Term Structure of Interest Rates

Question 1

Why have we introduced the term structure of interest rates?

Answer 1

In reality though interest rates do
tend to vary with the term of the investment. For instance, a different interest rate will apply to a
repayment mortgage of term 15 years than say to one of term 30 years.

Question 2

If we assume fixed interest for any term of investment describe the yield curve

Answer 2

Flat yield curve

Question 3

Define the term structure of interest rates and how is it denoted?

Answer 3

Term structure of interest rates defines the relationship between the
term of the investment itself and the (annualized) interest rate being charged on that investment. Yn
Set of all values of yt

Question 4

Define the yield curve

Answer 4

The
yield-curve is a graph of this relationship illustrating how the (annualized) interest rate being charged
varies by the term of the investment. Maps Term to Yn

Question 5

What types of investments do we consider on yield curves

Answer 5

Government investment which is considered to be ultra secure so return will not include a security risk yield margin.

Question 6

Define a pure discount bond

Answer 6

A unit zero-coupon bond. Has term t years and is an
agreement to pay €1 after t years. Note that no coupon payments are made under the bond, just a final redemption payment. We denote the price of a bond as such for term t as Pt

Question 7

Define the t-year discrete spot rate of interest

Answer 7

The (annual) yield on a unit zero-coupon bond of term t years and is denoted by .ty

Question 8

Define yn

Answer 8

Annualized return required on a government bond NOW of term n years (eff annual interest rate on investment term of n years)

Question 9

Define discrete time forward rate of interest and give its symbol

Answer 9

f t,r is the annualised rate of interest at time 0, for an investment made at time t for a period of r years under the term structure applying. It is an estimate at time 0 as we don’t know what the market estimate of interest will be in t years for term n

Question 10

By convention what does ft mean

Answer 10

ft,1 : 1 year forward rate of investment made at time t

Question 11

Explain the different between discrete time spot rates and discrete time forward rates

Answer 11

Discrete time spot rates are the current rates of interest being offered for investments of different
terms.
The discrete time forward rates of interest are estimates of what future interest rates will be
based on the current spot rates available -
estimates of a random quantity representing the value interest rates will take over certain future
terms.

Question 12

How is the t year spot force of interest denoted and give another name for it

Answer 12

Yt - continuous time spot rate

Question 13

How is the continuous time forward rate of interest denoted

Answer 13

Ft,r

Question 14

How is the instantaneous forward rate of interest denoted

Answer 14

Ft

Question 15

Define the the instantaneous forward rate of interest

Answer 15

instantaneous forward rate of interest is denoted by the limit as r goes to 0 of Ft,r .
Ft may
be thought of as the forward rate of interest applying in the next moment of time (from time t ).

Question 16

What is another term for the yield to maturity

Answer 16

(annual)

redemption yield

Question 17

Define the yield to maturity

Answer 17

Level effective (annual) rate of interest earned by the investor on the bond
transaction, i.e. the level rate of interest at which the discounted value of the proceeds from the bond
equal its (initial) price. It is the average return ont he bond

Question 18

What is the YTM used for and what are its drawbacks

Answer 18

Gives an excellent measure of the relationship between term and yield
for a zero-coupon bond.
For fixed interest bond the YTM will depend too much on the coupon rate and does not give a simple measure of relationship between term and yield.

Question 19

What spot rate is f0 equal to

Answer 19

y1

Question 20

Define the n-year par yield

Answer 20

For a certain n-year fixed interest bond the n-year par yield is the (annual) coupon amount per 100 nominal that would be payable under the bond with respect to the term structure of interest applying to give a bond price of 100 per 100 nominal if it was redeemed at par

Question 21

How is the n par yield denoted

Answer 21

ycn

Question 22

Why do we study the n par yield

Answer 22

Allows for fairer comparison of bonds with different coupon amounts. The par yield gives an alternative measure of the relationship between the yield and term of
investment.

Question 23

Define the coupon bias

Answer 23

he difference between the par yield rate and the spot rate

Question 24

Define inflation

Answer 24

Inflation is a sustained increase in the general price level of goods and services in an economy over a
period of time

Question 25

What will be an individuals view of inflation

Answer 25

individuals with ‘real assets’, such as shares or property, may like to see inflation
rise as that increases the value of their assets. Individuals holding cash or assets producing fixed
returns do not like high inflation as it erodes the value of such cash holdings

Question 26

If inflation is predicted to rise above a target value what may happen to interest rates and why

Answer 26

The central Bank may decide to increase
interest rates. The purpose of such increases is
to moderate economic growth and thereby curb future inflation.

Question 27

What will be the effects of a rise in interest rates

Answer 27

Increases in the cost of borrowing
Increase in mortgage interest payments
Increased incentive to save rather than spend
Reduced confidence - people are less likely to take out risky investments

Question 28

How can yield curves be used by investors

Answer 28

They can compare the yields offered by ‘short-term’,

‘medium-term’ and ‘long-term’ bonds. T

Question 29

Explain the normal yield curve or the upward sloping yield curve

Answer 29

Short-term yields are lower than long-term yields. Indicates that investors require a higher rate of
return for taking the added risk of
lending money for a longer period of time.

Question 30

Explain the inverted or negative yield curve or the downward sloping yield curve

Answer 30

Short-term yields are higher than long-
term yields. It has often been found that inverted
yield curves have preceded periods of
recession in an economy.

Question 31

What does a very steep positive yield curve imply

Answer 31

Many economists also believe that a steep
positive curve indicates that investors expect
strong future economic growth and higher
future inflation (and thus higher interest rates)

Question 32

What does a very steep negative yield curve imply

Answer 32

A sharply inverted yield curve means
investors expect sluggish economic growth
and lower inflation (and thus lower interest
rates).

Question 33

Explain a flat yield curve and what its implications are

Answer 33

Finally, a flat yield curve exists when there is little
or no difference between short-term and long-
term yields. A flat yield curve generally indicates
that investors are unsure about future economic
growth and inflation. A flat yield curve can also
arise when there is a transition being
experienced between the normal yield curve and
the inverted yield curve.

Question 34

What is the relation between Price and interest

Answer 34

Inversely proportional

Question 35

What shape of yield curve will arise if the market expectation is that short term interest rates will rise

Answer 35

Interest will decrease on short dated securities and increase on longer dated securities

Question 36

What shape of yield curve will arise if the market expectation is that short term interest rates will fall

Answer 36

Interest will increase on short dated securities and decrease on longer dated securities

Question 37

Name the three theories of yield curve shape

Answer 37

Expectations theory, liquidity preference theory, market segmentation theory

Question 38

Explain the shape of the yield curve under expectations theory

Answer 38

shape of the yield curve is completely dependent on investors’ views
of short-term interest rates. The expected short interest rate over t,t+1 is ft. An expectation of a rise in short-term interest rates will make short-term
investments more attractive and longer-term investments (relatively) less attractive. If short-term
investments become more attractive their price will increase and hence the yield on such will fall. Similarly, if long-term investments become less attractive the yield on such will increase. Overall this
will lead to an upward sloping yield curve.

Question 39

What is rt

Answer 39

Random variable representing the short interest rate over t, t+1. ft is an estimate of rt as a number

Question 40

Under expectation theory what is expectation of rt

Answer 40

E[rt] = ft

Question 41

What is a weakness of this theory

Answer 41

The one weakness of this theory is that it assumes that investors have no preference
when it comes to investing in bonds of different terms and the (liquidity) risks associated with such

Question 42

What is the premise of liquidity preference theory

Answer 42

Asserts that investors want to be compensated for longer term investment by a risk premium. The term structure is determined by the future expectations of
rates and the yield premium for interest-rate risk. So the yield curve will be higher than expectations theory

Question 43

What does liquidity preference theory suggest that Expected value of rt is

Answer 43

ft+qt where qt is an increasing function with respect to time representing extra return required by investors at each duration

Question 44

What is the premise of market segmentation theory

Answer 44

Theory suggests that short and long term interest rates are not related to each other. This theory deals with the supply and demand in a certain maturity sector, which determines the
interest rates for that sector.

Question 45

What sort of institutions determine the short term and long term section of the yield curve

Answer 45

Banks have short term liabilities and determine the short term.

Insurers and pension funds contain long term liabilities.

Question 46

What is a humped yield curve

Answer 46

A humped curve is where the yields in

the middle of the curve are higher than the short and long ends of the curve.