Deck 15: The Term Structure of Interest Rates

Question 1

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{ll}\text { Year } &\text { Forward Interest Rate }\\ 0 & 4\% \text { (today) } \\1 & 5\% \\2 & 6\%\\3&7\%\end{array}$
What is the price of a 3-year zero-coupon bond with a par value of $1,000?

A) $896.83
B) $863.92
C) $772.18
D) $765.55
E) None of the options are correct.

Answer 1

$863.92

Question 2

The yield curve shows at any point in time

A) the relationship between the yield on a bond and the duration of the bond.
B) the relationship between the coupon rate on a bond and time to maturity of the bond.
C) the relationship between yield on a bond and the time to maturity on the bond.
D) All of the options are correct.
E) None of the options are correct.

Answer 2

C

Question 3

If the value of a Treasury bond was higher than the value of the sum of its parts (STRIPPED cash flows),

A) arbitrage would probably occur.
B) arbitrage would probably not occur.
C) the FED would adjust interest rates.
D) None of the options are correct.

Answer 3

A

Question 4

The expectations theory of the term structure of interest rates states that

A) forward rates are determined by investors' expectations of future interest rates.
B) forward rates exceed the expected future interest rates.
C) yields on long- and short-maturity bonds are determined by the supply and demand for the securities.
D) All of the options are correct.
E) None of the options are correct.

Question 5

An upward sloping yield curve is a(n) _______ yield curve.

A) normal
B) humped
C) inverted
D) flat
E) None of the options are correct.

Question 6

The value of a Treasury bond should

A) be equal to the sum of the value of STRIPS created from it.
B) be less than the sum of the value of STRIPS created from it.
C) be greater than the sum of the value of STRIPS created from it.
D) All of the options are correct.

Question 7

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $$\begin{array} { c c } \text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 943.40 \\2 & 881.68 \\3 & 808.88 \\4 & 742.05\end{array}$$ According to the expectations theory, what is the expected forward rate in the third year?

A) 7.00%
B) 7.33%
C) 9.00%
D) 11.19%
E) None of the options are correct.

Question 8

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{ll}\text { Year } &\text { Forward Interest Rate }\\ 0 & 4\% \text { (today) } \\1 & 5\% \\2 & 6\%\\3&7\%\end{array}$ What is the price of a 2-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)

A) $1,092
B) $1,054
C) $986
D) $1,103
E) None of the options are correct.

Question 9

Which of the following are possible explanations for the term structure of interest rates?

A) The expectations theory
B) The liquidity preference theory
C) Modern portfolio theory
D) The expectations theory and the liquidity preference theory

Question 10

If the value of a Treasury bond was lower than the value of the sum of its parts (STRIPPED cash flows), you could

A) profit by buying the stripped cash flows and reconstituting the bond.
B) not profit by buying the stripped cash flows and reconstituting the bond.
C) profit by buying the bond and creating STRIPS.
D) not profit by buying the stripped cash flows and reconstituting the bond and profit by buying the bond and creating STRIPS.
E) None of the options are correct.

Question 11

According to the expectations hypothesis, an upward-sloping yield curve implies that

A) interest rates are expected to remain stable in the future.
B) interest rates are expected to decline in the future.
C) interest rates are expected to increase in the future.
D) interest rates are expected to decline first, then increase.
E) interest rates are expected to increase first, then decrease.

Question 12

An inverted yield curve implies that

A) long-term interest rates are lower than short-term interest rates.
B) long-term interest rates are higher than short-term interest rates.
C) long-term interest rates are the same as short-term interest rates.
D) intermediate-term interest rates are higher than either short- or long-term interest rates.
E) None of the options are correct.

Question 13

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{ll}\text { Year } &\text { Forward Interest Rate }\\ 0 & 4\% \text { (today) } \\1 & 5\% \\2 & 6\%\\3&7\%\end{array}$ If you have just purchased a 4-year zero-coupon bond, what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000)

A) 4%
B) 5%
C) 6%
D) 7%
E) None of the options are correct.

Question 14

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{ll}\text { Year } &\text { Forward Interest Rate }\\ 0 & 4\% \text { (today) } \\1 & 5\% \\2 & 6\%\\3&7\%\end{array}$ What is the yield to maturity of a 3-year zero-coupon bond?

A) 9.00%
B) 7.00%
C) 5.00%
D) 4.00%
E) None of the options are correct.

Question 15

Bond stripping and bond reconstitution offer opportunities for ______, which can occur if the _________ is violated.

A) arbitrage; law of one price
B) arbitrage; restrictive covenants
C) huge losses; law of one price
D) huge losses; restrictive covenants

Question 16

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $$\begin{array} { c c } \text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 943.40 \\2 & 881.68 \\3 & 808.88 \\4 & 742.05\end{array}$$ What is the yield to maturity on a 3-year zero-coupon bond?

A) 6.37%
B) 9.00%
C) 7.33%
D) 10.00%
E) None of the options are correct.

Question 17

______ can occur if _____.

A) Arbitrage; the law of one price is not violated
B) Arbitrage; the law of one price is violated
C) Low-risk economic profit; the law of one price is not violated
D) Low-risk economic profit; the law of one price is violated
E) Arbitrage and low-risk economic profit; the law of one price is violated

Question 18

If the value of a Treasury bond was lower than the value of the sum of its parts (STRIPPED cash flows),

A) arbitrage would probably occur.
B) arbitrage would probably not occur.
C) the FED would adjust interest rates.
D) None of the options are correct.

Question 19

Treasury STRIPS are

A) securities issued by the Treasury with very long maturities.
B) extremely risky securities.
C) created by selling each coupon or principal payment from a whole Treasury bond as a separate cash flow.
D) created by pooling mortgage payments made to the Treasury.

Question 20

If the value of a Treasury bond was higher than the value of the sum of its parts (STRIPPED cash flows), you could

A) profit by buying the stripped cash flows and reconstituting the bond.
B) not profit by buying the stripped cash flows and reconstituting the bond.
C) profit by buying the bond and creating STRIPS.
D) not profit by buying the stripped cash flows and reconstituting the bond and profit by buying the bond and creating STRIPS.
E) None of the options are correct.

Question 21

Forward rates ____________ future short rates because ____________.

A) are equal to; they are both extracted from yields to maturity
B) are equal to; they are perfect forecasts
C) differ from; they are imperfect forecasts
D) differ from; forward rates are estimated from dealer quotes while future short rates are extracted from yields to maturity
E) are equal to; although they are estimated from different sources, they both are used by traders to make purchase decisions

Question 22

$\begin{array}{cc}\text { Year } & \text { 1 Year Forward Rate } \\1 & 4.5\% \\2 & 5.2\% \\3 & 5.9\% \\4 & 6.3\% \\5 & 6.8 \% \\6 & 7.0\%\end{array}$
. What would the yield to maturity be on a four-year zero-coupon bond purchased today?

A) 7.80%
B) 6.30%
C) 5.47%
D) 4.25%
E) None of the options are correct.

Question 23

$\begin{array}{ll} \text { Par value } &\$1,000\\ \text { Time to Maturity } &20 \text { Years } \\ \text { Coupon} &10 \% \text { (paid annually)}\\ \text { Current price } &\$850\\ \text {Yield to Maturity } &12\%\\\end{array}$
Given the bond described above, if interest were paid semi-annually (rather than annually), and the bond continued to be priced at $850, the resulting effective annual yield to maturity would be

A) less than 12%.
B) more than 12%.
C) 12%.
D) Cannot be determined.
E) None of the options are correct.

Question 24

Which of the following combinations will result in a sharply-increasing yield curve?

A) Increasing future expected short rates and increasing liquidity premiums
B) Decreasing future expected short rates and increasing liquidity premiums
C) Increasing future expected short rates and decreasing liquidity premiums
D) Increasing future expected short rates and constant liquidity premiums
E) Constant future expected short rates and increasing liquidity premiums

Question 25

Given the yield on a 3-year zero-coupon bond is 8.2% and forward rates of 6.3% in year 1 and 7.1% in year 2, what must be the forward rate in year 3?

A) 11.84%
B) 11.27%
C) 10.95%
D) 10.87%
E) None of the options are correct.

Question 26

$\begin{array}{cc}\text { Year } & \text { 1 Year Forward Rate } \\1 & 4.5\% \\2 & 5.2\% \\3 & 5.9\% \\4 & 6.3\% \\5 & 6.8 \% \\6 & 7.0\%\end{array}$
What should the purchase price of a 2-year zero-coupon bond be if it is purchased at the beginning of year 2 and has face value of $1,000?

A) $897.61
B) $888.33
C) $883.32
D) $893.36
E) $871.80

Question 27

The pure yield curve can be estimated

A) by using zero-coupon Treasuries.
B) by using stripped Treasuries if each coupon is treated as a separate "zero."
C) by using corporate bonds with different risk ratings.
D) by estimating liquidity premiums for different maturities.
E) by using zero-coupon Treasuries and by using stripped Treasuries if each coupon is treated as a separate "zero."

Question 28

The most recently issued Treasury securities are called

A) on the run.
B) off the run.
C) on the market.
D) off the market.
E) None of the options are correct.

Question 29

$\begin{array}{cc}\text { Year } & \text { 1 Year Forward Rate } \\1 & 4.5\% \\2 & 5.2\% \\3 & 5.9\% \\4 & 6.3\% \\5 & 6.8 \% \\6 & 7.0\%\end{array}$
Calculate the price at the beginning of year 1 of a 10% annual coupon bond with face value $1,000 and 5 years to maturity.

A) $1,195
B) $1,181
C) $1,175
D) $1,162
E) $1,151

Question 30

An upward-sloping yield curve

A) may be an indication that interest rates are expected to increase.
B) may incorporate a liquidity premium.
C) may reflect the confounding of the liquidity premium with interest rate expectations.
D) All of the options are correct.
E) None of the options are correct.

Question 31

An inverted yield curve is one

A) with a hump in the middle.
B) constructed by using convertible bonds.
C) that is relatively flat.
D) that plots the inverse relationship between bond prices and bond yields.
E) that slopes downward.

Question 32

The yield curve

A) is a graphical depiction of term structure of interest rates.
B) is usually depicted for U.S. Treasuries in order to hold risk constant across maturities and yields.
C) is usually depicted for corporate bonds of different ratings.
D) is a graphical depiction of term structure of interest rates and is usually depicted for U.S. Treasuries in order to hold risk constant across maturities and yields.
E) is a graphical depiction of term structure of interest rates and is usually depicted for corporate bonds of different ratings.

Question 33

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $$\begin{array} { c c } \text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 943.40 \\2 & 881.68 \\3 & 808.88 \\4 & 742.05\end{array}$$ What is the price of a 4-year maturity bond with a 12% coupon rate paid annually? (Par value = $1,000.)

A) $742.09
B) $1,222.09
C) $1,000.00
D) $1,141.84
E) None of the options are correct.

Question 34

The on the run yield curve is

A) a plot of yield as a function of maturity for zero-coupon bonds.
B) a plot of yield as a function of maturity for recently-issued coupon bonds trading at or near par.
C) a plot of yield as a function of maturity for corporate bonds with different risk ratings.
D) a plot of liquidity premiums for different maturities.

Question 35

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{lc}\text { Year } & \text { Forward Interest Rate } \\0 & \text { (today) } 3\% \\1 & 4\% \\2 & 5\% \\3 & 6\%\end{array}$ What is the price of 3-year zero-coupon bond with a par value of $1,000?

A) $889.08
B) $816.58
C) $772.18
D) $765.55
E) None of the options are correct.

Question 36

Investors can use publicly available financial data to determine which of the following?I) The shape of the yield curveII) Expected future short-term rates (if liquidity premiums are ignored)III) The direction the Dow indexes are headingIV) The actions to be taken by the Federal Reserve

A) I and II
B) I and III
C) I, II, and III
D) I, III, and IV
E) I, II, III, and IV

Question 37

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{lc}\text { Year } & \text { Forward Interest Rate } \\0 & \text { (today) } 3\% \\1 & 4\% \\2 & 5\% \\3 & 6\%\end{array}$
If you have just purchased a 4-year zero-coupon bond, what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000.)

A) 5%
B) 3%
C) 9%
D) 10%
E) None of the options are correct.

Question 38

The "break-even" interest rate for year n that equates the return on an n-period zero-coupon bond to that of an n - 1 - period zero-coupon bond rolled over into a one-year bond in year n is defined as

A) the forward rate.
B) the short rate.
C) the yield to maturity.
D) the discount rate.
E) None of the options are correct.

Question 39

When computing yield to maturity, the implicit reinvestment assumption is that the interest payments are reinvested at the

A) coupon rate.
B) current yield.
C) yield to maturity at the time of the investment.
D) prevailing yield to maturity at the time interest payments are received.
E) the average yield to maturity throughout the investment period.

Question 40

The yield curve is a component of

A) the Dow Jones Industrial Average.
B) the consumer price index.
C) the index of leading economic indicators.
D) the producer price index.
E) the inflation index.

Question 41

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What is the yield to maturity of a 1-year bond?

A) 4.6%
B) 4.9%
C) 5.2%
D) 5.5%
E) 5.8%

Question 42

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What should the purchase price of a 2-year zero-coupon bond be if it is purchased today and has face value of $1,000?

A) $966.87
B) $911.37
C) $950.21
D) $956.02
E) $945.51

Question 43

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What should the purchase price of a 3-year zero-coupon bond be if it is purchased today and has face value of $1,000?

A) $887.42
B) $871.12
C) $879.54
D) $856.02
E) $866.32

Question 44

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What should the purchase price of a 5-year zero-coupon bond be if it is purchased today and has face value of $1,000?

A) $776.14
B) $721.15
C) $779.54
D) $756.02
E) $766.32

Question 45

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What is the yield to maturity of a 5-year bond?

A) 4.6%
B) 4.9%
C) 5.2%
D) 5.5%
E) 5.8%

Question 46

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What is the yield to maturity of a 3-year bond?

A) 4.6%
B) 4.9%
C) 5.2%
D) 5.5%
E) 5.8%

Question 47

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{lc}\text { Year } & \text { Forward Interest Rate } \\0 & \text { (today) } 3\% \\1 & 4\% \\2 & 5\% \\3 & 6\%\end{array}$
What is the price of a 2-year maturity bond with a 5% coupon rate paid annually? (Par value = $1,000.)

A) $1,092.97
B) $1,054.24
C) $1,028.50
D) $1,073.34
E) None of the options are correct.

Question 48

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 5\% \\2 & 5.5\% \\3 & 6.0\% \\4 & 6.5\% \\5 & 7.0\%\end{array}$
Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face value $1,000 and 5 years to maturity.

A) $1,105.47
B) $1,131.91
C) $1,084.35
D) $1,150.01
E) $719.75

Question 49

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $\begin{array}{cc}\text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 925.15 \\2 & 862.57 \\3 & 788.66 \\4 & 711.00\end{array}$

You have purchased a 4-year maturity bond with a 9% coupon rate paid annually. The bond has a par value of $1,000. What would the price of the bond be one year from now if the implied forward rates stay the same?

A) $995.63
B) $1,108.88
C) $1,000.00
D) $1,042.78

Question 50

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 5\% \\2 & 5.5\% \\3 & 6.0\% \\4 & 6.5\% \\5 & 7.0\%\end{array}$
What would the yield to maturity be on a four-year zero-coupon bond purchased today?

A) 5.75%
B) 6.30%
C) 5.65%
D) 5.25%

Question 51

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $\begin{array}{cc}\text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 925.15 \\2 & 862.57 \\3 & 788.66 \\4 & 711.00\end{array}$

What is the price of a 4-year maturity bond with a 10% coupon rate paid annually? (Par values = $1,000.)

A) $742.09
B) $1,222.09
C) $1,035.72
D) $1,141.84

Question 52

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What is the yield to maturity of a 4-year bond?

A) 4.69%
B) 4.95%
C) 5.02%
D) 5.05%
E) 5.08%

Question 53

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$ What should the purchase price of a 1-year zero-coupon bond be if it is purchased today and has face value of $1,000?

A) $966.37
B) $912.87
C) $950.21
D) $956.02
E) $945.51

Question 54

$\begin{array}{lc} \text {Par Value } &\$1,000\\ \text { Time to Maturity} & \text {18 Years}\\ \text { Coupon } &\text { 9 \% (paid annually) } \\ \text { Current price } &\$917.99\\ \text { Yield to Maturity } &12\%\\ &\\\end{array}$
Given the bond described above, if interest were paid semi-annually (rather than annually) and the bond continued to be priced at $917.99, the resulting effective annual yield to maturity would be

A) less than 10%.
B) more than 10%.
C) 10%.
D) Cannot be determined.
E) None of the options are correct.

Question 55

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What should the purchase price of a 4-year zero-coupon bond be if it is purchased today and has face value of $1,000?

A) $887.42
B) $821.15
C) $879.54
D) $856.02
E) $866.32

Question 56

Given the yield on a 3-year zero-coupon bond is 7% and forward rates of 6% in year 1 and 6.5% in year 2, what must be the forward rate in year 3?

A) 7.2%
B) 8.6%
C) 8.5%
D) 6.9%

Question 57

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 5\% \\2 & 5.5\% \\3 & 6.0\% \\4 & 6.5\% \\5 & 7.0\%\end{array}$
What should the purchase price of a 2-year zero-coupon bond be if it is purchased at the beginning of year 2 and has face value of $1,000?

A) $877.54
B) $888.33
C) $883.32
D) $894.21
E) $871.80

Question 58

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $\begin{array}{cc}\text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 925.15 \\2 & 862.57 \\3 & 788.66 \\4 & 711.00\end{array}$

What is the yield to maturity on a 3-year zero-coupon bond?

A) 6.37%
B) 9.00%
C) 7.33%
D) 8.24%

Question 59

The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000. $\begin{array}{cc}\text { Maturity } & \text { Price } \\\text { (Years) } & \\1 & \$ 925.15 \\2 & 862.57 \\3 & 788.66 \\4 & 711.00\end{array}$
According to the expectations theory, what is the expected forward rate in the third year?

A) 7.23%
B) 9.37%
C) 9.00%
D) 10.9%

Question 60

Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{lc}\text { Year } & \text { Forward Interest Rate } \\0 & \text { (today) } 3\% \\1 & 4\% \\2 & 5\% \\3 & 6\%\end{array}$
What is the yield to maturity of a 3-year zero-coupon bond?

A) 7.00%
B) 9.00%
C) 6.99%
D) 4.00%
E) None of the options are correct.

Question 61

What theory believes short-term investors dominate the market so that the forward rate will generally exceed the expected short rate?

A) Liquidity preference theory
B) Expectations theory
C) Market segmentation theory
D) Forward rate theory
E) Short rate theory

Question 62

The graphic representation of the term structure of interest rates is the _______________.

A) forward rate
B) volatility index
C) yield curve
D) expectations table
E) None of the options are correct.

Question 63

What theory believes forward rates equals the market consensus of what the future short interest rate will be?

A) Liquidity preference theory
B) Expectations theory
C) Market segmentation theory
D) Forward rate theory
E) Short rate theory

Question 64

_____________________ are created from coupon paying treasuries, where the coupon and principal are separated.

A) Stripped treasuries
B) Forward rates
C) A yield curve
D) Futures contracts
E) None of the options are correct.

Question 65

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$
What is the yield to maturity of a 2-year bond?

A) 4.6%
B) 4.9%
C) 5.2%
D) 4.7%
E) 5.8%

Question 66

The ___________ yield curve is created from stripped treasuries.

A) basic
B) forward
C) inverted
D) pure
E) None of the options are correct.