2018 CFA level 2 study note book4 unprotected

Table of Contents
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Getting Started Flyer
Table of Contents
Page List
Book 4: Fixed Income And Derivatives
Readings and Learning Outcome Statements
The Term Structure and Interest Rate Dynamics
1. LOS 35.a: Describe relationships among spot rates, forward rates, yield to
maturity, expected and realized returns on bonds, and the shape of the
yield curve.
2. LOS 35.b: Describe the forward pricing and forward rate models and
calculate forward and spot prices and rates using those models.
3. LOS 35.c: Describe how zero-coupon rates (spot rates) may be obtained
from the par curve by bootstrapping.
4. LOS 35.d: Describe the assumptions concerning the evolution of spot rates
in relation to forward rates implicit in active bond portfolio management.
5. LOS 35.e: Describe the strategy of riding the yield curve.
6. LOS 35.f: Explain the swap rate curve and why and how market participants
use it in valuation.
7. LOS 35.g: Calculate and interpret the swap spread for a given maturity.
8. LOS 35.h: Describe the Z-spread.
9. LOS 35.i: Describe the TED and Libor–OIS spreads.

10. LOS 35.j: Explain traditional theories of the term structure of interest rates
and describe the implications of each theory for forward rates and the
shape of the yield curve.
11. LOS 35.k: Describe modern term structure models and how they are used.
12. LOS 35.l: Explain how a bond’s exposure to each of the factors driving the
yield curve can be measured and how these exposures can be used to
manage yield curve risks.
13. LOS 35.m: Explain the maturity structure of yield volatilities and their effect
on price volatility.
14. Key Concepts
1. LOS 35.a
2. LOS 35.b
3. LOS 35.c
4. LOS 35.d
5. LOS 35.e
6. LOS 35.f
7. LOS 35.g
8. LOS 35.h
9. LOS 35.i


10. LOS 35.j
11. LOS 35.k
12. LOS 35.l
13. LOS 35.m
15. Concept Checkers
1. Answers – Concept Checkers
7. The Arbitrage-Free Valuation Framework
1. LOS 36.a: Explain what is meant by arbitrage-free valuation of a fixedincome instrument.
2. LOS 36.b: Calculate the arbitrage-free value of an option-free, fixed-rate

coupon bond.
3. LOS 36.c: Describe a binomial interest rate tree framework.
4. LOS 36.d: Describe the backward induction valuation methodology and
calculate the value of a fixed-income instrument given its cash flow at each
node.
5. LOS 36.e: Describe the process of calibrating a binomial interest rate tree
to match a specific term structure.
6. LOS 36.f: Compare pricing using the zero-coupon yield curve with pricing
using an arbitrage-free binomial lattice.
7. LOS 36.g: Describe pathwise valuation in a binomial interest rate
framework and calculate the value of a fixed-income instrument given its
cash flows along each path.
8. LOS 36.h: Describe a Monte Carlo forward-rate simulation and its
application.
9. Key Concepts
1. LOS 36.a
2. LOS 36.b
3. LOS 36.c
4. LOS 36.d
5. LOS 36.e
6. LOS 36.f
7. LOS 36.g
8. LOS 36.h
10. Concept Checkers
1. Answers – Concept Checkers
8. Valuation and Analysis: Bonds with Embedded Options
1. LOS 37.a: Describe fixed-income securities with embedded options.
2. LOS 37.b: Explain the relationships between the values of a callable or
putable bond, the underlying option-free (straight) bond, and the
embedded option.

3. LOS 37.c: Describe how the arbitrage-free framework can be used to value
a bond with embedded options.
4. LOS 37.f: Calculate the value of a callable or putable bond from an interest
rate tree.


5. LOS 37.d: Explain how interest rate volatility affects the value of a callable
or putable bond.
6. LOS 37.e: Explain how changes in the level and shape of the yield curve
affect the value of a callable or putable bond.
7. LOS 37.g: Explain the calculation and use of option-adjusted spreads.
8. LOS 37.h: Explain how interest rate volatility affects option-adjusted
spreads.
9. LOS 37.i: Calculate and interpret effective duration of a callable or putable
bond.
10. LOS 37.j: Compare effective durations of callable, putable, and straight
bonds.
11. LOS 37.k: Describe the use of one-sided durations and key rate durations to
evaluate the interest rate sensitivity of bonds with embedded options.
12. LOS 37.l: Compare effective convexities of callable, putable, and straight
bonds.
13. LOS 37.m: Calculate the value of a capped or floored floating-rate bond.
14. LOS 37.n: Describe defining features of a convertible bond.
15. LOS 37.o: Calculate and interpret the components of a convertible bond’s
value.
16. LOS 37.p: Describe how a convertible bond is valued in an arbitrage-free
framework.
17. LOS 37.q: Compare the risk–return characteristics of a convertible bond
with the risk–return characteristics of a straight bond and of the underlying
common stock.

18. Key Concepts
1. LOS 37.a
2. LOS 37.b
3. LOS 37.c
4. LOS 37.d
5. LOS 37.e
6. LOS 37.f
7. LOS 37.g
8. LOS 37.h
9. LOS 37.i
10. LOS 37.j
11. LOS 37.k
12. LOS 37.m
13. LOS 37.l
14. LOS 37.n
15. LOS 37.o
16. LOS 37.p
17. LOS 37.q
19. Concept Checkers
1. Answers – Concept Checkers


20. Challenge Problems
1. Answers – Challenge Problems
9. Credit Analysis Models
1. LOS 38.a: Explain probability of default, loss given default, expected loss,
and present value of the expected loss and describe the relative
importance of each across the credit spectrum.
2. LOS 38.b: Explain credit scoring and credit ratings.
3. LOS 38.c: Explain strengths and weaknesses of credit ratings.

4. LOS 38.d: Explain structural models of corporate credit risk, including why
equity can be viewed as a call option on the company’s assets.
5. LOS 38.e: Explain reduced form models of corporate credit risk, including
why debt can be valued as the sum of expected discounted cash flows after
adjusting for risk.
6. LOS 38.f: Explain assumptions, strengths, and weaknesses of both
structural and reduced form models of corporate credit risk.
7. LOS 38.g: Explain the determinants of the term structure of credit spreads.
8. LOS 38.h: Calculate and interpret the present value of the expected loss on
a bond over a given time horizon.
9. LOS 38.i: Compare the credit analysis required for asset-backed securities
to analysis of corporate debt.
10. Key Concepts
1. LOS 38.a
2. LOS 38.b
3. LOS 38.c
4. LOS 38.d
5. LOS 38.e
6. LOS 38.f
7. LOS 38.g
8. LOS 38.h
9. LOS 38.i
11. Concept Checkers
1. Answers – Concept Checkers
10. Credit Default Swaps
1. LOS 39.a: Describe credit default swaps (CDS), single-name and index CDS,
and the parameters that define a given CDS product.
2. LOS 39.b: Describe credit events and settlement protocols with respect to
CDS.
3. LOS 39.c: Explain the principles underlying, and factors that influence, the

market’s pricing of CDS.
4. LOS 39.d: Describe the use of CDS to manage credit exposures and to
express views regarding changes in shape and/or level of the credit curve.
5. LOS 39.e: Describe the use of CDS to take advantage of valuation disparities
among separate markets, such as bonds, loans, equities, and equity-linked
instruments.


6. Key Concepts
1. LOS 39.a
2. LOS 39.b
3. LOS 39.c
4. LOS 39.d
5. LOS 39.e
7. Concept Checkers
1. Answers – Concept Checkers
8. Self-Test: Fixed Income
1. Self-Test Answers: Fixed Income
11. Pricing and Valuation of Forward Commitments
1. LOS 40.a: Describe and compare how equity, interest rate, fixed-income,
and currency forward and futures contracts are priced and valued.
2. LOS 40.b: Calculate and interpret the no-arbitrage value of equity, interest
rate, fixed-income, and currency forward and futures contracts.
3. LOS 40.c: Describe and compare how interest rate, currency, and equity
swaps are priced and valued.
4. LOS 40.d: Calculate and interpret the no-arbitrage value of interest rate,
currency, and equity swaps.
5. Key Concepts
1. LOS 40.a, b
2. LOS 40.c, d

6. Concept Checkers
1. Answers – Concept Checkers
7. Challenge Problems
1. Answers – Challenge Problems
12. Valuation of Contingent Claims
1. LOS 41.a: Describe and interpret the binomial option valuation model and
its component terms.
2. LOS 41.b: Calculate the no-arbitrage values of European and American
options using a two-period binomial model.
3. LOS 41.e: Describe how the value of a European option can be analyzed as
the present value of the option’s expected payoff at expiration.
4. LOS 41.c: Identify an arbitrage opportunity involving options and describe
the related arbitrage.
5. LOS 41.d: Calculate and interpret the value of an interest rate option using
a two-period binomial model.
6. LOS 41.f: Identify assumptions of the Black–Scholes–Merton option
valuation model.
7. LOS 41.g: Interpret the components of the Black–Scholes–Merton model as
applied to call options in terms of a leveraged position in the underlying;
8. LOS 41.h: Describe how the Black–Scholes–Merton model is used to value
European options on equities and currencies.
9. LOS 41.i: Describe how the Black model is used to value European options


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on futures.
10. LOS 41.j: Describe how the Black model is used to value European interest
rate options and European swaptions.
11. LOS 41.k: Interpret each of the option Greeks.

12. LOS 41.l: Describe how a delta hedge is executed.
13. LOS 41.m: Describe the role of gamma risk in options trading.
14. LOS 41.n: Define implied volatility and explain how it is used in options
trading.
15. Key Concepts
1. LOS 41.a
2. LOS 41.b
3. LOS 41.c
4. LOS 41.d
5. LOS 41.e
6. LOS 41.f
7. LOS 41.g
8. LOS 41.h
9. LOS 41.i
10. LOS 41.j
11. LOS 41.k
12. LOS 41.l
13. LOS 41.m
14. LOS 41.n
16. Concept Checkers
1. Answers – Concept Checkers
17. Challenge Problems
1. Answers – Challenge Problems
13. Derivatives Strategies
1. LOS 42.a: Describe how interest rate, currency, and equity swaps, futures,
and forwards can be used to modify portfolio risk and return.
2. LOS 42.b: Describe how to replicate an asset replicating assets by using
options and by using cash plus forwards or futures.
3. LOS 42.c: Describe the investment objectives, structure, payoff, and risk(s)
of a covered call position.

4. LOS 42.d: Describe the investment objectives, structure, payoff, and risk(s)
of a protective put position.
5. LOS 42.e: Calculate and interpret the value at expiration, profit, maximum
profit, maximum loss, and breakeven underlying price at expiration for
covered calls and protective puts.
6. LOS 42.f: Contrast protective put and covered call positions to being long
an asset and short a forward on the asset.
7. LOS 42.g: Describe the investment objective(s), structure, payoffs, and risks
of the following option strategies: bull spread, bear spread, collar, and
straddle.


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8. LOS 42.h: Calculate and interpret the value at expiration, profit, maximum
profit, maximum loss, and breakeven underlying price at expiration of the
following option strategies: bull spread, bear spread, collar, and straddle.
9. LOS 42.i: Describe uses of calendar spreads.
10. LOS 42.j: Identify and evaluate appropriate derivatives strategies
derivatives strategies consistent with given investment objectives.
11. Key Concepts
1. LOS 42.a
2. LOS 42.b
3. LOS 42.c, e
4. LOS 42.d, e
5. LOS 42.f
6. LOS 42.g, h
7. LOS 42.i
8. LOS 42.j
12. Concept Checkers

1. Answers – Concept Checkers
14. Self-Test: Derivatives
1. Self-Test Answers: Derivatives
15. Formulas
16. Copyright


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BOOK 4 – FIXED INCOME AND DERIVATIVES
Readings and Learning Outcome Statements
Study Session 12 – Fixed Income: Valuation Concepts
Study Session 13 – Fixed Income: Topics in Fixed-Income Analysis
Self-Test – Fixed Income
Study Session 14 – Derivative Instruments: Valuation and Strategies
Self-Test – Derivatives
Formulas


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READINGS AND LEARNING OUTCOME STATEMENTS
READINGS
The following material is a review of the Fixed Income and Derivatives principles
designed to address the learning outcome statements set forth by CFA Institute.

STUDY SESSION 12
Reading Assignments
Fixed Income and Derivatives, CFA Program Curriculum,
Volume 5, Level II (CFA Institute, 2017)
35. The Term Structure and Interest Rate Dynamics (page 1)
36. The Arbitrage-Free Valuation Framework (page 34)

STUDY SESSION 13
Reading Assignments
Fixed Income and Derivatives, CFA Program Curriculum,
Volume 5, Level II (CFA Institute, 2017)
37. Valuation and Analysis: Bonds with Embedded Options (page 55)
38. Credit Analysis Models (page 92)
39. Credit Default Swaps (page 111)

STUDY SESSION 14
Reading Assignments
Fixed Income and Derivatives, CFA Program Curriculum,
Volume 5, Level II (CFA Institute, 2017)
40. Pricing and Valuation of Forward Commitments (page 128)
41. Valuation of Contingent Claims (page 166)
42. Derivatives Strategies (page 203)

LEARNING OUTCOME STATEMENTS (LOS)


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The CFA Institute Learning Outcome Statements are listed below. These are repeated in

each topic review; however, the order may have been changed in order to get a better
fit with the flow of the review.

STUDY SESSION 12
The topical coverage corresponds with the following CFA Institute assigned
reading:
35. The Term Structure and Interest Rate Dynamics
The candidate should be able to:
a. describe relationships among spot rates, forward rates, yield to maturity,
expected and realized returns on bonds, and the shape of the yield curve.
(page 1)
b. describe the forward pricing and forward rate models and calculate
forward and spot prices and rates using those models. (page 3)
c. describe how zero-coupon rates (spot rates) may be obtained from the
par curve by bootstrapping. (page 6)
d. describe the assumptions concerning the evolution of spot rates in
relation to forward rates implicit in active bond portfolio management.
(page 8)
e. describe the strategy of riding the yield curve. (page 11)
f. explain the swap rate curve and why and how market participants use it in
valuation. (page 12)
g. calculate and interpret the swap spread for a given maturity. (page 14)
h. describe the Z-spread. (page 16)
i. describe the TED and Libor-OIS spreads. (page 17)
j. explain traditional theories of the term structure of interest rates and
describe the implications of each theory for forward rates and the shape
of the yield curve. (page 18)
k. describe modern term structure models and how they are used. (page 21)
l. explain how a bond’s exposure to each of the factors driving the yield
curve can be measured and how these exposures can be used to manage

yield curve risks. (page 23)
m. explain the maturity structure of yield volatilities and their effect on price
volatility. (page 25)
The topical coverage corresponds with the following CFA Institute assigned
reading:
36. The Arbitrage-Free Valuation Framework


The candidate should be able to:
a. explain what is meant by arbitrage-free valuation of a fixed-income
instrument. (page 34)
b. calculate the arbitrage-free value of an option-free, fixed-rate coupon
bond. (page 35)
c. describe a binomial interest rate tree framework. (page 36)
d. describe the backward induction valuation methodology and calculate the
value of a fixed-income instrument given its cash flow at each node.
(page 38)
e. describe the process of calibrating a binomial interest rate tree to match a
specific term structure. (page 39)
f. compare pricing using the zero-coupon yield curve with pricing using an
arbitrage-free binomial lattice. (page 41)
g. describe pathwise valuation in a binomial interest rate framework and
calculate the value of a fixed-income instrument given its cash flows along
each path. (page 43)
h. describe a Monte Carlo forward-rate simulation and its application.
(page 44)

STUDY SESSION 13
The topical coverage corresponds with the following CFA Institute assigned
reading:

37. Valuation and Analysis: Bonds with Embedded Options
The candidate should be able to:
a. describe fixed-income securities with embedded options. (page 55)
b. explain the relationships between the values of a callable or putable
bond, the underlying option-free (straight) bond, and the embedded
option. (page 56)
c. describe how the arbitrage-free framework can be used to value a bond
with embedded options. (page 56)
d. explain how interest rate volatility affects the value of a callable or
putable bond. (page 59)
e. explain how changes in the level and shape of the yield curve affect the
value of a callable or putable bond. (page 60)
f. calculate the value of a callable or putable bond from an interest rate tree.
(page 56)
g. explain the calculation and use of option-adjusted spreads. (page 60)


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h. explain how interest rate volatility affects option adjusted spreads.
(page 62)
i. calculate and interpret effective duration of a callable or putable bond.
(page 63)
j. compare effective durations of callable, putable, and straight bonds.
(page 64)
k. describe the use of one-sided durations and key rate durations to evaluate
the interest rate sensitivity of bonds with embedded options. (page 65)
l. compare effective convexities of callable, putable, and straight bonds.
(page 67)
m. calculate the value of a capped or floored floating-rate bond. (page 68)

n. describe defining features of a convertible bond. (page 70)
o. calculate and interpret the components of a convertible bond’s value.
(page 71)
p. describe how a convertible bond is valued in an arbitrage-free framework.
(page 73)
q. compare the risk–return characteristics of a convertible bond with the
risk–return characteristics of a straight bond and of the underlying
common stock. (page 74)
The topical coverage corresponds with the following CFA Institute assigned
reading:
38. Credit Analysis Models
The candidate should be able to:
a. explain probability of default, loss given default, expected loss, and
present value of the expected loss and describe the relative importance of
each across the credit spectrum. (page 92)
b. explain credit scoring and credit ratings. (page 93)
c. explain strengths and weaknesses of credit ratings. (page 95)
d. explain structural models of corporate credit risk, including why equity
can be viewed as a call option on the company’s assets. (page 95)
e. explain reduced form models of corporate credit risk, including why debt
can be valued as the sum of expected discounted cash flows after
adjusting for risk. (page 98)
f. explain assumptions, strengths, and weaknesses of both structural and
reduced form models of corporate credit risk. (page 99)
g. explain the determinants of the term structure of credit spreads.
(page 101)
h. calculate and interpret the present value of the expected loss on a bond
over a given time horizon. (page 101)

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i. compare the credit analysis required for asset-backed securities to analysis
of corporate debt. (page 103)
The topical coverage corresponds with the following CFA Institute assigned
reading:
39. Credit Default Swaps
The candidate should be able to:
a. describe credit default swaps (CDS), single-name and index CDS, and the
parameters that define a given CDS product. (page 112)
b. describe credit events and settlement protocols with respect to CDS.
(page 113)
c. explain the principles underlying, and factors that influence, the market’s
pricing of CDS. (page 114)
d. describe the use of CDS to manage credit exposures and to express views
regarding changes in shape and/or level of the credit curve. (page 117)
e. describe the use of CDS to take advantage of valuation disparities among
separate markets, such as bonds, loans, equities, and equity-linked
instruments. (page 118)

STUDY SESSION 14
The topical coverage corresponds with the following CFA Institute assigned
reading:
40. Pricing and Valuation of Forward Commitments
The candidate should be able to:
a. describe and compare how equity, interest rate, fixed-income, and
currency forward and futures contracts are priced and valued. (page 133)
b. calculate and interpret the no-arbitrage value of equity, interest rate,
fixed-income, and currency forward and futures contracts. (page 133)
c. describe and compare how interest rate, currency, and equity swaps are

priced and valued. (page 147)
d. calculate and interpret the no-arbitrage value of interest rate, currency,
and equity swaps. (page 147)
The topical coverage corresponds with the following CFA Institute assigned
reading:
41. Valuation of Contingent Claims
The candidate should be able to:
a. describe and interpret the binomial option valuation model and its
component terms. (page 166)


b. calculate the no-arbitrage values of European and American options using
a two-period binomial model. (page 166)
c. identify an arbitrage opportunity involving options and describe the
related arbitrage. (page 174)
d. calculate and interpret the value of an interest rate option using a twoperiod binomial model. (page 176)
e. describe how the value of a European option can be analyzed as the
present value of the option’s expected payoff at expiration. (page 166)
f. identify assumptions of the Black-Scholes-Merton option valuation model.
(page 178)
g. interpret the components of the Black-Scholes-Merton model as applied
to call options in terms of leveraged position in the underlying. (page 179)
h. describe how the Black–Scholes–Merton model is used to value European
options on equities and currencies. (page 181)
i. describe how the Black model is used to value European options on
futures. (page 182)
j. describe how the Black model is used to value European interest rate
options and European swaptions. (page 183)
k. interpret each of the option Greeks. (page 185)
l. describe how a delta hedge is executed. (page 190)

m. describe the role of gamma risk in options trading. (page 192)
n. define implied volatility and explain how it is used in options trading.
(page 192)
The topical coverage corresponds with the following CFA Institute assigned
reading:
42. Derivative Strategies
The candidate should be able to:
a. describe how interest rate, currency, and equity swaps, futures, and
forwards can be used to modify portfolio risk and return. (page 203)
b. describe how to replicate an asset by using options and by using cash plus
forwards or futures. (page 205)
c. describe the investment objectives, structure, payoff, and risk(s) of a
covered call position. (page 208)
d. describe the investment objectives, structure, payoff, and risk(s) of a
protective put position. (page 209)
e. calculate and interpret the value at expiration, profit, maximum profit,
maximum loss, and breakeven underlying price at expiration for covered
calls and protective puts. (page 210)


f. contrast protective put and covered call positions to being long an asset
and short a forward on the asset. (page 212)
g. describe the investment objective(s), structure, payoffs, and risks of the
following option strategies: bull spread, bear spread, collar, and straddle.
(page 213)
h. calculate and interpret the value at expiration, profit, maximum profit,
maximum loss, and breakeven underlying price at expiration of the
following option strategies: bull spread, bear spread, collar, and straddle.
(page 213)
i. describe uses of calendar spreads. (page 221)

j. identify and evaluate appropriate derivatives strategies consistent with
given investment objectives. (page 222)


The following is a review of the Fixed Income: Valuation Concepts principles designed to address the learning
outcome statements set forth by CFA Institute. Cross-Reference to CFA Institute Assigned Reading #35.

THE TERM STRUCTURE AND INTEREST RATE
DYNAMICS
Study Session 12

EXAM FOCUS
This topic review discusses the theories and implications of the term structure of
interest rates. In addition to understanding the relationships between spot rates,
forward rates, yield to maturity, and the shape of the yield curve, be sure you become
familiar with concepts like the z-spread, the TED spread and the LIBOR-OIS spread.
Interpreting the shape of the yield curve in the context of the theories of the term
structure of interest rates is always important for the exam. Also pay close attention to
the concept of key rate duration.

INTRODUCTION
The financial markets both impact and are controlled by interest rates. Understanding
the term structure of interest rates (i.e., the graph of interest rates at different
maturities) is one key to understanding the performance of an economy. In this
reading, we explain how and why the term structure changes over time.
Spot rates are the annualized market interest rates for a single payment to be received
in the future. Generally, we use spot rates for government securities (risk-free) to
generate the spot rate curve. Spot rates can be interpreted as the yields on zerocoupon bonds, and for this reason we sometimes refer to spot rates as zero-coupon
rates. A forward rate is an interest rate (agreed to today) for a loan to be made at
some future date.

Professor’s Note: While most of the LOS is this topic review have Describe or Explain as the
command words, we will still delve into numerous calculations, as it is difficult to really
understand some of these concepts without getting in to the mathematics behind them.

LOS 35.a: Describe relationships among spot rates, forward rates, yield to
maturity, expected and realized returns on bonds, and the shape of the yield
curve.
CFA® Program Curriculum, Volume 5, page 6

SPOT RATES


The price today of $1 par, zero-coupon bond is known as the discount factor, which we
will call PT. Because it is a zero-coupon bond, the spot interest rate is the yield to
maturity of this payment, which we represent as ST. The relationship between the
discount factor PT and the spot rate ST for maturity T can be expressed as:

The term structure of spot rates—the graph of the spot rate ST versus the maturity T—
is known as the spot yield curve or spot curve. The shape and level of the spot curve
changes continuously with the market prices of bonds.

FORWARD RATES
The annualized interest rate on a loan to be initiated at a future period is called the
forward rate for that period. The term structure of forward rates is called the forward
curve. (Note that forward curves and spot curves are mathematically related—we can
derive one from the other.)
We will use the following notation:
f(j,k) = the annualized interest rate applicable on a k-year loan starting in j
years.

F(j,k) = the forward price of a $1 par zero-coupon bond maturing at time j+k
delivered at time j.
F(j,k) = the discount factor associated with the forward rate.

YIELD TO MATURITY
As we’ve discussed, the yield to maturity (YTM) or yield of a zero-coupon bond with
maturity T is the spot interest rate for a maturity of T. However, for a coupon bond, if
the spot rate curve is not flat, the YTM will not be the same as the spot rate.
Example: Spot rates and yield for a coupon bond
Compute the price and yield to maturity of a three-year, 4% annual-pay, $1,000 face value bond given the
following spot rate curve: S1 = 5%, S2 = 6%, and S3 = 7%.
Answer: