering this question.
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Answer
1. A
2. B

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Clean vs. Dirty Prices
1. Accrued interest: Interest accrued on a bond from the last coupon date and the date of sale of the bond
2. Full Price/Dirty Price: Total amount paid by the buyer to the seller for the bond
3. Clean price: Full price less the accrued interest
4. Dirty Price = Clean Price + Accrued Interest
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1. A person pays $1,050 for a bond. The accrued interest till the date of purchase was $36. The clean price of the bond is:
A. $1,050
B. $1,086
C. $1,014
D. I need to wash this bond first to clean it. Which soap should i use? Is RIN ok? Or Should i use Surf Excel? Once i clean it
then i can read the value printed on its face and tell you the clean price.
Answer (C)

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Returns From Investing In A Bond
A person realizes the following returns from a coupon paying security
 Interest payment made by the issuer
 Reinvestment income from reinvesting the interest payments received
 Recovery of the principal. includes the capital gain/loss on selling the security.
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Traditional Yield Measures
Traditional Yield Measures
1. Coupon: In a way, coupon is the return generated by a bond
but it‘s not a suitable measure for return calculation because it
ignores:
 The premium / discount in a bond
 Capital gain / loss at redemption
 Reinvestment rate of preiodic cash flows
2. Current Yield: the annnual interest income from the bond
Current Yield = Annual Coupon interest received ÷ Bond Price
The current yield is simply the coupon payment (C) as a
percentage of the (current) bond price (P).
Current yield = C / P
Drawbacks :
1. Only Considers coupon interest
2. Capital Gains/Losses not taken into account
3. No consideration for reinvestment income
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Traditional Yield Measures (Cont’d…)
1. Yield to Maturity(YTM): YTM is the IRR of the bond. It is the annualised rate of return on the bond
2. Yield Measure Relationships:
3. Advantages:
1. Considers both coupon income and capital gain/loss if held to maturity.
2. Considers the timing of cashflows
4. Limitations
1. It considers the reinvestment income; the interim coupon payments are reinvested at a rate equal to the YTM.
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Bond Selling at: Relationship
Par Coupon rate = Current Yield = Yield to Maturity
Discount Coupon rate < Current Yield < Yield to Maturity
Premium Coupon rate > Current Yield > Yield to Maturity
 
2N2
2
YTM
1
ParC
.....
2
YTM
1
C
2
YTM
1
C

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
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Imp

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Traditional Yield Measures (Cont‘d...)
YTM of Annual Coupon Bond:
A 10 year, $1000 par value bond has a coupon of 7%. If it is priced at $920 what is the YTM?
PV = -920; N=10; FV=1000; PMT=70
I/Y = 8.20%
YTM for zero coupon bond:
The price of a 5-year Treasury bond is $804. Calculate the semiannual-pay YTM and annual-pay YTM.
Semiannual-pay YTM =
Annual-pay YTM =
22
%41.42*1
804
1000 10
1
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%46.41
804
1000 5
1












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Traditional Yield Measures (Cont‘d...)
Bond Equivalent Yield: Doubling the semiannual yield to maturity.
Yield to Call: yield on callable bonds (bonds can be called before maturity) that are selling at a premium. The calculation is the same
as for normal bonds. The par value is substitued with the call price and the total period is substituted with the period upto the call
date
Yield to Put: yield on puttable bonds that are selling at a discount
Yield to Worst: A yield can be calculated for every possible call date and put date. The lowest of these YTM‘s is called Yield to
Worst.
Cash Flow Yield: used for Amortisinfg Securities. The limitation with this measure is that the actual prepayment rates may differ
from those assumed for calculation purposes.
Yield to maturity (YTM): most popular yield measure of all the above. The limitation with this measure is that it assumes that cash
flows are reinvested at the YTM and the bond is held till maturity
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Calculate And Compare Yield Spread
Absolute yield spread :
 It is Simply the difference between yields of two bonds.
( Yield on higher yield bond - yield on lower yield bond )
Relative yield Spread :
 It is the Absolute yield spread expressed as percentage of the yield on benchmark bond.
Yield Ratio : It is the ratio of yield on the subject bond to the yield on the benchmark bond
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bondbenchmarkon theYield
spreadyieldAbsolute
spreadyieldRelative 
yieldbondbenchmark
yieldbondSubject
RatioYield 

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Reinvestment Income
If the reinvestment rate is less than the YTM then the actual yield realised will be less than YTM
How to calculate the Reinvestment Income earned???
20-year Treasury bond purchased at par, 7% coupon rate, how much reinvestment income should be generated to earn a YTM of
7%?
 Total Value generated in 20 years = 100(1.035)40 = 395.9260
 Reinvestment income required = 395.9260 – 100 – 40*3.50 = 155.9260
Factors Affecting:
 Higher the coupon rate higher the reinvestment risk
 Longer the maturity higher the reinvestment risk
If the above problem was for a 10 year bond with a coupon of 5%, the reinvestment income required would have been
$13.8616 as compared to $ 155.9260
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Bond Equivalent Yield And Annual-pay Yield
The following formula identifies the relationship between the two.
Bond Equivalent Yield(BEY) of an Annual-pay Bond
Yield on an annual pay basis
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  1YTMAnnual1*2 2
1
BEY
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

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 1
2
BEY
1
2
YTM

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Holding Period Return
Holding Period Return (HPR) is the true return measure
But the only problem is HPR can be calculated only ex post and not ex ante because the reinvestment rate can be obtained
only after expiry of the relevant period.
Consider a 10%, 3 year annual coupon bond at par.
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At the end
of Year
Coupon & Redemption
amount (Rs.)
Reinvestment
Period (Years)
Reinvestment Rate Amount (Rs.) Formula
1.00 10.00 2.00 8.0% 11.66 =10*(1+8%)^2
2.00 10.00 1.00 7.5% 10.75 =10*(1+7.5%)^1
3.00 110.00 - 110.00 =110
Total Cash at the end of
tenure
132.41
Holding Period Return 9.81% =(132.41/100)^(1/3)-1
So, HPR is 9.81% against YTM of 10%. HPR is a function of reinvestment rate while YTM is not.

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Practise Questions
1. Interest rate risk is a type of
A. Credit risk
B. Market risk
C. Operational risk
D. All the above
2. Which of the following is not a type of credit risk ?
A. Default risk
B. Credit spread risk
C. Intrinsic risk
D. Basis risk
3. 8% Government of India security is quoted at RS 120/-
The current yield on the security, will be----
A. 12%
B. 9.6%
C. 6.7%
D. 8%
4. A debenture of face value of As. 100 carries a coupon
of 15%. If the current yield is 12.5%. What is the
current market price ?
A. Rs.100
B. Rs.120
C. Rs.150
D. Rs.125
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Answers
1. B
2. B
3. C
4. B

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Session 9
6.4 PVBP

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Theories Of Term Structure Of Interest Rates
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Shape of Term Structure Implication According to Pure Expectations Theory
Upward sloping (normal) Rates expected to rise
Downward sloping (inverted) Rates expected to decline
Flat Rates not expected to change

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Liquidity Preference Theory:
 States that investors are risk-averse and will demand a premium for securities with longer maturities
 States that shape is a function of expectation about future ST rate but also by investors’ preference for liquidity and risk
 Yield curve can be normal, inverted or flat as long as yield premium for interest rate risk increases with maturity.
 Investor demand premium for LT rate because:
• Commitment for long term induces liquidity risk
• Increased exposure to interest rate risk
• Higher credit risk in long term for non sovereign bond
 It implies natural shape of term structure to be normal and inverted shape results when the fall in future ST rate >
premium for LT liquidity and risks
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Market Segmentation Theory:
 States that most investors have set preferences regarding the length of maturities they will invest in
 Example: a bank having large amount of short term liabilities will prefer to invest in short term securities.
 Different tenors are not perfect substitute of each other. It implies current 1 year spot and 1F2 can’t substitute for
current 2 year spot
An offshoot to above theory is that an investor can be induced to invest outside their term of preference, if they are
compensated for taking on that additional risk by moving out of their preferred range. This is known as the Preferred
Habitat Theory
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Questions
1. The pure expectation theory can be used to explain any shape of the yield curve. This statement is most likely
A. Incorrect; The market segmentation theory can be used to explain any shape of the yield curve
B. Incorrect; The liquidity preference theory can be used to explain any shape of the yield curve
C. Correct; The pure expectation theory explains any shape of the yield curve
D. Useless; no theory in this world…mind it no theory…and not even Lord Brahma, Vishnu or Mahesh can explain the shape of
yield curve. It’s futuristic and takes whatever shape it wants.
2. With respect to the term structure of interest rates, the market segmentation theory holds that :
A. An increase in demand for long term borrowings could lead to an inverted yield curve
B. Expectations about the future of short term interest rates are the major determinants of the shape of the yield curve
C. The yield curve reflects the maturity demands of financial institutions and investors
D. Different segments exist in the market based on different interest level in James Bond movies…
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Questions (Cont...)
3. As per the Liquidity Preference Theory :
A. Investors will demand a premium for shorter maturity securities.
B. Investors will demand a premium for longer maturity securities.
C. Investors will not demand any premium.
D. Investors are very easy to fool, they don’t understand any theory; they prefer liquid water to solid gold
4. As per the Preference habitat Theory :
A. Investors are will not move out of their preference habitat
B. Investors demand a premium to invest outside their preference range
C. Investors pay a premium to invest outside their preference range
D. Investors prefer to make forest as their habitat as they are social animal
5. The impact of an expanding economy on the yield spread is:
A. To increase the yield spread
B. To decrease the yield spread
C. Will not effect the yield spread
D. To expand the shrinking mind of investors
6. Which of the following will have the least Yield Spread:
A. Callable Bond
B. Putable Bond
C. A plain Fixed Coupon Bond
D. A plain vanilla ice cream
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Solutions
1. A. The market segmentation theory asserts that the supply and demand for funds within the different maturity sectors
of the yield curve determine the interest rate for that sector.
2. C. The correct answer is the yield curve reflects the maturity demands of financial institutions and investors.
3. B. Investors will demand a premium for longer maturity securities
4. B. Investors demand a premium to invest outside their preference range
5. B. To decrease the yield spread
6. B. Puttable Bond
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36
Session 9
6.4 PVBP

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Duration
Duration of a Bond:
1. Duration is the measure of how long on an average the holder of the bond has to wait before he receives his
payments on the bond. A coupon paying bond’s duration would be lower than “n” as the holder gets some of his
payments in the form of coupons before “n” years
2. In simple words, duration of a bond is sensitivity of bond price to change in its interest rate / YTM
3. Duration = – (Percentage change in bond price/Percentage change in Yield); negative sign is used because of the
inverse relation between yield and bond prices
4. Thus, increase in the yield results in a fall in the bond price
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Effective Duration
Effective duration is calculated as:
Percentage change in Bond Price = -Effective Duration * Change in yield in percent. (Δy)
Example: Consider a bond trading at 96.54 with duration of 4.5 years. In this case
ΔB = - 96.54* 4.5 Δy
ΔB = -434.43 Δy
If there is 10 basis points increase ( + Δy) in the yield then the bond price would change by:
ΔB = -434.43 * ( 0.001) = – 0.43443
Hence, B = 96.54 – 0.43443 = 96.10
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decimals)inyieldin(Change*Price)(Initial*2
rises)yieldwhenpriceBond–fallsyieldwhenprice(Bond
DurationEffective 

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Percentage Change In Price Using Duration
1. Approximate percentage price change = - Duration * Dy * 100
2. For example, you hold a bond that has a duration of 7.8 years. The interest rates fell by 25 bps. Calculate the
approximate percentage price change.
3. Answer: Approximate percentage price change = - Duration * Dy * 100 = -7.8 *(- .0025) * 100 = 1.95%
4. For large changes in yield, convexity should also be used. Percentage change in price becomes inaccurate with
only taking duration into account.
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Alternative Definitions Of Duration
Macaulay Duration: is the weighted average of the times when the payments are made. And the weights are a ratio of the coupon
paid at time “t” to the present bond price.
Macaulay duration is also used to measure how sensitive a bond or a bond portfolio's price is to changes in interest rates.
where:
t = Respective time period
C= Periodic Coupon payments ; y =Periodic yield : n = Total number of periods
M = maturity Value
Calculating Macaulay Duration:
Note that this is 3.77 six-month periods, which is about 1.89 years
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 
 
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77.3
54.964
76.3636
54.964
4
05.1
1040
3
05.1
40
2
05.1
40
1
05.1
40
432
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D
0 1 2 3 4
40
1,000
40 40 40-964.54
PriceBondCurrent
y)(1
M*n
y)(1
C*t
DurationMacaulay
n
1t
nt 



Equivalent to centre of gravity in the bond’s cash flows

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Change In Bond Price With Change In Discount Rate
Modified Duration
 The modified duration is equal to the percentage change in price for a given change in yield.
Example:
The current price of a bond is 98.75. Its modified duration is 5.2 years. The YTM of the bond is 7.5%. What would the
price be if the yield became 8%?
Solution:
DV = -98.75 * 5.2 * 0.005
= -2.57
The new price of the bond is 96.18
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yModDVV
y
V
DD
D
D
 ..
V
1
-ModD

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Alternative Definitions Of Duration
Modified Duration: is derived from Macaulay Duration. It is better than Macaulay Duration as it takes into account the current
YTM.
Effective Duration calculations explicitly take into account the a bond‘s option provisions such as embedded options. The other
methods of calculation ignore the option provision
In summary duration is,
 The first derivative of the price-yield function
 The slope of the price-yield curve.
 A weighted average of the time till the cash flows willl be received.(Macaulay Duration)
 The approximate percentage change in price for a 1% change in yield.(Effective Duration)
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)
yearperpaymentsinterestofno
YTM
(1
DurationMacaulay
DurationModified
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Alternative Interpretation of Modified Duration
1. When YTM rises, price falls but reinvestment
income rises because of new higher yield. And vice
versa.
2. Thus the two always work in opposite direction.
3. Consider a time frame in future when the offsetting
effect of the two cancel each other so that there is
no change in the payoff of the investor.
4. This point of time in future is modified duration.
5. This fact is used by pension funds for portfolio
immunization of bond portfolios.
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Duration Of A Portfolio
Duration of a portfolio is the weighted average of the duration of the individual securities in the portfolio.
Portfolio Duration =
The problem with the above equation is that it holds good only for a parallel shift in the yield curve. This is because
securities with different maturities may have different changes in yield.
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NN2211 DW.........DWDW 

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Convexity Measure Of A Bond
Convexity is the measure of the curvature of a price-yield cuve.
Duration is an appropriate measure for small changes in the yield. For larger changes in yield convexity should also be used.
Percentage Change in Price = Duration Effect + Convexity Effect =[(-Duration * Δy) + (Convexity * Δy2) ] * 100
Note: In this formula all the values are used as numbers. E.g. 1% must be written as 0.01.
This is also the reason to multiply it by 100
45
Y
P=BondPrice($)
Price based on
Duration.
Actual Price – Yield Curve
Curvature effect not
incorporated by Duration
2
decimals)inyieldin(Change*Price)(Initial*2
Price)BondInitial*2-risesyieldwhenpriceBondfallsyieldwhenprice(Bond
Convexity


Note: To be covered only at
conceptual level, need not go
into mathematics

© Pristine
Practise Question
1. The YTM of a 5 year duration bond fell sharply from 10% to 6%. Shalini Bhargava is frustrated to see the fall. She is
worried how to assess the impact of this on the bond price? Can you help her?
A. Why worry? She knows the duration and the changes in yield. She can calculate the proportionate change in the price of the bond.
These girls na…they get worried over small issues…
B. I can help her. But before that I need to know who she is? It’s like she had been all throughout with us in this CCRA course and we
are still unaware who she is, where she is…and so on. I will help but first tell me more about her.
C. She needs to find convexity. Duration is not the right measure of sensitivity of bond prices if yield changes are large.
D. You are asking me to help her…no one can help her!!! The fall in YTM has defied all the laws of gravity. Had Newton been alive
today, he would have committed suicide seeing such a sharp fall.
46
Answers (C)

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Price Value Of A Basis Point (PVBP)
1. This is a measure of interest rate risk.
2. This is also known as the dollar value of an 01 (DV01)
3. PVBP – It is the absolute value of the change in the price of a bond for a 1 basis point change in yield.
4. The PVBP is the same for both increase and decrease (because change in yield is small)
5. The PVBP is a special case of dollar duration.
48
pointbasis1bychangesyieldwhenPrice-PriceInitialPVBP 
ValueBond*0.01%*DurationPVBP 

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Questions
1. A 5 year bond paying 8% annual pay coupon is currently trading for $1023.56 and having YTM of 7.42%, calculate the
effective duration of the bond given 25 basis point in YTM.
Given : V- = 1033.88, V+ = $1013.29
A. 5.03%
B. 4.02%
C. 4.56%
D. Why are you confusing us with so much data? Duration of a (movie of James) Bond is roughly two hours.
2. Calculate the duration of the portfolio of two bonds A and B having weights of 60% and 40% respectively. Duration of
bond A is 7.9 and duration of bond B is 6.7.
A. 7.64
B. 7.42
C. 7.24
D. Hey dude! I am busy dancing in Ganpati Visarjan right now. At an appropriate time, I will ask Ganpati this question. Please bear with
me till that time.
49

© Pristine
Questions (Cont...)
3. The most accurate measure for arriving at the effect of duration is?
A. Duration Approach
B. Full valuation approach
C. PVBP
D. Every thing in this world is ephemeral. Whatever is born will ultimately die. So why worry about the effect of duration?
4. A bond manager has collected the following information regarding a portfolio of fixed income investments which have a par value of
$10mn. The current market price is $11.25mn. If the duration is 5.2 the most likely estimate of the price change for the bond issue for a 25
bps change is
A. 1.3% of $10mn
B. 1.3% of $11.25mn
C. 2.1% of $11.25mn
D. This portfolio manager needs to do this CCRA course. He should be able to calculate it himself then.
5. A portfolio manager notices the following in his portfolio has a portfolio duration of 4.35. How much will be the change in the portfolio if
the interest rate declines by 25 bps
A. $ 28,280
B. $ 14,250
C. $ 27,100
D.The portfolio manager should get his eyes tested. Duration doesn‘t change with interest rate. It‘s surpsising how he has still noticed a change.
50
Issue Maturity Market Value
A 2 $8.5mn
B 5 $4.6mn
C 10 $12.9mn

© Pristine
Solutions
1. B. V = $1023.56, V- = 1033.88, V+ = $1013.29, Change in yield is = 25 bps = 0.0025
So effective duration is = ($1033.88 - $1013.29)/2 * $1023.88 *0.0025 = 4.02
2. B. The portfolio duration is =0.6 * 7.9 + 0.4 *6.7 = 7.42
3. B. Full valuation approach
4. B. The estimated change = 5.2*0.25 = 1.3%. (The par value of $10mn is given to confuse the candidate. Par value never
changes. Current value of $11.25mn is more important)
5. A. 26mn * 4.35 * (0.25)% = $ 28,280
51

© Pristine
Extra-Quiz Questions
1. What is least likely to be true regarding Macaulay and modified duration
1. Both are calculated from the bond’s expected cash flows with no
adjustments for embedded options on cash flows
2. For bonds with no options, modified duration is similar to effective
duration
3. Macaulay duration takes into consideration embedded options in the
bond
2. A fixed income analyst makes the following two statements:
1. Statement 1: YTM assumes that coupon payments are reinvested at the
rate equal to the cash flow yield.
2. Statement 2: The bond is assumed to be held till maturity.
3. Consider the following two statements:
1. Statement 1: The static spread is the spread over the Treasury spot rate
that makes the PV of all the cash flows from a non-Treasury security equal
to its price.
2. Statement 2: The Z-spread ignores the interest rate volatility and assumes
it to be zero.
52
Statement 1 Statement 2
A Correct Correct
B Correct Incorrect
C Incorrect Correct
Statement 1 Statement 2
A Correct Correct
B Correct Incorrect
C Incorrect Correct

© Pristine
4. Sally states that there are a number of yield measures that are used traditionally in the bond market. The least
likely yield measure that is used
A. Yield to call
B. Yield to worst
C. Yield to settlement
D. Yield to death – this is measured just once – at the time of death
5. Duration is not a good measure for large changes in yield. Duration also assumes that the yield curve will shift in
a parallel fashion. The statements are most likely
A. Both statements are correct.
B. Only one statement is correct.
C. Both the statements are incorrect.
D. A source of pain in our lives
6. An 8% coupon bond is valued at 104.35. When the yield increases by 20 bps the price of the bond declines to
103.44. The PVBP for the bond is closest to
A. $0.0455
B. $0.0512
C. $0.0519
D. The heart of the bond
53

© Pristine
7. Which of the following 10-year fixed-coupon bonds has the least price volatility? All else equal, the bond with a coupon rate of:
A. 6.50%
B. 5.00%
C. 8.00%
D. Just give me a few days, let me trade these bonds in the market and see which one is least volatile. Just wait for a few days
8. Carl manages the following portfolio
The value for the portfolio duration is
closest to
A. 5.833
B. 4.351
C. 4.555
D. My head. In fact this is the prime source of my headache.
54
Coupon Maturity Par Value
Market
Value
Duration
8% 5 years $ 5 mn $ 4 mn 4.87
11% 7 years $ 10 mn $ 11.4 mn 5.72
9.75% 10 years $ 15 mn $ 14.5 mn 8.50
10.25% 5 years $ 20 mn $ 21.2 mn 4.25

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Solutions
1. C.
2. A.
3. A.
 The Z-spread is also known as the static spread and it is the spreads that should be added on top of spot rates to
calculate the PV of cash flows of a bond. It also assumes the volatility of interest rates is zero hence it is also known as
the zero-volatility OAS.
4. C.
 Yield to settlement is not a traditional measure of yield. The yield measures that are generally used are a) yield to
maturity b) yield to call c) yield to put d) yield to worst e)current yield f) cash flow yield.
5. A.
 As the duration measure is not useful for measuring changes in price when there are large changes in yield. The
duration also assumes that yields change is parallel across the entire yield curve.
6. A.
 The PVBP = 104.35 – 103.44 / 20 = 0.0455
55

© Pristine
Solutions
7. C.
 If bonds are identical except for the coupon rate, the one with the lowest coupon will exhibit the most price volatility.
This is because a bond’s price is determined by discounting the cash flows. A lower-coupon bond pays more of its cash
flows later (more of the cash flow is comprised of principal at maturity) than a higher-coupon bond does. Longer-term
cash flows are discounted more heavily in the present value calculation. Another way to think about this: The relationship
between the coupon rate and price volatility (all else equal) is inverse – a greater coupon results in less price volatility.
Examination tip: If you get confused on the examination, remember that a zero-coupon bond has the highest interest rate
risk because it delivers all its cash flows at maturity. Since a zero-coupon bond has a 0.00% coupon, a low coupon equates
to high price volatility.
8. A.
56
Issue Market Value
MV % of Portfolio
Value
Duration
MV% * Duration
A $ 4 mn 7.83% 4.87 0.3813
B $ 11.4 mn 22.31% 5.72 1.2761
C $ 14.5 mn 28.38% 8.50 2.4123
D $ 21.2 mn 41.49% 4.25 1.7633
Total $ 51.1 mn 100% 5.8330

© Pristine
5 Minutes Recap
57
N32
YTM)(1
PARC
......
YTM)(1
C
YTM)(1
C
YTM)(1
C
bondaofValue









Bond Selling at: Relationship
Par Coupon rate = Current Yield = Yield to Maturity
Discount Coupon rate < Current Yield < Yield to Maturity
Premium Coupon rate > Current Yield > Yield to Maturity
yModDVV
y
V
DD
D
D
 ..
V
1
-ModD
)
yearperpaymentsinterestofno
YTM
(1
DurationMacaulay
DurationModified


ValueBond*0.01%*DurationPVBP 
Yield Spread Measures:
1. Absolute Yield Spread = (Yield on the
subject - Yield on benchmark)
2. Relative Yield Spread = (Absolute Yield
Spread/Yield on benchmark )
3. Yield Ratio = (Subject Bond
Yield/Benchmark Bond Yield)
1. Value of a Zero Coupon Bond = Maturity
Value / (1+i) ^ (2N)
2. Duration = - (%age change in bond price /
%age change in Yield)
3. Value of a callable bond = Value of a
option-free bond – Value of embedded
option
4. Value of a puttable bond = Value of a
option-free bond + Value of embedded
option
5. Dirty Price = Clean Price + Accrued
Interest
• Pure Expectations Theory
• Liquidity Preference Theory
• Market Segmentation Theory
Traditional Measures of Yield:
1. Coupon
2. Current Yield
3. Yield to Maturity
4. Yield to Call
5. Yield to Put
6. Yield To Worse
7. Cash Flow Yield
8. Bond Equivalent Yield
9. Holding Period Return

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