Immunisation Flashcards
What does Va and Vl represent
Present value of a series of assets or liabilities
When dealing with investment to account for a future series of liability payments at a fixed rate of interest what’s the minimum requirement
We require that the present value of the liabilities equals the present value of the assets
What is the matching position
When we find at fixed rate of interest point where assets meet liabilities
What is the problem with matching
If interest changes we can be left with a surplus or left short
What is a full immunisation strategy and when is it achieved
Idealistic situation meaning position is immunised if given a change in interest rate at Time t we will have a match or a surplus
full immunisation strategy is achieved if, for a given effective
rate of interest i0 , we have matching of assets and liabilities and then given a one time shift in interest rates from i0 to i we have:
S(i)=Va(i)-Vl(i)>=0
What is S
We refer to the function S as the
surplus position at the interest rate applying.
Why is a full immunisation strategy seldom pursued
Complex to implement initally and complex to constantly have to re balance over the term of the investment as interest rates change
Also it requires use of complex and expensive derivative instruments and so could be quite costly for the party
Define derivative
Derivatives are financial contracts, set between two or more parties, that derive their value from an underlying asset, group of assets, or benchmark.
How is redington immunisation strategy different to a full immunisation strategy
So a Redington immunisation strategy immunises the financial institution
against small changes in interest rates.
Define redington immunisation strategies
Redington immunisation strategy is achieved if, for a given effective
rate of interest i0 , we have matching of assets and liabilities and then given a one time SMALL shift in interest rates from i0 to i we have:
S(i)=Va(i)-Vl(i)>=0
Drawbacks of redington immunisation
Only applies to small interest changes
Only for 1 time shift in interest rate.
Need to continuously rebalance assets held to apply and a on a regular basis through the term which can eb costly
If insurers liabilities are long term can be hard to find bonds to rebalance
R. Immunisation did not apply probabilities, does not apply to a portfolio with probability the liability is not realised ex: insurance claims
Name three measures of asset cash flows
Present value
Discounted mean term
Convexity
What’s another name for discounted mean term (3 terms)
Duration, Macaulay duration
What is modified duration Another name
Volatility
In general in a bond what will be noticeable about the DMT
It will generally be close to the term of the bond because of the nature of investment
What is the interpretation of present value
The Present Value gives us a measure of the value of the (future) cash-flows in current money terms.
What is the interpretation of discounted mean term
Measures the weighted average payment date of
the cash-flows where the weights used are the present value of the individual
cash-flow amounts.
What is the interpretation of volatility
Volatility measures the percentage change in the value of the cash-flow series per unit (additive) increase in the interest rate. A 1% additive change in interest rate will mean that price of the portfolio changes by Volatility%
What is the interpretation of convexity
Measures the percentage change in the duration of the cash-flow
series per unit (additive) increase in the interest rate. Convexity gives a measure of the curvature of an
associated function. Can measure as well how spread out the Series is - more spread out generally means higher convexity
Why is there a minus in the volatility formula
Minus in front of the Volatility definition
means that an increase in interest rates will mean a decrease in the price of the
bond
Duration of a portfolio of bonds
Weighted average of the individual bond durations
What is P(i)
PV
Why should we use second order taylor approximation is asked to approximate the revised asset price after a change in interest rates
We can reduce the absolute error of our method by including a convexity term;
essentially using a second-order Taylor approximation.
What weights would I use to determine the DMT of a prortfolio of bonds
PV of bond / total PV
What are the three conditions that need to hold for redington immunisation to be achieved at effective interest rate i0
- PV of assets =PV of liabilities at the given effective interest rate
- Volatility of assets equals volatility of liabilities at the given effective interest rate. Or equivalently the DMTs are equal
- Convexity of assets>= convexity of liabilities at given rate of interest
How can we visually confirm condition three
Convexity is the spread of the cash flows - can visually determine if condition three holds by noting or if the asset cash flows are more spread out than liabilitiy cash flows
If interest rates increase what happens to PV of assets and PV of liabilities
If interest rates rise in the future then both
Va and VL will decrease.
If interest rates decreases what happens to PV of assets and PV of liabilities
Now if interest
rates fall in the future then both Va and Vl will increase
Given a change in interest rates what do we not want to see with PV of assets and liabilities that would cause a possibly deficit
With downward movement in
interest rates the value of the assets held increases by less than the value of the liabilities due, or that,
following an upward movement in interest rates, the value of the assets held decreases by more than
the value of the liabilities due
Both cases meaning assets are not sufficient to cover liabilities
Describe the idea of a cashflow matching strategy how it would work in theory and why it often doesnt in reality
An obvious investment strategy to meet a future liability payment
is to purchase a zero-coupon bond with a ‘face-value’ equal to that of the liability payment and
maturing as the liability payment falls due. In theory would work and is referred to as a cash-flow matching strategy. The liability payment is always met even if there is some fluctuation in the interest rate. However zero-coupon bonds of the required maturity may not always be available for purchase in
the market by the financial institution.
Time horizon of a bond
weighted average of the time of the individual cash-flows where we choose the weights
to the be present value, at the fixed rate of interest applying, of the individual cash-flow amounts
