Immunization

 

Interest Rate Risk = Price risk and Reinvestment Risk

 

Classical Immunization = Price risk offset Reinvestment Risk

 

In index, usually the effective duration is calculated by using average of sector instead of individual bonds

 

Effective duration is easier to calculate than standard deviations

 

Duration contribution = weight x duration

 

Dollar Duration = – duration * change of interest rate * price

 

Portfolio Dollar Duration = sum(dollar duration_i) (No weight!)

 

Rebalancing dollar duration:

 

1. Find rebalancing ratio = Old DD/ New DD
2. Add cash to brief up the portfolio by rebalancing ratio
3. Or: use controlling position: choose on portfolio to change

 

Spread Duration: Change due to the change of spread

 

i.e. spread risk

 

1. Nominal
2. Zero-volatility Spread
3. Option Adjusted Spread

 

Classical Immunization: Construct a portfolio with the same duration as the time horizon of the liability

 

This can only immune 1-time (because of convexity?), immediate, parallel shift

 

If Portfolio duration<liability’s, decrease in interest rate can be problem

If Portfolio duration>liability’s, increase in interest rate can be problem

 

(Reinvestment risk has nothing to do with duration=> constant, then think of price risk as result of interest rate)

 

Need to rebalance and consider the followings:

1. Credit Rating
2. Embedded Option
3. Liquidity – for rebalancing

 

Immunization Risk:

 

The terminal value falls short of target value as a result of arbitrage interest rate change

 

1. Interest Rate Risk
2. Contingent Claim Risk (call risk, prepayment risk) – lose stream of high coupon income and has to reinvest in low coupon rate
3. Cap risk – if the portfolio has floating rate with caps

 

When the cash flows concentrate on the horizon date, the reinvestment and immunization risks are the lowest

 

Extensions to Classical Immunization:

 

1. Multifunctional duration – key rate duration
2. Multiple Liability Immunization – numerous horizon dates
3. Allowed for increased risk as long as it does not jeopardize meeting the liability structure
4. Contingent Immunization

 

Contingent Immunization:

1. Determine the target returns
2. Indentify the appropriate safety net return
3. Establish effective monitoring

 

Calculate the PV all the horizon date value to determine if should use active management or should lock into the immunization rate

 

If safety net return is too low, rebalancing is infrequent and the portfolio can experience significant decrease in value before the immunization is triggered.

 

If too high, means no room for active management. Also means put all money in immunization and left very few for active management to maximize return

 

Single Liability Immunization:

 

Bullet Strategies – concentrating the maturities of bonds around the liability date

 

Barbell Strategies – 1^st bond matures several years before the liability date (huge reinvestment risk) and 2^nd bond matures several years after the liability date (huge price risk and other immunization risk)

 

Maturity Variance = M²: the variance of the difference between the maturity of the bond and the liability

 

Multiple Liability Immunization is possible (assume parallel rate shift) if:

1. Assets and Liabilities have the same present values
2. Assets and Liabilities have the same aggregate durations
3. The range of the distribution of durations of asset exceeds that of the liabilities

 

Cash Flow Matching

 

Find a bond with the right par and last payment and same maturity as the last liability payment.

 

Then reduce the liabilities by the coupon of that bond (only use coupons before liabilities matured dates) and do that recursively

 

reinvestment risk is large

 

-short term reinvestment rate is critical

 

Since only coupons before liabilities can be used, usually need extra cash compared to immunization

 

General Cash Flow: Treat the future cash flow as zero and to minimize the needs for today’s investment

 

Combination matching: (aka horizon matching): Cash flow matched + multiple liabilities immunization

 

-       Provide liquidity for the first few years

-       Reduce risk associated with non-parallel shift of yield curve (usually occurs in the 1^st few years)