ccra session 9_new

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Certified Credit Research Analyst ProgramModule 3: Understanding on Bonds

Session 9

1

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Module 3 – Understanding on Bonds

2

Session 7

Chapter 1 – Understanding Covenants, Types & Indenture Analysis

Chapter 2 – Types of FIS, Spreads & Valuation Curves

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3

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

21

YTM)(1

PARC......

YTM)(1

C

YTM)(1

C

YTM)(1

Cbond a of Value

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 anappropriate 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 adjustcoupon 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 expectedfuture 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%.

9

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 theprice of a bond converges to parvalue as time passes. At maturity theprice of a debt instrument in goodstanding should equal its par or facevalue.

2. Pull to Par is the phenomenon that astime passes, the price of a creditinstrument in good standing movestowards its par value. The nearer tomaturity the greater the influencebecause the security will only pay outthe 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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periodsrate/2Spot 1

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 theeyes 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 ofVodka. 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 somany days. Once I get up I will immediately go online to check mails, update my status on Facebook, Twitter. I plan to return some ofthe important calls I would have missed while watching movie….; I really appreciate your question…really appreciate, but just that Idon’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, goand find out yourself. I don’t want to spoil your habits by answering this question.

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Answer

1. A2. 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 itthen 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

YTM1

ParC.....

2

YTM1

C

2

YTM1

C

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*1804

1000 101

%46.41804

1000 51

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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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bondbenchmark on the Yield

spread yield Absolutespread yield Relative

yield bondbenchmark

yield bondSubject Ratio Yield

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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 21

BEY

1

2

BEY1

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 couponof 15%. If the current yield is 12.5%. What is thecurrent 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 ofyield 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)in yieldin (Change*Price) (Initial*2

rises) yield when price Bond– falls yield when price (BondDuration Effective

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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 theapproximate 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 withonly 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

40

77.354.964

76.3636

54.964

405.1

10403

05.1

402

05.1

401

05.1

40432

D

0 1 2 3 4

401,000

40 40 40-964.54

PriceBondCurrent

y)(1

M*n

y)(1

C*t

DurationMacaulay

n

1tnt

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 theprice 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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yModDVVy

VDD

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)

42

)yearper paymentsinterest of no

YTM(1

DurationMacaulayDurationModified

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Alternative Interpretation of Modified Duration

1. When YTM rises, price falls but reinvestmentincome rises because of new higher yield. And viceversa.

2. Thus the two always work in opposite direction.

3. Consider a time frame in future when the offsettingeffect of the two cancel each other so that there isno 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 portfolioimmunization 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

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Y

P =

Bo

nd

Pri

ce($

)

Price based on Duration.

Actual Price – Yield Curve

Curvature effect not incorporated by Duration

2decimals)in yieldin (Change*Price) (Initial*2

Price) Bond Initial *2 - rises yield when price Bond falls yield when price (BondConvexity

Note: To be covered only at conceptual level, need not go

into mathematics

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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 isworried 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 weare 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 alivetoday, he would have committed suicide seeing such a sharp fall.

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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.

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point basis 1by changes yield when Price - Price InitialPVBP

Value Bond * 0.01% *Duration PVBP

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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 theeffective 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 ofbond 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 withme till that time.

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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 25bps 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.

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Issue Maturity Market Value

A 2 $8.5mn

B 5 $4.6mn

C 10 $12.9mn

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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

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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 noadjustments for embedded options on cash flows

2. For bonds with no options, modified duration is similar to effectiveduration

3. Macaulay duration takes into consideration embedded options in thebond

2. A fixed income analyst makes the following two statements:

1. Statement 1: YTM assumes that coupon payments are reinvested at therate 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 ratethat makes the PV of all the cash flows from a non-Treasury security equalto its price.

2. Statement 2: The Z-spread ignores the interest rate volatility and assumesit to be zero.

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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

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4. Sally states that there are a number of yield measures that are used traditionally in the bond market. The leastlikely 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 ina 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 to103.44. The PVBP for the bond is closest to

A. $0.0455

B. $0.0512

C. $0.0519

D. The heart of the bond53

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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.

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Coupon Maturity Par ValueMarket Value

Duration

8% 5 years $ 5 mn $ 4 mn 4.8711% 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 tocalculate the PV of cash flows of a bond. It also assumes the volatility of interest rates is zero hence it is also known asthe 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 tomaturity 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. Theduration also assumes that yields change is parallel across the entire yield curve.

6. A.

The PVBP = 104.35 – 103.44 / 20 = 0.0455

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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 cashflows later (more of the cash flow is comprised of principal at maturity) than a higher-coupon bond does. Longer-termcash flows are discounted more heavily in the present value calculation. Another way to think about this: The relationshipbetween 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 raterisk because it delivers all its cash flows at maturity. Since a zero-coupon bond has a 0.00% coupon, a low coupon equatesto high price volatility.

8. A.

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Issue Market ValueMV % of Portfolio

ValueDuration

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

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5 Minutes Recap

57

N32 YTM)(1

PARC......

YTM)(1

C

YTM)(1

C

YTM)(1

Cbond a of Value

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

yModDVVy

VDD

D

D ..

V

1-ModD

)yearper paymentsinterest of no

YTM(1

DurationMacaulayDurationModified

Value Bond * 0.01% *Duration PVBP

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

Theories Of Term Structure Of Interest Rates• 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

ccra session 9_new

Economy & Finance