SOA6: Immunization question

[New at pd]

Immunization requires that duration of assets = duration of liabilities

Question is -- exactly which duration do the mean?

Here is my answer:
If embedded options are used, we need to use the effective duration, as that incorporates the interest sensitivity of the cash flows.

Suppose we use non-callable bonds. Suppose the assets and liabilities have different yields. We would then need to use the modified duration.

If assets and liabilities have the same yield, can use Macaulay duration.

Do you agree? disagree?

[MetsMan]

I don't believe that there is a "right" duration measure to use, other than the one that best captures the interest rate sensitivity of your assets or liabilities. Rather than thinking of Immunization as the same as matching durations, you can think of it as matching the interest rate sensitivity of the assets and liabilities.

[zapped]

from what i can tell, BPM text (worthless) specifies effective duration (handles embedded options), and the HB seems to mean macaulay.

[mr.c]

I agree with you, new at c6. Obviously, if there are embedded options (or any type of interest-sensitive cash flow), effective duration is necessary. If the assets and liablilities are straight, it is enough to have the modified durations be the same. If the yield on the assets and liabilities are the same, then having equal Macauley durations is equivalent to having equal modified durations.

When in doubt go with effective.

[EdFrog]

Since effective = modified when cash flows are not interest sensitive...
- If the cash flows are interest sensitive, always use effective.
- If the cash flows are not interest sensitive, you can use either one.
- Note that you can't duration match using Macaulay duration. So remember to divide Macaulay by (1+i) before using it.

[zapped]

effective <> modified. modified = macaulay / (1 + yield)

where did you get effective = modified?

effective = [V(-) - V(+)] / [2V(0)delta(y)] where V(-) is the value if the rates go down by delta(y) & V(+) is the value if the rates go up by delta(y). that's how it handles embedded options; it doesn't depend on one interest rate (yield over life of security) like modified & macaulay.

[chucky almendinger]

for optionless bonds and small interest rate shifts (and I'm assuming this is away from the extreme interest rates) Macaulay is approximately equal to Effective

[llll]

Originally Posted by zapped

effective <> modified. modified = macaulay / (1 + yield)

where did you get effective = modified?

effective = [V(-) - V(+)] / [2V(0)delta(y)] where V(-) is the value if the rates go down by delta(y) & V(+) is the value if the rates go up by delta(y). that's how it handles embedded options; it doesn't depend on one interest rate (yield over life of security) like modified & macaulay.

For securities thet are not interest sensitive, I think Modified Duration should be the same as effective duration. Both can be obtained using the formula you stated (Equition (5-1) of HB), since cash flow will not change with interest rate, you will get the same number for effective and modified duration. Is this right?

[zapped]

maybe that's true, but that's not the point. Actuary2000 was talking about interest sensitive bonds when Actuary2000 posted this:
"Since effective = modified...
- If the cash flows are interest sensitive, always use effective. "

if someone memorizes only the MD=Mac/(1+y), assumes it is equal to effective duration, and uses that for an interest sensitive calculation, their answer will get a big fat ZERO.