Question 1

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

Accepted Answer

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

Question 2

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?

Accepted Answer

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

Question 3

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:

Accepted Answer

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. 
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. A

Question 4

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

Accepted Answer

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

Question 5

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?

Accepted Answer

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. 
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 6

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

Accepted Answer

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. 
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 7

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?

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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:

Accepted Answer

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

Question 10

If the forward rate curve is downward sloping,then

Accepted Answer

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. 
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 11

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

Accepted Answer

A) 5.19% 
B) 5.34% 
C) 5.67% 
D) 5.88% 
A) 5.19% 
B) 5.34% 
C) 5.67% 
D) 5.88%

Question 12

The yield-to-maturity (ytm)is the

Accepted Answer

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. 
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 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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. 
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 15

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

Accepted Answer

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% 
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 16

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:

Accepted Answer

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 
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

Question 17

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:

Accepted Answer

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

Question 18

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,

Accepted Answer

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 
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 19

The zero-coupon rate (zcr)is

Accepted Answer

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. 
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.

Question 20

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

Accepted Answer

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
 $t _ { 2 }$
) 
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
 $t _ { 2 }$
)

Exam 24: Term Structure of Interest Rates: Concepts

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

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?

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:

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

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

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

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?

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

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:

If the forward rate curve is downward sloping,then

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

The yield-to-maturity (ytm)is the

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

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

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

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:

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:

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

The zero-coupon rate (zcr)is

Today's forward rate f(t1,t2)f \left( t _ { 1 } , t _ { 2 } \right)f(t1​,t2​) for a period (t1,t2)\left( t _ { 1 } , t _ { 2 } \right)(t1​,t2​) in the future ( t1<t2t _ { 1 } < t _ { 2 }t1​<t2​ )is

Overview

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Pricing Forwards and Futures I

Pricing Forwards Futures II

Hedging With Futures Forwards

Interest-Rate Forwards Futures

Options Markets

Options: Payoffs Trading Strategies

No-Arbitrage Restrictions

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Option Pricing: An Introduction

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Mathematics of Black-Scholes

Beyond Black-Scholes

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Path-Independent Exotic Options

Exotic Options II: Path-Dependent Options

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Estimating the Yield Curve

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Factor Models of the Term Structure

The Heath-Jarrow-Morton Hjmand Libor Market Model LMM

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Modeling Correlated Default

Filters

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?

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

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,

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