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2011 CFA Program Curriculum: Level 2, Volume 5

CFA Institute

Chapter 55

TERM STRUCTURE AND VOLATILITY OF INTEREST RATES - all with Video Answers

Educators


Chapter Questions

01:35

Problem 1

What are the four types of shanes observed for the vield curve?

Mitchel Vereen
Mitchel Vereen
Numerade Educator
02:21

Problem 2

How is the slope of the yield curve defined and measured?

David Alvarez-Carbonell
David Alvarez-Carbonell
Numerade Educator
00:50

Problem 3

Historically, how has the slope of the long end of the yield curve differed from that of the short end of the yield curve at a given point in time?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator

Problem 4

A. What are the three factors that have empirically been observed to affect Treasury returns?
B. What has been observed to be the most important factor in affecting Treasury returns?
C. Given the most important factor identified in Part B, justify the use of duration as a measure of interest rate risk.
D. What has been observed to be the second most important factor in affecting Treasury returns?
E. Given the second most important factor identified in Part D, justify the use of a measure of interest rate risk in addition to duration.

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Problem 5

A. What are the limitations of using just the on-the-run Treasury issues to construct the theoretical spot rate curve?
B. Why if all Treasury bills and Treasury coupon securities are used to construct the theoretical spot rate curve is it not possible to use the bootstrapping method?

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Problem 6

A. What are the problems with using the yield on Treasury strips to construct the theoretical spot rate curve?
B. Why, even if a practitioner decides to use the yield on Treasury strips to construct the theoretical spot rate curve despite the problems identified in Part A, will the practitioner restrict the analysis to Treasury coupon strips?

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04:10

Problem 7

What are the advantages of using the swap curve as a benchmark of interest rates relative to a government bond yield curve?

Pragya Ahuja
Pragya Ahuja
Numerade Educator

Problem 8

How can a spot rate curve be constructed for a country that has a liquid swap market?

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Problem 9

A. What is a swap spread?
B. What is the swap spread indicative of?

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Problem 10

A. What is the pure expectations theory?
B. What are the shortcomings of the pure expectations theory?

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Problem 11

Based on the broadest interpretation of the pure expectations theory, what would be the difference in the 4-year total return if an investor purchased a 7 -year zero-coupon bond or a 15 -year zero-coupon bond?

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Problem 12

Based on the local expectations form of the pure expectations theory, what would be the difference in the 6 -month total return if an investor purchased a 5-year zero-coupon bond or a 2-year zero-coupon bond?

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Problem 13

Comment on the following statement made by a portfolio manager to a client:
Proponents of the unbiased expectations theory argue that the forward rates built into the term structure of interest rates are the market's consensus of future interest rates. We disagree with the theory because studies suggest that forward rates are poor predictors of future interest rates. Therefore, the position that our investment management firm takes is that forward rates are irrelevant and provide no information to our managers in managing a bond portfolio.

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Problem 14

Based on arbitrage arguments, give two interpretations for each of the following three forward rates:
A. The 1-year forward rate seven years from now is $6.4 \%$.
B. The 2-year forward rate one year from now is $6.2 \%$.
C. The 8-year forward rate three years from now is $7.1 \%$.

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Problem 15

There are two forms of the "biased" expectations theory. Why are these two forms referred to as "biased" expectations?

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Problem 16

You are the financial consultant to a pension fund. After your presentation to the trustees of the fund, you asked the trustees if they have any questions. You receive the two questions below. Answer each one.
A. "The yield curve is upward-sloping today. Doesn't this suggest that the market consensus is that interest rates are expected to increase in the future and therefore you should reduce the interest rate risk exposure for the portfolio that you are managing for us?"
B. "I am looking over one of the pages in your presentation that shows spot rates and I am having difficulty in understanding it. The spot rates at the short end (up to three years) are increasing with maturity. For maturities greater than three years but less than eight years, the spot rates are declining with maturity. Finally, for maturities greater than eight years the spot rates are virtually the same for each maturity. There is simply no expectations theory that would explain that type of shape for the term structure of interest rates. Is this market simply unstable?"

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Problem 17

Below are the key rate durations for three portfolios of U.S. Treasury securities, all with the same duration for a parallel shift in the yield curve.
A. For each portfolio describe the type of portfolio (barbell, ladder, or bullet).
$$
\begin{array}{lccc}
\hline \text { Key Rate Maturity } & \text { Portfolio A } & \text { Portfolio B } & \text { Portfolio C } \\
\hline \text { 3-month } & 0.04 & 0.04 & 0.03 \\
\text { 1-year } & 0.06 & 0.29 & 0.07 \\
\text { 2-year } & 0.08 & 0.67 & 0.31 \\
\text { 3-year } & 0.28 & 0.65 & 0.41 \\
\text { 5-year } & 0.38 & 0.65 & 1.90 \\
\text { 7-year } & 0.65 & 0.64 & 0.35 \\
\text { 10-year } & 3.38 & 0.66 & 0.41 \\
\text { 15-year } & 0.79 & 0.67 & 0.70 \\
\text { 20-year } & 0.36 & 0.64 & 1.95 \\
\text { 25-year } & 0.12 & 0.62 & 0.06 \\
\text { 30-year } & 0.06 & 0.67 & 0.01 \\
\hline
\end{array}
$$
B. Which portfolio will benefit the most if the spot rate for the 10 -year decreases by 50 basis points while the spot rate for all other key maturities changes very little?
C. What is the duration for a parallel shift in the yield curve for the three portfolios?

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05:34

Problem 18

Compute the 10-day daily standard deviation of the percentage change in yield assuming continuous compounding and assuming the following daily yields.
$$
\begin{array}{rc}
\hline \boldsymbol{t} & \boldsymbol{y}_t \\
\hline 0 & 5.854 \\
1 & 5.843 \\
2 & 5.774 \\
3 & 5.719 \\
4 & 5.726 \\
5 & 5.761 \\
6 & 5.797 \\
7 & 5.720 \\
8 & 5.755 \\
9 & 5.787 \\
10 & 5.759 \\
\hline
\end{array}
$$

Uma Kumari
Uma Kumari
Numerade Educator
04:43

Problem 19

For the daily yield volatility computed in the previous question, what is the annual yield volatility assuming the following number of days in the year?
A. 250 days.
B. 260 days.
C. 365 days.

Anurag Kumar
Anurag Kumar
Numerade Educator

Problem 20

Comment on the following statement: "Two portfolio managers with the same set of daily yields will compute the same historical annual volatility."

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View

Problem 21

Suppose that the annualized standard deviation for the change in the 2 -year Treasury yield based on daily yields is $7 \%$ and the current level of the 2 -year Treasury yield is $5 \%$. Assuming that the probability distribution for the percentage change in 2-year Treasury yields is approximately normally distributed, how would you interpret the $7 \%$ annualized standard deviation?

Ana Carolina Da Cruz
Ana Carolina Da Cruz
Numerade Educator

Problem 22

A. What is implied volatility?
B. What are the problems associated with using implied volatility as a measure of yield volatility?

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Problem 23

A. In forecasting yield volatility, why would a manager not want to weight each daily yield change equally?
B. In forecasting yield volatility, what is recommended for the sample mean in the formula for the variance or standard deviation?

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Problem 24

Is Bauer's first statement most likely correct?
A. Yes.
B. No, the quality of the servicer is not considered by the rating agencies.
C. No, the seller's operating cash flow is not considered by the rating agencies.

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Problem 25

Is Bauer's second statement most likely correct?
A. Yes.
B. No, the servicer is responsible for collateral maintenance so that it generates sufficient net cash flow.
C. No, the servicer is required to maintain collateral quality so that the asset-backed securities remain investment grade.

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Problem 26

Is Hinault's first remark most likely correct?
A. Yes.
B. No, because sovereign debt will carry the same rating no matter the currency of denomination.
C. No, because differential credit ratings on sovereign debt depend on the country's fiscal and monetary policy when the debt is issued.

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Problem 27

Under which theory of the term structure of interest rates would Hinault's second remark most likely be correct?
A. Preferred habitat theory.
B. Pure expectations theory.
C. Liquidity preference theory.

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02:01

Problem 28

Given Lane"s expected change in interest rates, which of the following best describes the relation between Investments \#1 and \#2?
A. Investment \#1 would have approximately a $0.7 \%$ greater value than Investment \#2.
B. Investment \#2 would have approximately a $0.7 \%$ greater value than Investment \#1.
C. Investment \#1 would have approximately a $1.0 \%$ greater value than Investment \#2.

AG
Ankit Gupta
Numerade Educator
00:58

Problem 29

The duration of Investment \#3 is closest to:
A. 7.5 .
B. 11.3.
C. 17.5 .

James Kiss
James Kiss
Numerade Educator

Problem 30

Which factor in Moss's list has the least impact on zero-coupon
U.S. Treasury bond returns?
A. The level of the yield curve.
B. The slope of the yield curve.
C. The curvature of the yield curve.

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Problem 31

Is Moss's response regarding theories about the term structure of interest rates correct?
A. Yes.
B. No, preferred habitat theory does not make an assumption of market's expectations.
C. No, pure expectations theory does not make an assumption of market's expectations.

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02:01

Problem 32

Is the first statement from Moss's report correct?
A. Yes.
B. No, servicing history is not a factor.
C. No, costs to the special purpose vehicle are not a factor:

Brenda Sanchez
Brenda Sanchez
Numerade Educator

Problem 33

Is the second statement from Moss's report correct?
A. Yes.
B. No, flow-of-funds structure is not addressed in the legal opinion.
C. No, stability of the excess spread is not addressed in the legal opinion.

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06:21

Problem 34

The third statement from Moss's report is most likely incorrect with respect to the:
A. balance of payments.
B. fiscal policy and budgetary flexibility.
C. monetary policy and inflation pressures.

Mohan Jain
Mohan Jain
Numerade Educator

Problem 35

If the 2-year key rate shifts up by 10 bps and the 30 -year key rate shifts down by 20 bps, the difference in total return between portfolio III over portfolio I would be closest to:
A. $1.45 \%$.
B. $2.90 \%$.
C. $4.35 \%$.

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