Term Structure of interest

Question 1

Instantaneous forward rate(Ft)

Answer 1

lim as r -> 0 of 1/r log(Pt/Pt+r)

-1/Pt d/dt Pt

Question 2

Term structure of interest rates

Answer 2

variation by term of interest rates

Question 3

Why interest rates vary over time

Answer 3

Supply and Demand
Base rates(Repo rate)
International interest rates
Expected future inflation
Tax rates
Risk associated with changes in interest rates

Question 4

3 most popular explanations

Answer 4

Expectation Theory
the relative attractive of short and longer term investment will vary according to the expectations of future movements in interest rates

an expectation of a fall in interest rates will make short term investment less attractive and longer term more attractive

in these circumstances yields on short term will rise and yields on longer term investment will fall

Liquidity Preference
-longer dated bonds are more sensitve to interest rates movements than short term investments/dates

it is assumed that risk averse investor require compensation in the form of higher yield for the greater risk of loss on longer dated bonds

Market Segmentation
-bonds of different terms are attractive to different investors who will choose assets similar in term to their liabilities
-demand and supply

Question 5

yield to maturity vs par yield

Answer 5

yield to maturity also known as redemption yield is the effective rate of interest at which the PV of the proceeds of the bond is equal to the price.

n year par yield represents the coupon per E1 nominal that would be payable on a bond with term n years, which would give the bond a current price under the current term structure of 1E per E1 nominal, assuming the bond is redeemed at par. gives an alternative measure between the yield and term of investment

Question 6

difference between the par yield and spot rate

Answer 6

coupon bias
(spot rate for a given term is the yield on a ZCB and par yield for a given term is the yield on a notional coupon paying bond

Question 7

Define duration

Answer 7

also known as Macaulay duration or discounted mean term(DMT), mean term of the cashflows weighted by the present value

Question 8

Limitations of immunisation

Answer 8

There may be options or other uncertainties in the assets or in the liabilities, making the assessment of the cashflows approximate rather than known

Assets may not exist to provide the necessary overall asset volatility to match liability volatility

The theory relies upon small changes in interest rates. The fund may not be protected against large changes

The theory assumes a flat yield curve and requires the same change in interest rates at all times. In practise, this is rarely the case.

Immunisation removes the likelihood of making large profits