Deck 24: Term Structure of Interest Rates: Concepts

Question 1

The zero-coupon rate (zcr) is

A) The rate of return each period on a bond that pays no coupons.
B) The yield-to-maturity of a zero-coupon bond.
C) The return on the bond's appreciation excluding coupon payments.
D) Zero.

Answer 1

The yield-to-maturity of a zero-coupon bond.

Question 2

If zero rates (i.e., discount rates) are the same for all maturities and remain the same over the next year, the price of a zero-coupon bond that matures ten years from today will:

A) Decrease over the next year
B) Remain the same over the next year
C) Increase over the next year
D) Cannot tell with the given information

Answer 2

Increase over the next year

Question 3

The price of a three-year 5% coupon Treasury bond in the Wall Street Journal is quoted at 101-20. The yield-to-maturity of the bond is
(a) 5.19%
(b) 5.34%
(c) 5.67%
(d) 5.88%

Answer 3

A.

Question 4

If the forward rate curve is downward sloping, then

A) The zero-coupon curve will lie above the yield curve.
B) The zero-coupon curve will lie below the yield curve.
C) The zero-coupon curve will lie above the yield curve in the near maturities and then lie below the yield curve for later maturities.
D) Not enough information to be able to answer the question.

Question 5

The 6-months risk-free zero rate is 2.84%, and the one-year zero rate is 3.17%. Assuming no-arbitrage, the yield-to-maturity on a $1,000 par of a one-year, 12% Treasury bond, that pays $60 after 6 months and $1060 after one-year, must be

A) Greater than 0% and less than 2.84%
B) Greater than 2.84% and less than 3.17%
C) Greater than 3.17% and less than 6.01%
D) 6.01%

Question 6

You are to receive a cash-flow of $40 after three years. If the ytm of this cash-flow is 6%, what is its present value? (Assume a semi-annual basis for compounding and discounting.)

A) $28.20
B) $33.50
C) $33.58
D) $37.74

Question 7

Assume that the risk-free zero rates are increasing with maturity (That is, the 6-months zero rate is lower than the one-year zero rate, which is lower than the two-year zero rate, etc). It must be that:

A) The yield-to-maturity curve for coupon bonds lies below the yield-to-maturity curve for zeros
B) The yield-to-maturity curve for coupon bonds equals the yield-to-maturity curve for zeros
C) The yield-to-maturity curve for coupon bonds lies above the yield-to-maturity curve for zeros
D) The yield-to-maturity curve for coupon bonds lies above the yield-to-maturity curve for zeros for maturities less than one year, but lies below the yield-to-maturity curve for zeros for maturities greater than one year.

Question 8

Under a semi-annual compounding convention, the present value of a $n$ -period cashflow using its ytm $y$ is given by $P = C / ( 1 + y / 2 ) ^ { n }$ . Which of the following is an equivalent way of expressing the same present value?

A) $P = C \cdot d _ { n } \cdot ( n / 2 )$ , where $d _ { n }$ is the discount function for $n$ periods, and $n / 2$ is the time to maturity of the cash-flow.
B) $P = C e ^ { - z _ { n } \times n / 2 }$ , where $Z _ { n }$ is the semi-annual basis zero-coupon rate for $n$ periods.
C) $P = C / \prod _ { j = 1 } ^ { n } \left( 1 + f _ { j } \right)$ , where $f _ { j }$ is the forward rate for period $j$ .
D) None of the above.

Question 9

The one-year discount factor today is 0.95. You buy a one-year zero-coupon bond today and hold it until maturity. Suppose that at maturity, the one-year discount factor is 0.92. The return you realize, expressed in simple terms, is:

A) 3.43%
B) 5.26%
C) 8.69%
D) 9.50%

Question 10

If the price of a two-year semi-annual pay bond is par (say, $100), and the coupon on the bond is 6%, the yield-to-maturity expressed with semi-annual compounding is

A) 5.87%
B) 5.96%
C) 6.00%
D) 6.12%

Question 11

The prices of a one-year 4% coupon bond, a two-year 5% coupon bond, and a three-year 6% coupon bond are $101, $100 and $99, respectively. Coupons are paid annually. What is the price of a bond that pays $37 each year?

A) $99.00
B) $100.08
C) $101.21
D) $111.43

Question 12

Today's forward rate $f \left( t _ { 1 } , t _ { 2 } \right)$ for a period $\left( t _ { 1 } , t _ { 2 } \right)$ in the future ( $t _ { 1 } < t _ { 2 }$ ) is

A) Unknown until $t _ { 1 }$ .
B) Settled when we get to $t _ { 2 }$ .
C) Depends on the ytm of coupon bonds of maturities $t _ { 1 }$ and $t _ { 2 }$ .
D) Depends on the ytm of zero-coupon bonds of maturities $t _ { 1 }$ and $t _ { 2 }$ .

Question 13

If the one year rate expressed with semi-annual compounding is 6%, what is the equivalent rate with quarterly compounding.

A) 3.00%
B) 5.87%
C) 5.96%
D) 6.00%

Question 14

The yield-to-maturity (ytm) is the
(a) Return on the bond at maturity.
(b) The coupon rate on the bond.
(c) The internal rate of return of the bond.
(d) The coupon rate divided by the current price of the bond.

Question 15

If zero rates (also known as discount rates) are positive for any maturity, the discount function $d ( t )$ , which gives the present value of a dollar receivable at time $t$ in the future,

A) Must be between 0 and 1
B) Must be greater than 0 and can be greater than 1
C) Can be a negative number
D) is usually 0.99

Question 16

Which of the following is not a typical property of a discount function $d ( t )$ ?

A) $d ( t )$ is non-decreasing in the maturity $t$ .
B) $d ( t )$ is non-increasing in the maturity $t$ .
C) $d ( t )$ decreases as the zero-coupon rate $z ( t )$ for maturity $t$ increases.
D) $d ( t )$ is independent of compounding convention.

Question 17

Assuming annual compounding and annual coupon payments, the prices of a one-year 4% coupon bond and a two-year 5% coupon bond are $101 and $99, respectively. The zero-coupon rate for two years is:

A) 4.5%
B) 5.1%
C) 5.6%
D) 6.2%

Question 18

If the ytm curve is upward sloping then which of the following orderings of yield, zero-coupon rates (zcr) and forward rates (fwr) is most valid?

A) ytm < zcr < fwr
B) ytm < fwr < zcr
C) zcr < fwr < ytm
D) fwr < zcr < ytm

Question 19

Assuming annual compounding, the prices of a one-year 4% coupon bond and a two-year 5% coupon bond are $101 and $99, respectively. Assume coupons are paid annually. The fair price of a two-year 6% coupon bond will be

A) $99.86
B) $100.11
C) $100.57
D) $100.87

Question 20

Assuming annual compounding, the prices of a one-year 4% coupon bond and a two-year 5% coupon bond are $101 and $99, respectively. The forward rate between one and two years is:

A) 4.5%
B) 5.0%
C) 6.8%
D) 8.3%

Question 21

If the ytm of a bond falls, which of the following is most valid?

A) The bond price rises.
B) The bond price falls.
C) The bond price may rise or fall, depending on the maturity of the bond.
D) Not enough information to answer the question.

Question 22

As the ytm of a bond rises, which of the following is most valid?

A) The bond price rises, slowly at low ytm, then more rapidly at higher ytm.
B) The bond price falls, slowly at low ytm, then more rapidly at higher ytm..
C) The bond price rises, rapidly at low ytm, then more slowly at higher ytm.
D) The bond price falls, rapidly at low ytm, then more slowly at higher ytm.

Question 23

The "rule of 72" states that invested money doubles in value if the product of the interest rate (in percentage form) and time invested (in years) equals 72. Assuming continuous compounding, what exactly must the product be for money to double?

A) 69
B) 71
C) 73
D) 75

Question 24

The "rule of 72" states that invested money doubles in value if the product of the interest rate (in percentage form) and time invested (in years) equals 72. Assuming continuous compounding, at least what must the product be for money to triple?

A) 90
B) 100
C) 110
D) 120

Question 25

Find the yield-to-maturity of a 5% two-year bond that has a price of $102. Assume coupons are paid quarterly.

A) 4.33%
B) 4.44%
C) 4.55%
D) 4.66%