Immunisation

Question 1

What does Va and Vl represent

Answer 1

Present value of a series of assets or liabilities

Question 2

When dealing with investment to account for a future series of liability payments at a fixed rate of interest what’s the minimum requirement

Answer 2

We require that the present value of the liabilities equals the present value of the assets

Question 3

What is the matching position

Answer 3

When we find at fixed rate of interest point where assets meet liabilities

Question 4

What is the problem with matching

Answer 4

If interest changes we can be left with a surplus or left short

Question 5

What is a full immunisation strategy and when is it achieved

Answer 5

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

Question 6

What is S

Answer 6

We refer to the function S as the

surplus position at the interest rate applying.

Question 7

Why is a full immunisation strategy seldom pursued

Answer 7

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

Question 8

Define derivative

Answer 8

Derivatives are financial contracts, set between two or more parties, that derive their value from an underlying asset, group of assets, or benchmark.

Question 9

How is redington immunisation strategy different to a full immunisation strategy

Answer 9

So a Redington immunisation strategy immunises the financial institution
against small changes in interest rates.

Question 10

Define redington immunisation strategies

Answer 10

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

Question 11

Drawbacks of redington immunisation

Answer 11

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

Question 12

Name three measures of asset cash flows

Answer 12

Present value
Discounted mean term
Convexity

Question 13

What’s another name for discounted mean term (3 terms)

Answer 13

Duration, Macaulay duration

Question 14

What is modified duration Another name

Answer 14

Volatility

Question 15

In general in a bond what will be noticeable about the DMT

Answer 15

It will generally be close to the term of the bond because of the nature of investment

Question 16

What is the interpretation of present value

Answer 16

The Present Value gives us a measure of the value of the (future) cash-flows in current money terms.

Question 17

What is the interpretation of discounted mean term

Answer 17

Measures the weighted average payment date of
the cash-flows where the weights used are the present value of the individual
cash-flow amounts.

Question 18

What is the interpretation of volatility

Answer 18

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%

Question 19

What is the interpretation of convexity

Answer 19

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

Question 20

Why is there a minus in the volatility formula

Answer 20

Minus in front of the Volatility definition
means that an increase in interest rates will mean a decrease in the price of the
bond

Question 21

Duration of a portfolio of bonds

Answer 21

Weighted average of the individual bond durations

Question 22

What is P(i)

Answer 22

PV

Question 23

Why should we use second order taylor approximation is asked to approximate the revised asset price after a change in interest rates

Answer 23

We can reduce the absolute error of our method by including a convexity term;
essentially using a second-order Taylor approximation.

Question 24

What weights would I use to determine the DMT of a prortfolio of bonds

Answer 24

PV of bond / total PV

Question 25

What are the three conditions that need to hold for redington immunisation to be achieved at effective interest rate i0

Answer 25

1. PV of assets =PV of liabilities at the given effective interest rate
2. Volatility of assets equals volatility of liabilities at the given effective interest rate. Or equivalently the DMTs are equal
3. Convexity of assets>= convexity of liabilities at given rate of interest

Question 26

How can we visually confirm condition three

Answer 26

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

Question 27

If interest rates increase what happens to PV of assets and PV of liabilities

Answer 27

If interest rates rise in the future then both

Va and VL will decrease.

Question 28

If interest rates decreases what happens to PV of assets and PV of liabilities

Answer 28

Now if interest

rates fall in the future then both Va and Vl will increase

Question 29

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

Answer 29

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

Question 30

Describe the idea of a cashflow matching strategy how it would work in theory and why it often doesnt in reality

Answer 30

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.

Question 31

Time horizon of a bond

Answer 31

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