Classical Single Period Immunization (Vol 4, Pg 31, Example 7)

The conclusion of example 7 suggests that $1,079,012 of cash is required for rebalancing. I’ve read and reread this whole section numerous time and I am confused.

  1. Aside from the fact that it is a given in the problem, why would there be a requirement to maintain the dollar duration at the intial level? Shouldn’t the liability duration decrease with the passage of time?
  2. Where is this $1 million coming from and why aren’t we considering the borrowing cost?
  3. What is the logic of adding so much cash when we could just as well extend the duration by trading out the portfolio for longer duration bonds?


  1. Liability duration could increase with the passage of time e.g. addition of younger workers to a pension plan

  2. what the rebalancing effectively does is to set aside $1million to cover a potential $30,000 ($112,000 - $82,000) asset-liability shortfall (per 100bps rate change given that we are referriing to duration) if rates moved adversely. that $1mn additional bond investment would generate coupon income (to offset the cost of funds) + gains (to offset the $30,000 dollar duration differential between assets/liabilities in the adverse rate movement scenario)

  3. trading out into longer duration bonds could be constrained by cash / liquidity requirements e.g. low coupon bonds (higher duration) may not provide sufficient cash flow to meet periodic disbursements

  1. I see what the $1 million is used for. I don’t see where it comes from. In the case of, say a pension plan or a life insurance company, do we assume they pull this from other assets on the balance sheet?

Even still, the logic of using additional cash (instead of trading out to longer duration bonds) escapes me. What happens the next year and the year after as the effective duration of the bond portfolio invetibly draws toward zero? Do we keep throwing in buckets of cash to maintain a constant DD?

they never said how the cash is used. They just said MORE is needed.

even if effective duration of the bond portfolio goes down to zero - what they seem to be talking about (at least to me) is

a. It is not a static thing. You are bound to find differences between assets and liabs and need to be aware of that difference.

b. How much more is needed is a function of the Dollar Duration and the current market value.

If, for example, this were a pension plan, and the company suddenly went belly up, to liquidate you would need to find 1.x million $ of cash - since you owe that much more.In this case - they would need the cash.

Again, why isn’t the curicullum addressing the source and cost of those funds? When, in 9,000 pages of text, has CFAI ever left a stone like this unturned?

Then what happens the following year when the duration drops from 3 to 2? You need $1.5m to rebalance. Then from 2 to 1, you need even more.

I’m not following the logic!!!

fiill it, shut it, forget it for now. you have been on this same “stone unturning” with this special thing from Sept… go thro’ 4 more months (or is it 3 now) leaving that unturned, then after you have your charter - go ahead and investigate.


I dont think it is correct to assume that the duration draws towards zero. maturing bonds will be reinvested to maintain the duration profile (assuming a going concern). hence you would not necessarily need to keep throwing in cash (unless poor asset returns relative to liabilities warrant doing so).

the $1m investment is a surplus (after the $1m additional contribution, assets become $4m but liabilities are still $3m - for illustrative simplicity i am assuming that the liabilities are fully funded to begin with). you do not use the additional principal to fund liabilities per se (it serves only to generate returns that may be required to cover shortfalls). hence the $1m is still yours, and not consumed by liabilities. given that its a surplus, it could be funded through a) surplus i.e. overfunded status (b) borrowing © additional contributions. i think option (a) is most likely because in general a business would not borrow / use operating cash to fund a pension surplus when that cash could be deployed in the business to generate better returns.