Hi group. I am not a CFA so go easy on me. I was wondering what the proper technique is to immunize a bond portfolio which has multiple liability payouts. Do you take a weighted average duration of the payouts and construct a bond portfolio whose aggregate duration is equal to the weighted average duration of the liability payouts? Thanks Gina
Thanks. I had already read that. No where does it address the multiple liability concern and how to immunize for such. Do you construct a bond portfolio whose duration is equal to the weighted average liability duration?
Approach to immunizing multiple liabilities is similar to single bond immunization. Each of the immunization approaches can be extended to multiple bonds.
So for example, Suppose you have 5 liablities 100k in year 1 200 k in year 2 100 k year 3 100 k in year 4 200 k in year 5 Weighted average = 3.14 years Can you immunize these sets of liablities by constructing a bond portfolio with a duration of 3.14? Thanks Gina.
It is the weighted average, but it is not of the payouts. It is the present value of the payouts. Also the present value of the assets should equal the present value of the liabilities and the range of the assets’ durations must be wider than the range of the liabilities durations. Read the cash flow matching portion of the wiki article again. If this is an academic question, then you can just say buy and hold bonds (plural) that meet the required future individual cash flows. Here, there is no reinvestment (immunization) risk.
Thanks Eureka for your response. Do you mind me asking how then would you construct a bond portfolio for my above example (in my last post). If you do not mind, can you please show your calculations. Thanks so much.
Using your example, assuming 100K is the future value of the liability at year 1, the easiest way to immunize your cash flow is via purchaing OID securities that will mature at par to pay for your liabilities.
I will not do your homework for you, sorry. The day is slow, but not that slow. Also, you should be skeptical of homework answers provided by an anonymous forum. I will give you advice. You can use many many different combinations of bonds to immunize that portfolio as long as you stick to my three criteria above. Use google and put multiple liability immunization in quotes. You will quickly find your answers.
Thanks for your response. This is not homework fwiw. How will you know if your multiple liabilities are fully immunized? When calculating the PV of the liabilities, do you use multiple spot rates for the different years? “assets’ durations must be wider than the range of the liabilities durations.” Why is that? If your longest liability duration is 5 years (and 100k), would having a bond with the duration of 7 years and only worth 25k suffice, or does it have to equal the nominal value of the liability with the longest duration? Thanks again for all your help.
I’ll do your “not homework” if you send a couple of pics to ptcrook78 at gmail.
^^What he said. Just check this link: http://books.google.com/books?id=Yr0aZdSQA2kC&pg=PT390&dq="multiple+liability+immunization"&cd=2#
Hahaha. You guys are funny:) Even CFA’s have an overactive libido:) Thanks eureka for the link. I will take a look.