Fixed Income Investments
Fixed Income
Fixed Income Investments
Fixed Income
Study Session 12
Study Session 12
Fixed Income (1)
Fixed Income (1)
32. The Term Structure and Interest Rate
Dynamics
Topic Weight: 10%‒15%
33. The Arbitrage-Free Valuation Framework
Fixed Income Investments
Fixed Income
Term Structure
Spot Rates

Fixed Income (1)
Spot rates: Yield on zero-coupon bonds
 No coupons  no reinvestment risk
1
Discount factor = PT =
(1+ ST )T
(price today of a $1
zero coupon bond)
32. The Term Structure and
Interest Rate Dynamics

Spot yield curve (spot curve): Graph of the spot
rate ST versus the maturity T
 Shape and level changes continuously
© Kaplan, Inc.
3
1
Term Structure
Term Structure
Forward Rates (cont.)
Forward Rates




Forward rate: The annualized interest rate on a
loan to be initiated at a future period
Tj+k
Tj
T0
Forward curve: Forward rates vs. maturity
F(j,k)
Forward curves and spot curves are
mathematically related
F(j,k) =
Forward rate
Notation:
 f(j,k) = the annualized interest rate applicable
on a k-period loan starting at time period j
 F(j,k) = forward price at time j, of a $1 par
zero-coupon bond maturing at time j+k
4
© Kaplan, Inc.
Pj+k
Pj+k =
1
(1+ S j+k ) j+k
-2
Term Structure
Example: Yield to Maturity
Solution: Yield to Maturity
T0
Using the spot rates given in the table, value a 3
year 5% annual coupon bond with a $1,000 face
value.
Compute the bond’s yield to maturity.
© Kaplan, Inc.
Rate %
4%
5%
6%
5
© Kaplan, Inc.
Term Structure
Period
1 year spot rate (S1)
2 year spot rate (S2)
3 year spot rate (S3)
1
(1 + f(j,k) )k
Upward sloping
spot curve
6
T1
T2
T3
$1,050
$
$50
$50
38.10
48.08
50
50
1,050
35.60
45.35
2
(1.05)
(1.06)3
(1.04)
881.60
848.95
975.03
S1 < y3< S3 and
922.65
y3 is closest to S3
Yield-to-maturity (y3):
N = 3; PV = –975.03; PMT = 50; FV = 1,000;
7
CPT I/Y→ 5.93, y3= 5.93%
© Kaplan, Inc.
-4
2
Term Structure
Term Structure
Expected Return



Forward Pricing Model
Expected return: Ex-ante holding period return an
investor expects to earn from a bond

The expected return will be equal to the bond’s
yield only when:
 The bond is held to maturity, and
 Coupon and principal received on-time; and
 All coupons reinvested at the original YTM

Reinvesting coupons at the YTM is the least
realistic assumption


Investor A purchases a $1 par, zero-coupon bond
maturing in (j+k) years for P(j+k)
Investor B enters into a j-year forward contract to
purchase a $1 par, zero-coupon bond maturing in
k-years. Cost today is PjF(j,k)
The two investments should have the same price:
P(j+k) = PjF(j,k)
8
© Kaplan, Inc.
Forward pricing model: Values forward
contracts using arbitrage-free pricing
9
© Kaplan, Inc.
Term Structure
Term Structure
Forward Rate Model


Example: Forward Rates
The forward rate model relates forward and spot
rates as follows:

[1+S(j+k)](j+k) = (1+Sj)j[1+f(j,k)]k

[1+f(j,k)]k = [1+S(j+k)](j+k) / (1+Sj)j
(1.08)5
Buying a 5-year zero (return of S5), versus buying
a 2-year zero (return of S2) and at maturity
reinvesting the principal for 3 additional years at
locked-in f(2,3)
© Kaplan, Inc.
S2= 6%, S5 = 8%. Calculate the implied 3-year
forward rate for a loan starting in 2 years:
T5
T2
T0
10
(1.06)2
(1+ f(2,3))3
(1.08) = (1.06 ) (1 + f2,3 ) 
5

3
2
(1 +f ) =1.30770
(2,3)
© Kaplan, Inc.
3

(1 + f ) = (
3
(2,3)
1
f( 2,3 ) = (1.30770 ) 3 –1
1.08 )
5
(1.06 )2
f( 2,3 ) = 9.35%
11
-7
3
Term Structure
Term Structure
Spot and Forward Rate Relationships

Par Rates
For an upward-sloping yield curve, the forward rate
f(j,k) rises as j increases.
 Par rate is the YTM for a bond trading at par
Spot curves
and forward
curves as of
July 2013
 Par rate = coupon rate
 For a bond with a single cash flow remaining
(i.e., last coupon + principal), par rate = spot rate
 Typically, par rates are used to generate spot
rates using bootstrapping (next slide)

Because the yield curve is upward sloping, the
forward curves lie above the spot curve.
12
© Kaplan, Inc.
13
© Kaplan, Inc.
Term Structure
Term Structure
Bootstrapping Spot Rates (cont.)
Example: Bootstrapping Spot Rates
1-year, 2-year, and 3-year par rates are 3%, 4%, and
5%, respectively. Using bootstrapping, calculate S1,
S2, and S3.
3-year bond:
100=
S1 = 1-year par rate = 3% by definition
2 year bond: 100=
4.0
1.03
+
104
(1+S2 )
2
96.11650
© Kaplan, Inc.
= (1+S2 )
2
1.03
S1
96.11650=
104
(1+S2 )2
90.52463 =
1
104
5.0
5.0
(1.04020 )
2
3
+
105
(1+S3 )3
S2
105
105
(1+S3 )
+
90.52463
= (1+S3 )
3
1
 104  2 –1 = 4.020%

 96.11650 
 105  3 –1 = 5.069%
S3 = 

 90.52463 
S2 = 
14
-4
© Kaplan, Inc.
15
-4
4
Term Structure
Term Structure
Spot and Forward Rate Relationships
Example: Spot Rate Evolution
Return on a LT bond (over one year) is always
equal to the one-year risk-free rate if spot rates
develop as predicted by today’s forward curve.
 An active portfolio manager will try to outperform
the market by predicting how the future spot rates
will differ from those predicted by the current
forward curve.
 If the future spot rates are below the current
forward rates, the portfolio manager will earn a
return greater than the one-year risk-free rate.


Spot Rates Today
Period
Rate
1 year (S1)
4%
2 year (S2)
6%
3 year (S3)
8%
16
© Kaplan, Inc.
Calculate the HPR of a 1-year ZCB, 2-year ZCB
and 3-year ZCB (face value $100) given the
following interest rate information:
17
© Kaplan, Inc.
Term Structure
Term Structure
Solution: Spot Rate Evolution


Solution: Spot Rate Evolution
1-year ZCB:
 $100 
$100
Price
− 1= 4%
= $96.15 Return = 
=
today
1.04
 96.15 
2-year ZCB:
Price = $100 = $89.00
2
today
1.06
(
)
 $92.56 
− 1= 4%
Return = 
 89.00 
$100
Price in
= $92.56
=
1 year
1.0804
© Kaplan, Inc.
Spot Rates in 1 Year
Period
Rate
1 year (S1)
8.04%
2 year (S2)
10.06%
18
-4

3-year ZCB:
Price = $100 = $79.38
3
today
1.08
 $82.55 
− 1= 4%
Return = 
 79.38 
$100
Price in
= $82.55
=
1 year
(1.1006)2
(
)
Note that all bonds generated the same 1 period
HPR, as the future spot rates were consistent
with current forward rates.
© Kaplan, Inc.
19
-3
5
Term Structure
Term Structure
Spot Rate Evolution: Appendix
Riding the Curve
Computation of forwards from today’s spots:
Spot Rates Today
Period
Rate
1 year (S1)
4%
2 year (S2)
6%
3 year (S3)
8%
(
(
)(
) (
(
(1.06)2 =  1.04 1+ f1,1 


2
3
1 + 0.06
1 + f(1,1) =
1
1 + 0.04
f(1,1) = 8.04%
(
2

(1.08)3 =  1.04 1+ f1,2 


3
2
1 + 0.08
1 + f(1,2) =
1
© Kaplan, Inc.
1 + 0.04
)
)
)

(
) (
(
)(
)
)
)


2
(1 + f ) = 1.211
(1,2)
f(1,2) = 10.06%

20
Riding the yield curve: If the yield curve is
upward-sloping, investor will purchase bonds with
maturity higher than their holding period
As time passes and maturity shortens, the bond’s
cash flows will be discounted at successively lower
yields
Will produce superior returns if the yield curve
remains stable over the investment horizon
Disadvantage: Increases interest rate risk
21
© Kaplan, Inc.
Term Structure
Term Structure
Example: Riding the Curve
Solution: Riding the Curve
An investor has a 5-year time horizon
 Two investment choices:
1. Buy a bond maturing in 5 years’ time
2. Buy a 30-year bond and sell it after 5 years

All bonds are 3% annual pay coupon $100 face
value treasuries
Maturity
YTM
Price
Spot rate
curve is
5 year
3%
$100.00
upward
25 year
4%
$84.38
sloping.
The investor buying the 3% treasury with 5 years to
maturity earns the coupon of 3%, no capital gains.

30 year
© Kaplan, Inc.
6%
$58.71
22
The investor buying the 30 year bond and selling it
after 5 years earns the 3% coupon plus the return
from the capital gain.
Price
Sale
Purchase
Gain
© Kaplan, Inc.
$
84.38
(58.71)
25.67
Yield:
N = 5; PV = –58.71;
PMT = 3; FV = 84.38;
CPT I/Y → 11.99%
23
-2
6
Term Structure
Term Structure
The Z-Spread



Example: The Z-spread
Z-spread: When added to each spot rate on the
default-free spot curve, makes the present value
of a bond’s cash flows equal to the bond’s
market price
Constant spread added to default-free spot curve
1-year risk free spot rate is 2%.
 2-year risk free spot rate is 4%.
 The market price of a 2-year bond with annual
coupon payments of 5% is $100.84. The Z-spread
is the spread that solves the following equation:

$100.84 =
The Z-spread is a spread over the entire spot
rate curve

24
© Kaplan, Inc.
$5
(1 + 0.02 + Z )
+
$105
(1 + 0.04 + Z )
In this case, the Z-spread is 0.006 = 60 bps.
(You will not be required to calculate the Z-spread.)

The term zero volatility in the Z-spread refers to
the assumption of zero interest rate volatility
Why does the yield curve take a particular shape?
Z-spread is not appropriate to use to value bonds
with embedded options
If used for bonds with embedded options, the Zspread includes the risk premium for option risk (in
addition to credit and liquidity risk premium)
© Kaplan, Inc.
Term Structure
Traditional Theories of the Term
Structure of Interest Rates
The Z-Spread (cont.)

25
© Kaplan, Inc.
Term Structure

2
26
Traditional theories:
1. Unbiased Expectations Theory
2. Local Expectations Theory
3. Liquidity Preference Theory
4. Segmented Markets Theory
5. Preferred Habitat Theory
© Kaplan, Inc.
27
7
Term Structure
Term Structure
1. Unbiased Expectations Theory
2. Local Expectations Theory
Also known as pure expectations theory
 “Investors’ expectations determine the shape of
the interest rate term structure”
 Forward rates = expected future spot rates
 Long-term interest rates equal the mean of future
expected short-term rates
 If the yield curve is upward sloping, short-term
rates are expected to rise

28
© Kaplan, Inc.




Local expectations does not say that every
maturity strategy should have the same return over
a given investment horizon
Over longer periods, risk premium exists
Risk-neutrality is preserved for only short-term
under local expectations
Shown not to work
Short-holding period returns
of long-maturity bonds are higher than those of
short-maturity bonds
© Kaplan, Inc.
Term Structure
Term Structure
3. Liquidity Preference Theory (cont.)
3. Liquidity Preference Theory

Proposes that forward rates reflect investors’
expectations of future spot rates, plus a liquidity
premium for interest rate risk



Interest rate risk: longer dated cash flows more
sensitive to rate changes


29
Forward rates are biased estimates of future rates
because of the liquidity premium
A positive-sloping yield curve may be due to future
expectations or to the liquidity premium
Premium is positively related to maturity.
25-year bond will have a larger premium
compared to a 2-year bond.
© Kaplan, Inc.
30
© Kaplan, Inc.
31
8
Term Structure
Term Structure
4. Segmented Markets Theory


Yield at each maturity is determined
independently of yields at other maturities

Various market participants only deal in securities
of a particular maturity


5. Preferred Habitat Theory
Because they are prevented from operating at
different maturities
Yield determined by supply and demand
32
© Kaplan, Inc.
Also proposes that forward rates are expected
future spot rates plus a premium
 Does not state that premium is directly related to
maturity
 Investors prefer a particular maturity
 Investors are willing to leave preferred maturity
habitat to obtain a lower price (and higher yield)
 Can be used to explain almost any yield curve
shape
Term Structure
Single-factor
models
2. Arbitrage-Free Models
a. The Ho-Lee Model
© Kaplan, Inc.
Suggests that interest rates are mean reverting to
a long-run value.
∆ in time
deterministic
stochastic
∆ in short
Random
term interest
walk
rates
dr = a(b−r)dt + σdz movement
Mean reversion Long-run mean
Current rate
parameter reverting level

1. Equilibrium Term Structure Models
b. The Cox–Ingersoll–Ross Model
Term Structure
The Vasicek Model 1977
Modern Theories of the Term
Structure of Interest Rates
a. The Vasicek Model
33
© Kaplan, Inc.
Think: binomial
trees (later)

34
The a(b−r)dt term forces the interest rate r to
mean-revert towards the long-run value b, at a
speed determined by a.
© Kaplan, Inc.
35
-3
9
Term Structure
Term Structure
The Cox–Ingersoll–Ross
(CIR) Model 1985

Vasicek vs. CIR Model

Two terms: drift and random
stochastic

dr = a b - r dt +σ r dz

deterministic
( )

Under the Vasicek model:

Deterministic term same as the Vasicek model
Improvement over the Vasicek model in the
stochastic term
36
© Kaplan, Inc.
-1
Interest rates could become negative
Under the CIR model:


Volatility does not increase as the level of
interest rates increase
Volatility related to the current level of the
interest rate (prevents negative rates)
37
© Kaplan, Inc.
Term Structure
Term Structure
The Ho-Lee Model 1986

Yield Curve Shifts
The Ho-Lee model takes the following form:
Yield curve shifts can be either simple parallel shifts
or more-complex non-parallel shifts.
drt = θt dt + σ dzt
Parallel shift
(level change)
Where θt is a time-dependent drift term
 Calibrated by using market prices to find the θt
that generates the current term structure
 Model can then be used to price zero-coupon
bonds and determine the spot curve
 Produces a normal distribution of rates

Nonparallel shift
(steepness change)
Nonparallel shift
(curvature change)
Think: binomial trees (later)
© Kaplan, Inc.
38
© Kaplan, Inc.
39
10
Term Structure
Methods of Measuring
Yield Curve Sensitivity
Term Structure
1. Effective Duration
Effective duration: Measures price risk for small
parallel shifts in yield curve
1. Effective duration

2. Key rate duration

3. Sensitivity to parallel, steepness, and curvature
movements
40
© Kaplan, Inc.
Problem: Most yield curve shifts have nonparallel
characteristics
Solution: Use key rate duration which measures
impact of nonparallel shifts
Term Structure
Term Structure
3. Sensitivity to Level, Steepness,
and Curvature Movements
2. Key Rate Duration


A more sophisticated method used to quantify
price sensitivity to nonparallel yield curve shifts

Key rate duration is price sensitivity to 1% change
in a single par rate, holding other par rates
constant
Decomposes risk into sensitivity to these
categories of yield curve movements:



© Kaplan, Inc.
41
© Kaplan, Inc.
42
Level (∆xL): A parallel increase or decrease of
interest rates
Steepness (∆xS): Long maturity interest rates
increase, and short rates decrease
Curvature (∆xC): Short and long rates increase;
intermediate rates don’t change
© Kaplan, Inc.
43
11
Fixed Income Investments
Fixed Income
Term Structure
Sensitivity to Parallel, Steepness,
and Curvature Movements

Fixed Income (1)
We can then model the change in the value of our
portfolio as follows:
33. The Arbitrage-Free
Valuation Framework
∆P/P ≈ –DL ∆XL –DS ∆X S –DC ∆X C
Sensitivities to changes in:
 Level
→ DL
 Steepness
→ DS
 Curvature
→ DC
44
© Kaplan, Inc.
The Arbitrage-Free
Valuation Framework
Arbitrage-Free Valuation

Example: Arbitrage-Free Valuation
Value a 3-year, 4.5% annual pay, $100 par
benchmark security
Arbitrage-free: Consistent with market price of
other securities


The Arbitrage-Free
Valuation Framework
Upholds value additivity principle
 Stripping
 Reconstitution
Does not allow for dominance
 One security cannot be priced more attractively
than an otherwise-identical security
© Kaplan, Inc.
46
Value =
© Kaplan, Inc.
Maturity
Spot Rate
1
1.00%
2
1.25%
3
1.50%
Bond price
lower → Strip
Bond price
higher →
Reconstitute
4.50
4.50
104.50
+
+
= $108.78
1.01 (1.0125)2 (1.0150)3
47
-2
12
The Arbitrage-Free
Valuation Framework
The Arbitrage-Free
Valuation Framework
Binomial Interest Rate Model
Binomial Interest Rate Tree
Nodal values → forward interest rates
Model: System for building interest rate trees



Rate tree represents possible paths
i
Assumes equal probability of upward or
downward interest rate movements
0.5
Lognormal random walk based on assumed
volatility in interest rates (non-negative rates
and higher volatility at higher rates)
i
48
i
0
0.5
i
0.5
i
0.5
2,LU
i2,LU = i2,LL (e2σ)
1,L
0.5
i
© Kaplan, Inc.
2,LL
The Arbitrage-Free
Valuation Framework
7%, 2-year bond with no embedded
options: use given interest rate tree
to find bond values
$???.??
for each node
$7.0
8%
$???.??
3%
$???.??
$7.0
5%
Things to know:


© Kaplan, Inc.
-6
Example: Backward Induction
Approach: Value bond by moving backward from
last period to time zero

49
The Arbitrage-Free
Valuation Framework
Backward Induction Methodology

2,UU
i2,UU = i2,LU (e2σ)
1,U
i1,U = i1,L (e2σ)
Your job: Know how to use the tree, you won’t be
creating the tree on the exam
© Kaplan, Inc.
0.5
Spot rate
i2,UU =i2,LLe4σ
Value at maturity is known.
Value at any node is average PV of two
possible values from next period.
Discount rate is forward rate for that node.
50
© Kaplan, Inc.
T0
T1
$100.00
$7.0
$100.00
$7.0
$100.00
$7.0
T2
51
13
The Arbitrage-Free
Valuation Framework
The Arbitrage-Free
Valuation Framework
Example: Backward Induction
Example: Backward Induction
V1,U =
1  100 +7 100 +7 
V1,U = × 
+
= 99.07
2  1.08
1.08 
V1,L =
V0 =
1  106.07 108.90 
V0 = × 
+
= 104.35
2  1.03
1.03 
1  100 +7 100 +7 
×
+
=101.90
2  1.05
1.05 
$99.07
$7.0
8%
52
© Kaplan, Inc.
1  107 107 
V1,L = × 
+
=101.90
2  1.05 1.05 

Calibrate arbitrage-free interest rates


© Kaplan, Inc.
-2
Value the same 7%, 2-year, option-free bond using
spot rates.
Maturity Spot Rate
Interest rate tree should generate values for
on-the-run benchmark securities equal to
market prices
Think Ho Lee model (developed from Ho-Lee
by Black, Derman and Toy 1990; big
difference = lognormal distribution)
54
53
Example: Valuation Using
Spot or Zero-Coupon Yield
Arbitrage-free pricing:
Create tree
$100.00
$7.0
The Arbitrage-Free
Valuation Framework
Tree Should Be Arbitrage-Free

$100.00
$7.0
$101.90
$7.0
5%
The Arbitrage-Free
Valuation Framework

$100.00
$7.0
$104.35
3%
1  99.07 +7 101.90 +7 
×
+
= 104.35
2  1.03
1.03 
© Kaplan, Inc.
1  107 107 
= 99.07
×
+
2  1.08 1.08 
Value =
1
3.00%
2
4.73%
7
107
+
= $104.35
1.03 (1.0473)2
Valuation would be same for an option-free bond!
© Kaplan, Inc.
55
-1
14
The Arbitrage-Free
Valuation Framework
The Arbitrage-Free
Valuation Framework
Pathwise Valuation
Example: Pathwise Valuation
 Mathematically identical approach to binomial
model. Rates are from binomial tree!
 Number of paths = 2(n-1)
(where n = number of periods)
Value the 2-year,
7% bond using
pathwise
valuation
Value
1
3.00% 8.00% $102.98
2
3.00% 5.00% $105.73
Average $104.35
 Each cash flow is discounted at appropriate
1-period spot and/or forward rate(s)
Value for path 1 =
7
107
+
= $102.98
1.03 (1.03)(1.08)
Value for path 2 =
7
107
+
= $105.73
1.03 (1.03)(1.05)
 Differs from valuation using spot rate curve
 Based on equal weight for each path
56
© Kaplan, Inc.
Path Year 1 Year 2
The Arbitrage-Free
Valuation Framework
© Kaplan, Inc.
57
-3
Fixed Income Investments
Fixed Income
Monte Carlo Method
Generate many random interest rate paths based
on a probability distribution and assumed
volatility—uses pathwise valuation
 Model may impose upper and lower bounds
consistent with mean reversion of rates



Paths are calibrated to ensure arbitrage-free
valuation of benchmark securities
Study Session 12
Discussion Questions
CFA Institute Program Curriculum, Level II,
Volume 5, page 59, Questions 30–36
Useful for valuation of securities whose value is
path-dependent (e.g., MBS)
© Kaplan, Inc.
58
15
Discussion Questions
Discussion Questions
Question 30
Solution 30
Bootstrapping spot rates:
Based on Exhibit 1, the five-year spot rate is
closest to:
100=
A. 4.40%.
B. 4.45%.
4.37
4.37
4.37
4.37
104.37
+
+
+
+
2
3
4
1.025 (1.03)
(1.035)
(1.04)
(1+S5 )5
83.94=
C. 4.50%.
104.37
(1+S5 )
(1+S5 )5 =
5
5
(1+S5 ) =1.2434
60
© Kaplan, Inc.
-1
104.37
83.94
S5 = 5 1.2434 − 1 = 0.0445
61
© Kaplan, Inc.
-5
Discussion Questions
Discussion Questions
Solution 30
Question 31
Based on Exhibit 1, the market is most likely
expecting:
Based on Exhibit 1, the five-year spot rate is
closest to:
A. deflation.
A. 4.40%.
B. inflation.
B. 4.45%.
C. no risk premiums.
C. 4.50%.
Exhibit 1 shows upward
sloping spot rate curve
© Kaplan, Inc.
62
-1
© Kaplan, Inc.
63
-2
16
Discussion Questions
Discussion Questions
Question 32
Question 33
Based on Exhibit 1, the forward rate of a one-year
loan beginning in three years is closest to:
Based on Exhibit 1, which of the following forward
rates can be computed?
A. 4.17%.
A. A one-year loan beginning in five years. f(5,1)
f(3,1) = ?
B. 4.50%.
B. A three-year loan beginning in three years. f(3,3)
C. 5.51%.
C. A four-year loan beginning in one year. f(1,4)
f(3,1) =
(1+S4 )4
(1.04)4
−
1
=
− 1 = 0.0551
(1+S3 )3
(1.035)3
To calculate f(j,k) we need Sj and S(j+k)
64
© Kaplan, Inc.
-3
65
© Kaplan, Inc.
Discussion Questions
Discussion Questions
Question 34
Solution 34
For Assignment 1, the yield to maturity for Bond Z
is closest to the:
First calculate the price of Bond Z using spot rates:
60
60
1,060
+
+
= 1,071.15
2
1.025 (1.03)
(1.035)3
A. one-year spot rate.
B. two-year spot rate.
Next calculate the YTM of Bond Z:
C. three-year spot rate.
PV = –1,071.15, N = 3, PMT = 60, FV = 1,000,
CPT I/Y = 3.46 (closest to S3)
© Kaplan, Inc.
66
-6
© Kaplan, Inc.
67
-2
17
Discussion Questions
Discussion Questions
Solution 34
Question 35
For Assignment 1, the yield to maturity for Bond Z
is closest to the:
For Assignment 2, Alexander should conclude that
Bond Z is currently:
Expected future spot
A. undervalued.
rates lower than forward
rates current priced in
B. fairly valued.
the valuation.
C. overvalued.
A. one-year spot rate.
B. two-year spot rate.
C. three-year spot rate.
68
© Kaplan, Inc.
-1
69
© Kaplan, Inc.
Discussion Questions
-2
Discussion Questions
Question 36
Solution 36
Nguyen’s investment horizon is given as 2
years and she wants to “ride the yield curve.”
Bond Z has 3-year maturity.
By choosing to buy Bond Z, Nguyen is most likely
making which of the following assumptions?
A. Bond Z will be held to maturity.
Riding the yield curve is appropriate when the
yield curve is upward sloping → forward curve
is above the spot curve.
B. The three-year forward curve is above the spot
curve.
C. Future spot rates do not accurately reflect future
inflation.
© Kaplan, Inc.
70
© Kaplan, Inc.
71
-2
18
Discussion Questions
Solution 36
By choosing to buy Bond Z, Nguyen is most likely
making which of the following assumptions?
A. Bond Z will be held to maturity.
B. The three-year forward curve is above the spot
curve.
C. Future spot rates do not accurately reflect future
inflation.
© Kaplan, Inc.
72
-1
19