LOS 67 Introduction to the Valuation of Debt Securities
a. explain the steps in the bond valuation process;
Steps involved in bond valuation
The fundamental principle of valuation is that the value is equal to the present value of its expected cash flows. The valuation process involves the following three steps:
1. Estimate the expected cash flows.
2. Determine the appropriate interest rate or interest rates that should be used to discount the cash flows.
3. Calculate the present value of the expected cash flows found in step one by using the interest rate or interest rates determined in step two.
Showing posts with label Fixed income securities. Show all posts
Showing posts with label Fixed income securities. Show all posts
Monday, March 10, 2008
Estimating Expected Cash Flows - Difficulties
b. identify the types of bonds for which estimating the expected cash flows is difficult,
and explain the problems encountered when estimating the cash flows for
these bonds;
Bonds With Difficult Expected Cash Flow Estimation
The bonds for which it is difficult to estimate expected cash flows fall into three categories:
1.Bonds for which the issuer or investor has an option or right to change the contract due date for the payment of the principal. These include callable bonds, puttable bonds, MBSs and ABSs.
2.Bonds for which coupon payment rate is reset occasionally based on a formula with values that change, such as reference rates, prices or exchange rates. A floating-rate bond would be an example of this type of category.
3. Bonds for which investor has the option to convert or exchange the security for common stock.
For more See
http://www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa35.asp
The above page has information useful for the next LOS 67.c also.
and explain the problems encountered when estimating the cash flows for
these bonds;
Bonds With Difficult Expected Cash Flow Estimation
The bonds for which it is difficult to estimate expected cash flows fall into three categories:
1.Bonds for which the issuer or investor has an option or right to change the contract due date for the payment of the principal. These include callable bonds, puttable bonds, MBSs and ABSs.
2.Bonds for which coupon payment rate is reset occasionally based on a formula with values that change, such as reference rates, prices or exchange rates. A floating-rate bond would be an example of this type of category.
3. Bonds for which investor has the option to convert or exchange the security for common stock.
For more See
http://www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa35.asp
The above page has information useful for the next LOS 67.c also.
Computing Value of Bond for a Change in Dicount Rate
c. compute the value of a bond and the change in value that is attributable to a
change in the discount rate;
see
http://www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa36.asp
change in the discount rate;
see
http://www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa36.asp
Price of a Bond near Maturity Date
d. explain how the price of a bond changes as the bond approaches its maturity
date, and compute the change in value that is attributable to the passage
of time;
See
www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa36.asp
date, and compute the change in value that is attributable to the passage
of time;
See
www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa36.asp
Arbitrage-free Valuation Approach Bonds
LOS
67
.f. explain the arbitrage-free valuation approach and the market process that forces
the price of a bond toward its arbitrage-free value, and explain how a dealer can
generate an arbitrage profit if a bond is mispriced.
The value of the bond based on the spot rates is the arbitrage-free value.
How Does a Dealer Generate Arbitrage Profits?
A dealer has the ability to strip a security or to take apart the cash flows that make up the bond and create new securites out of them. These Treasury strips can be sold to investors. So if the market price of a Treasury security is less than the value using the arbitrage-free valuation, a dealer will buy the security, strip the bond (break the bond into strips) and then sell the Treasury strips at a higher amount than the purchase price for the whole bond.
See for more
http://www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa37.asp
67
.f. explain the arbitrage-free valuation approach and the market process that forces
the price of a bond toward its arbitrage-free value, and explain how a dealer can
generate an arbitrage profit if a bond is mispriced.
The value of the bond based on the spot rates is the arbitrage-free value.
How Does a Dealer Generate Arbitrage Profits?
A dealer has the ability to strip a security or to take apart the cash flows that make up the bond and create new securites out of them. These Treasury strips can be sold to investors. So if the market price of a Treasury security is less than the value using the arbitrage-free valuation, a dealer will buy the security, strip the bond (break the bond into strips) and then sell the Treasury strips at a higher amount than the purchase price for the whole bond.
See for more
http://www.investopedia.com/study-guide/cfa-exam/level-1/fixed-income/cfa37.asp
LOS 68 Yield Measures, Spot Rates, and Forward Rates
a. explain the sources of return from investing in a bond;
Interest
Capital appreciation
Reinvestment income
-------------
return of Principal
Interest
Capital appreciation
Reinvestment income
-------------
return of Principal
Traditional Yield Measures for Bonds
b. compute and interpret the traditional yield measures for fixed-rate bonds, and
explain their limitations and assumptions;
Current yield
To obtain the current yield, the annual coupon interest is divided by the market price.
Yield to maturity
The yield on any investment is the interest rate that will make the present value of the cash flows from the investment equal to the price of the investment.
Yield to call
For bonds that may be called prior to the stated maturity date another yield measure is commonly quoted: it is the yield to call.
To compute the yield to call, the cash flows that occur if the issue is called on its first call date are used.
http://www.paranzasoft.com/help/pages/glBondYieldMeasures.html
explain their limitations and assumptions;
Current yield
To obtain the current yield, the annual coupon interest is divided by the market price.
Yield to maturity
The yield on any investment is the interest rate that will make the present value of the cash flows from the investment equal to the price of the investment.
Yield to call
For bonds that may be called prior to the stated maturity date another yield measure is commonly quoted: it is the yield to call.
To compute the yield to call, the cash flows that occur if the issue is called on its first call date are used.
http://www.paranzasoft.com/help/pages/glBondYieldMeasures.html
Reinvestment Income and Reinvestment Risk
c. explain the importance of reinvestment income in generating the yield computed
at the time of purchase, calculate the amount of income required to generate
that yield, and discuss the factors that affect reinvestment risk;
Read about it from
The Handbook of Fixed Income Securities By Frank J. Fabozzi
http://books.google.co.in/books?id=jup2d1pEyWcC&pg=PA22&lpg=PA22&dq=reinvestment+income+and+reinvestment+risk&source=web&ots=wJORArm5cR&sig=cHzpjvT_6hs_vYEg0Vr397jLIdk&hl=en
at the time of purchase, calculate the amount of income required to generate
that yield, and discuss the factors that affect reinvestment risk;
Read about it from
The Handbook of Fixed Income Securities By Frank J. Fabozzi
http://books.google.co.in/books?id=jup2d1pEyWcC&pg=PA22&lpg=PA22&dq=reinvestment+income+and+reinvestment+risk&source=web&ots=wJORArm5cR&sig=cHzpjvT_6hs_vYEg0Vr397jLIdk&hl=en
Option Adjusted Spread
f. differentiate between the nominal spread, the zero-volatility spread, and the
option-adjusted spread;
If a bond has embedded options, its Option-adjusted spread (OAS) is the spread at which it presumably would be trading over a benchmark if it had no embedded optionality. More precisely, it is the instrument's current spread over the benchmark minus that component of the spread that is attributable to the cost of the embedded options:
OAS = spread - spread due to option
For more see
http://www.riskglossary.com/link/option_adjusted_spread.htm
option-adjusted spread;
If a bond has embedded options, its Option-adjusted spread (OAS) is the spread at which it presumably would be trading over a benchmark if it had no embedded optionality. More precisely, it is the instrument's current spread over the benchmark minus that component of the spread that is attributable to the cost of the embedded options:
OAS = spread - spread due to option
For more see
http://www.riskglossary.com/link/option_adjusted_spread.htm
OAS - Option Cost Relation
g. describe how the option-adjusted spread accounts for the option cost in a bond
with an embedded option;
with an embedded option;
LOS 69 Interest Rate Risk Measurement
a. distinguish between the full valuation approach (the scenario analysis approach)
and the duration/convexity approach for measuring interest rate risk, and explain
the advantage of using the full valuation approach;
The primary focus of interest rate risk is measuring the impact after an adverse rate change. Two approaches are used to measuring interest rate risk: the full valuation approach and the duration/convexity approach.
The full valuation approach also known as scenario analysis. It examines the value of bonds under a variety of interest rate scenario changes. For example, a portfolio manager might examine the change in a bond with assumed interest rate increases of 50, 100,150 and 200 basis point increases and decreases. This approach is useful when there is a good valuation model and can be used for parallel and nonparallel shifts in the yield curve.
Highly leveraged investors (such as hedge fund investors) often use extreme scenario tests, known as stress testing, to examine the impact of wide interest rate changes. This is fine so long as the manager has a good valuation model to estimate what the price of the bonds will be in each interest rate scenario.
The advantage of the duration/convexity measure is that it is a simpler measure that will show how a portfolio or single bond will change if there is change in a parallel fashion.
Material to be added
and the duration/convexity approach for measuring interest rate risk, and explain
the advantage of using the full valuation approach;
The primary focus of interest rate risk is measuring the impact after an adverse rate change. Two approaches are used to measuring interest rate risk: the full valuation approach and the duration/convexity approach.
The full valuation approach also known as scenario analysis. It examines the value of bonds under a variety of interest rate scenario changes. For example, a portfolio manager might examine the change in a bond with assumed interest rate increases of 50, 100,150 and 200 basis point increases and decreases. This approach is useful when there is a good valuation model and can be used for parallel and nonparallel shifts in the yield curve.
Highly leveraged investors (such as hedge fund investors) often use extreme scenario tests, known as stress testing, to examine the impact of wide interest rate changes. This is fine so long as the manager has a good valuation model to estimate what the price of the bonds will be in each interest rate scenario.
The advantage of the duration/convexity measure is that it is a simpler measure that will show how a portfolio or single bond will change if there is change in a parallel fashion.
Material to be added
c. describe positive convexity, negative convexity, and their relation to bond price
and yield;
Convexity is a measure of the curvedness of the price-yield relationship. This curvedness is different for each bond.
The lower the coupon, the greater the convexity.
The longer the maturity, the greater the convexity.
The lower the yield to maturity, the greater the convexity.
In summary, the change in price of a bond comes from two sources: its modified duration and its convexity.
The computation of the price change for a bond that is due to the convexity:
Convexity Effect = 1/2 * Price * Convexity * Δyield²
Callable bonds will exhibit negative convexity at certain price-yield combinations. Negative convexity means that as market yields decrease, duration decreases as well.
See
http://www.investopedia.com/university/advancedbond/advancedbond6.asp
and yield;
Convexity is a measure of the curvedness of the price-yield relationship. This curvedness is different for each bond.
The lower the coupon, the greater the convexity.
The longer the maturity, the greater the convexity.
The lower the yield to maturity, the greater the convexity.
In summary, the change in price of a bond comes from two sources: its modified duration and its convexity.
The computation of the price change for a bond that is due to the convexity:
Convexity Effect = 1/2 * Price * Convexity * Δyield²
Callable bonds will exhibit negative convexity at certain price-yield combinations. Negative convexity means that as market yields decrease, duration decreases as well.
See
http://www.investopedia.com/university/advancedbond/advancedbond6.asp
Duration Measures
LOS
69.e. distinguish among the alternative definitions of duration, and explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options;
DURATION MEASURES
Macaulay Duration: The weighted average time to full recovery of principal and interest payments.
= [ΣCt*t/(1+i)t]/[ΣCt/(1+i)t]
Characteristics of Macaulay Duration:
1. The duration of a bond with a coupon is always less than the term to maturity.
2. The larger the coupon, the smaller the duration.
3. There is normally a positive relationship between term to maturity and duration. As term to maturity increases, so does duration, but at a decreasing rate.
4. There is an inverse relationship between the yield to maturity and duration.
5. Sinking funds and call features can reduce the duration significantly.
Modified duration: an adjusted measure of duration called modified duration can be used to approximate the interest rate sensitivity of a noncallable bond. Modified duration equals Macaulay duration divided by 1 plus the current yield to maturity divided by the no. of payments in a year.
Modified Duration = Macaulay duration[1+(ytm/number of payments per year)]
The percentage change in the price of a bond for a given change in interest rates can be approximated by:
100*ΔP/P = -Dmod*Δi
ΔP = change in price
Δi = change in interest rate
Dmod = Modified duration
For More
http://www.duke.edu/~charvey/Classes/ba350/bondval/duration.htm
69.e. distinguish among the alternative definitions of duration, and explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options;
DURATION MEASURES
Macaulay Duration: The weighted average time to full recovery of principal and interest payments.
= [ΣCt*t/(1+i)t]/[ΣCt/(1+i)t]
Characteristics of Macaulay Duration:
1. The duration of a bond with a coupon is always less than the term to maturity.
2. The larger the coupon, the smaller the duration.
3. There is normally a positive relationship between term to maturity and duration. As term to maturity increases, so does duration, but at a decreasing rate.
4. There is an inverse relationship between the yield to maturity and duration.
5. Sinking funds and call features can reduce the duration significantly.
Modified duration: an adjusted measure of duration called modified duration can be used to approximate the interest rate sensitivity of a noncallable bond. Modified duration equals Macaulay duration divided by 1 plus the current yield to maturity divided by the no. of payments in a year.
Modified Duration = Macaulay duration[1+(ytm/number of payments per year)]
The percentage change in the price of a bond for a given change in interest rates can be approximated by:
100*ΔP/P = -Dmod*Δi
ΔP = change in price
Δi = change in interest rate
Dmod = Modified duration
For More
http://www.duke.edu/~charvey/Classes/ba350/bondval/duration.htm
Duration of a bond portfolio
f. compute the duration of a portfolio, given the duration of the bonds comprising
the portfolio, and explain the limitations of portfolio duration;
duration writeup
http://www.treasurer.ca.gov/cdiac/publications/duration.pdf
Duration, Convexity, and Other Bond Risk Measures By Frank J. Fabozzi
http://books.google.co.in/books?id=7i6ob9SB5jgC&pg=PA6&lpg=PA6&dq=%22duration+of+a+portfolio%22&source=web&ots=ZmSpP6g2Ks&sig=Jgf-3gdgb2O47YENTrQvTtwJ-OI&hl=en
Osborne, Mike J., "A Simple, Accurate Formula for the Duration of a Portfolio of Bonds Under a Non-Parallel Shift of a Non-Flat Yield Curve" (September 5, 2004). Available at SSRN:
http://ssrn.com/abstract=587242
the portfolio, and explain the limitations of portfolio duration;
duration writeup
http://www.treasurer.ca.gov/cdiac/publications/duration.pdf
Duration, Convexity, and Other Bond Risk Measures By Frank J. Fabozzi
http://books.google.co.in/books?id=7i6ob9SB5jgC&pg=PA6&lpg=PA6&dq=%22duration+of+a+portfolio%22&source=web&ots=ZmSpP6g2Ks&sig=Jgf-3gdgb2O47YENTrQvTtwJ-OI&hl=en
Osborne, Mike J., "A Simple, Accurate Formula for the Duration of a Portfolio of Bonds Under a Non-Parallel Shift of a Non-Flat Yield Curve" (September 5, 2004). Available at SSRN:
http://ssrn.com/abstract=587242
Convexity of a bond
g. describe the convexity measure of a bond, and estimate a bond’s percentage
price change, given the bond’s duration and convexity and a specified change in
interest rates;
Advanced Bond Concepts: Convexity
http://www.investopedia.com/university/advancedbond/advancedbond6.asp
price change, given the bond’s duration and convexity and a specified change in
interest rates;
Advanced Bond Concepts: Convexity
http://www.investopedia.com/university/advancedbond/advancedbond6.asp
Modified Convexity and Effective Convexity
h. differentiate between modified convexity and effective convexity;
From Google books
The Handbook of Fixed Income Securities By Frank J. Fabozzi
http://books.google.co.in/books?id=jup2d1pEyWcC&pg=PA116&lpg=PA116&dq=modified+convexity+and+effective+convexity&source=web&ots=wJORAlm2kL&sig=Bv5apvCK-H50KWpySX0uzIRGnrI&hl=en
From Google books
The Handbook of Fixed Income Securities By Frank J. Fabozzi
http://books.google.co.in/books?id=jup2d1pEyWcC&pg=PA116&lpg=PA116&dq=modified+convexity+and+effective+convexity&source=web&ots=wJORAlm2kL&sig=Bv5apvCK-H50KWpySX0uzIRGnrI&hl=en
Price value of a basis point (PVBP) Fixed Income Securities
LOS
69.i. compute the price value of a basis point (PVBP), and explain its relationship to
duration.
What is basis point value, (BPV)?
BPV is a method that is used to measure interest rate risk. It is sometimes referred to as a delta or DV01. It is often used to measure the interest rate risk associated with swap trading books, bond trading portfolios and money market books.
It is not new. It has been used for years. In many financial institutions it has been replaced or is used in conjunction with value at risk.
What does it show?
BPV tells you how much money your positions will gain or lose for a 0.01% parallel movement in the yield curve. It therefore quantifies your interest rate risk for small changes in interest rates.
How does it work?
Let's suppose you own a $10m bond that has a price of 100%, a coupon of 5.00% and matures in 5 years time. Over the next 5 years you will receive 5 coupon payments and a principal repayment at maturity. You can value this bond by:
A. Using the current market price from a dealer quote, or
B. Discounting the individual bond cash flows in order to find the sum of the present values
Let's assume you use the second method. You will use current market interest rates and a robust method for calculating accurate discount factors. (Typically swap rates are used with zero coupon methodology).
For the sake of simplicity we will use just one interest rate to discount the bond cash flows. That rate is 5.00%. Discounting the cash flows using this rate will give you a value for the 5 year bond of $10,000,000. (How to do this using a financial calculator is explained on the second page of this document).
We will now repeat the exercise using an interest rate of 5.01%, (rates have increased by 0.01%). The bond now has a value of $9,995,671.72.
There is a difference of $4,328.28.
It shows that the 0.01% increase in interest rates has caused a fall in the value of the bond. If you held that bond you would have lost $4,328.28 on a mark-to-market basis.
This is the BPV of the bond.
For some more details see
http://www.barbicanconsulting.co.uk/quickguides/bpv
69.i. compute the price value of a basis point (PVBP), and explain its relationship to
duration.
What is basis point value, (BPV)?
BPV is a method that is used to measure interest rate risk. It is sometimes referred to as a delta or DV01. It is often used to measure the interest rate risk associated with swap trading books, bond trading portfolios and money market books.
It is not new. It has been used for years. In many financial institutions it has been replaced or is used in conjunction with value at risk.
What does it show?
BPV tells you how much money your positions will gain or lose for a 0.01% parallel movement in the yield curve. It therefore quantifies your interest rate risk for small changes in interest rates.
How does it work?
Let's suppose you own a $10m bond that has a price of 100%, a coupon of 5.00% and matures in 5 years time. Over the next 5 years you will receive 5 coupon payments and a principal repayment at maturity. You can value this bond by:
A. Using the current market price from a dealer quote, or
B. Discounting the individual bond cash flows in order to find the sum of the present values
Let's assume you use the second method. You will use current market interest rates and a robust method for calculating accurate discount factors. (Typically swap rates are used with zero coupon methodology).
For the sake of simplicity we will use just one interest rate to discount the bond cash flows. That rate is 5.00%. Discounting the cash flows using this rate will give you a value for the 5 year bond of $10,000,000. (How to do this using a financial calculator is explained on the second page of this document).
We will now repeat the exercise using an interest rate of 5.01%, (rates have increased by 0.01%). The bond now has a value of $9,995,671.72.
There is a difference of $4,328.28.
It shows that the 0.01% increase in interest rates has caused a fall in the value of the bond. If you held that bond you would have lost $4,328.28 on a mark-to-market basis.
This is the BPV of the bond.
For some more details see
http://www.barbicanconsulting.co.uk/quickguides/bpv
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