15.6 Forward Rates as Forward Contracts

Question 1

Calculate the forward rate for the second year

• the price of 1-year maturity zero-coupon bonds with face value $1,000 is $952.38
• the price of 2-year zeros with $1,000 face value is $890
• the yield-to-maturity on the 1-year bond is therefore 5%
• the yield-to-maturity on the 1-year bond is therefore 6%

Forward Rates as Forward Contracts

Answer 1

f₂ = (1+y₂)² / (1+y₁) - 1 = 0.0701
f₂ = (1+0.06)² / (1+0.05) - 1 = 0.0701

Forward Rates as Forward Contracts

Question 2

Create a synthetic forward loan

• the price of 1-year maturity zero-coupon bonds with face value $1,000 is $952.38
• the price of 2-year zeros with $1,000 face value is $890
• the yield-to-maturity on the 1-year bond is therefore 5%
• the yield-to-maturity on the 1-year bond is therefore 6%

Forward Rates as Forward Contracts

Answer 2

buy a 1-year zero-coupon bond
* ICF -952.38
* EQ -B₀(1)

sell 1.0701 2-year zeros
* ICF +890 x 1.0701 = 952.38
* EQ +B₀(2) x (1+f₂)

You effectively will borrow $1,000 a year from now and repay $1,070.10 a year later.

Forward Rates as Forward Contracts

Question 3

Describe

B₀T

Forward Rates as Forward Contracts

Answer 3

today’s price of a zero coupon bond with face value $1,000 maturing at time T

Forward Rates as Forward Contracts

Question 4

Concept

the break-even future interest rate that would equate the total return from a rollover strategy to that of a longer-term zero-coupon bond.

Forward Rates as Forward Contracts

Answer 4

forward rate

Forward Rates as Forward Contracts

Question 5

Define

forward rate

Forward Rates as Forward Contracts

Answer 5

the break-even future interest rate that would equate the total return from a rollover strategy to that of a longer-term zero-coupon bond.

Forward Rates as Forward Contracts

Question 6

Define

the term structure of interest rates

Forward Rates as Forward Contracts

Answer 6

refers to the interest rates for various terms to maturity embodied in the prices of default-free zero-coupon bonds.

Forward Rates as Forward Contracts

Question 7

Concept

refers to the interest rates for various terms to maturity embodied in the prices of default-free zero-coupon bonds.

Forward Rates as Forward Contracts

Answer 7

the term structure of interest rates

Forward Rates as Forward Contracts

Question 8

Fill in the blank

A common version of the ____ hypothesis holds that forward interest rates are unbiased estimates of expected future interest rates.

Forward Rates as Forward Contracts

Answer 8

expectations

Forward Rates as Forward Contracts

Question 9

Fill in the blank

There are good reasons to believe that forward rates differ from expected short rates because of a risk premium known as ____

Forward Rates as Forward Contracts

Answer 9

liquidity premium

Forward Rates as Forward Contracts

Question 10

Effects of

positive liquidity premium

Forward Rates as Forward Contracts

Answer 10

can cause the yield curve to slope upward even if no increase in short rates is anticipated

Forward Rates as Forward Contracts

Question 11

Complete the statement

The existence of liquidity premiums makes it extremely difficult to infer …

Forward Rates as Forward Contracts

Answer 11

expected future interest rates from the yield curve

Forward Rates as Forward Contracts

Question 12

What does empirical and theoretical considerations say about the constancy of liquidity premiums

Forward Rates as Forward Contracts

Answer 12

the constancy is unlikely despite the assumption making calculations easier

Forward Rates as Forward Contracts

Question 13

Define

bond stripping

Forward Rates

Answer 13

selling bond cash flows as stand-alone zero-coupon securities

Forward Rates

Question 14

Define

bond reconstitution

Forward Rates as Forward Contracts

Answer 14

combining zero-coupon stripped securities to re-create the original cash flows of a coupon bond

Forward Rates as Forward Contracts