Contingent immunization calculation - so confused

  • If the manager invests the entire $500m in 4.75%, 10-year notes at par and the YTM immediately changes, what will happen to the dollar safety margin?
  • If the YTM suddenly drops to 3.75%, the value of the portfolio will be $541.36m. The initial asset value required to satisfy the terminal value of $546.72 at 3.75% YTM is $489.06m, so the dollar safety margin has grown to $541.36 – 489.06 = $52.3m. The manager may therefore commit a larger proportion of her assets to achieve management.
  • If the rates rise so that YTM is now 5.8%, the portfolio value will be $460.55m and the initial asset value required will be $460.52m. The dollar safety margin has gone to zero, and thus the portfolio must be immunized immediately.

Hi all, above is an classic question on contingent immunization while I can put the calculation on BA II, I dont understand the intuition behind it,

My question is, say if you YTM drop, your PV becomes different, if you use FV = 500 to calculate the PV of asset, why you use FV = 546.72 to calculate the liability? help!

where you got this question from?

h21,

Saw that in CFAI book. You are confusing value of portfolio with the desired (target) value of portfolio in future.

In this example, You had $500m with you and first you decide up to what value you would want your portfolio to grow in future, hence $546.72. Now this is your target value that you want to achieve.

Then, you invested $500m in bonds, 4.75%coupon, 10yr at par, to achieve that target. Suddenly the YTM changes and drops to 3.75%. This would change value of your bond investment. Now to calculate the worth of your bond portfolio, you have to hit all those buttons with new YTM figure to know PV of your bond portfolio and during that you take FV=500.

But this was the change in your bond investment holdings due to market changes, you still want to earn the target value you decided at the first place right? so the FV of that target ($546.72) doesn’t change unless you would want to change it yourself.

546.72 = 500* (1 + 0.03/2)^(2*3) = 500 * 1.105^6

The manager’s minimum required yield is 3% BEY and the holding period is 3 years.