Having a bit of trouble here and would appreciate some help on multi-liability immunization, Page 45 of the Fixed Income book.
It says that 3 conditions are required
PV A = PV L
Composite duration of the portfolio must = composite duration of the liabilities
Individual portfolio assets must have at least one asset duration less than the lowest liability duration and at least one asset with a duration higher than the longest liability duration, ie: have a wider range.
Goes on to say that it isn’t necessary to have a portfolio with a duration of 30, but does that mean that it is still required to have at least one asset with a duration longer than the longest liability, even if it is a 25 year liability, in order to meet requirement 2?
Suppose that you have a liability due is 2 years. You want to invest in a bond with 2 years or less to maturity (so that you have cash to pay the liability), but its duration will likely be too short for classical immunization. So you also have to have a bond whose maturity is longer than 2 years so that the duration of the portfolio matches that of the liability. One longer, one shorter.
Assuming the immunization rates for each liability and the investable asset classes all follow the treasury yield curve, doesn’t that mean you need to borrow money (or reinvest the first asset proceeds) in order to pay off the first liability? Will selling the last asset to pay off the last liability give the same return as borrowing the whole amount and paying it off using the last reciept? This sometimes confuses me.
Does this mean the shorter asset is to pay the liability and the longer one to match overall duration?
This is implying you cannot invest in a 2.0 year bond, right? Because if you could, you already have your matched duration for classical immunization. I don’t know if I’m right…
You can if it’s available, if you have a liability due in 2 years, you can have an asset that pays in 1 year, and another that pays in 3 years. What you do is take the proceeds of the first asset, reinvest it for an additional year, and borrow the remaining due payment for another year, and use the proceeds of the final asset to pay off the borrrowing, if the yield curve doesn’t change (and upward sloping), then you can also bag in a spread gain.
Example (all zero bonds):
1 year spot = 1%
2 year spot = 2%
3 year spot = 3%
PV assets = PV liability ~ $9.6
Duration A = Duration L ~ 2 years
FV asset year 1 = $5
FV liability year 2 = $10
FV asset year 3 = $5.1
Year 2 proceeds = 5*1.01 - 10 = -$4.95 (amount needs to be borrowed to pay off liability)
Year 3 proceeds = 5.1 - 4.95*1.01 = $0.1 gain
If the yield curve moves according to the implied forward curve, then you have no gain. (1f1 = 3%, 1f2 = 5%)
the longer bond provides you with more protection.
What is the guarantee that you would be able to liquidate your shorter duration asset and have all the proceeds necessary to meet your liability? All bonds (short or long) provide you with coupons - that can go towards defeasing the liability. As and when each bond gets matured - you would liquidate it, and get the funds necessary (based on the market yield at that time) - to further defease your liability. But given a volatile interest rate environment (which is one of the risks) - you could end up with rates suddenly rising - and your bonds falling short. So from the perspective of your goal of meeting the liability - you need something that has maturity beyond the liability…
Dude, i don’t think you need to apply the concept as far as you fix the main message in your head which is that you must to respect 3 conditions if you want to immunize a multiple liability, one of these is a wider spectrum of duration at asset level than liability level full stop :
PV Assets = PV Liabilities
DUR Assets = DUR Liabilities
spectrum of durations of assets >> spectrum of duration of liabilities
S2000? cbk?