Term Structure of interest Flashcards
Instantaneous forward rate(Ft)
lim as r -> 0 of 1/r log(Pt/Pt+r)
-1/Pt d/dt Pt
Term structure of interest rates
variation by term of interest rates
Why interest rates vary over time
Supply and Demand
Base rates(Repo rate)
International interest rates
Expected future inflation
Tax rates
Risk associated with changes in interest rates
3 most popular explanations
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
yield to maturity vs par yield
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
difference between the par yield and spot rate
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
Define duration
also known as Macaulay duration or discounted mean term(DMT), mean term of the cashflows weighted by the present value
Limitations of immunisation
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
volatility (nu)
also known as effective duration.
v(i) sum(Ctk . tk . vi ^(tk+1) / PV
measure of the RATE of change of the PV with i, which is independent of the size of the PV. Equation assumes the cashflows do not depend on the rate of interest
Approximate the PV using volatility and movement in interest rate
small movement i to i+E the relative change in value of the Present value is +- Ev(i) so new PV = A(1 - Ev(i))
Express the duration in terms of the volatility
(i+i) v(i)
dependents on interest rate used to calculate the PV as well as the amounts and the timing
calculated as a average, hence must take a value between the first payment and last payment.
Explain the 3 most popular explanations for the fact that interest rates vary according to the term of investment
Expectation Theory
The relative attraction of short- and long-term investments will vary according to expectations of future movements in interest rates. An expectation of a fall in interest rates will make short-term investments less attractive and longer-term investments more attractive.Hence, yields on short-term investment will rise and yields on long-term investment will fall. An expectation of a rise in interest rates will have the converse effect.
Liquidity Preference
Longer-dated bonds are more sensitive to interest rate movements than short-dated bonds. Hence it is assumed that risk-averse investors will require compensation in the form of higher yields for the greater risk of loss on longer bonds.
Market Segmentation
Bonds of different terms are attractive to different investors, who choose assets that are similiar in term to their liabilities. (give example banks (short term) and pensions(long term)). The demand for bonds will therefore differ for different terms
The supply for bonds will also vary by term as government and companies’ strategies may not correspond to the investors’ requirements
The market segmentation hypothesis argues that the term structure emerges from these different forces of supply and demand
ft,r
the discrete time forward rate agreed at time 0 for an investment made at time t , t>0 for a period of r years
yt
a measure of the average (per annum) interest rate over the period from now until t years time
Pt
price at issue of a unit ZCB maturing in t years
