I have been through the curriculum a few times now and the only place I am not connecting the dots is the idea of ALM and matching duration of assets and liabilities (fixed income has never been my favorite)
Can someone please put this concept in laymen’s terms? When I see duration I think of sensitivity to interest rates, but it is also referenced as a measure of time in this concept and they are connected but I just can’t seem to grasp that?
I understand how assets can have duration impact. Obviously with fixed income assets put how does duration impact liabilities (I.E payouts with life and non-life companies).
I am close I just feel like I need the concept explained in a different way?
This is an area in which the curriculum is particularly sloppy.
The price-sensitivity-to-interest-rate-changes interpretation applies to modified duration (and effective duration); although the curriculum doesn’t mention it explicitly, the units on these measures are years.
The measure-of-time interpretation applies to Macaulay duration.
The problem is that the curriculum seems to be advocating that the (modified or effective) duration of assets match the (Macaulay) duration of liabilities. This is silly: the measures aren’t compatible. You should be matching modified or effective duration of assets to modified or effective duration of liabilities.
In any case, the objective is to have the interest rate sensitivity matched so that any change in asset value is the same as the change in liability value, leaving equity unchanged.
(As for liabilities having duration: the present value of a liability will change as interest rates (e.g., the discount rate) change.)
Duration is the weighted average time for the present value of payments.
A bond that matures in 5 years and pays no coupons, has a duration of 5, which also means a 5% change in it’s price for every 1% change in interest rates (approximately). A bond with a 100% coupon that matures in 5 years will have a duration somewhere between 2 and 2.5, since that’s the weighted average present value of payments by time period.
Matching assets and liabilities durations eliminates interest rate risk, but only for a single movement in interest rates, meaning that, you need to rebalance your portfolio to match the durations again, since they likely have changed by disimillar magnitudes. Duration matching is not the only ALM you need to take into account (although it’s still mandatory), you also need to match the time due to pay your liabilities. To do that, you either cashflow match every single obligation with a principal, principal+coupon, or coupon from your asset portfolio, since this is expensive to do, you use a wider dispersion of cash flows on your asset side, so the shortest asset payment has a shorter duration than the shortest liability payment, with a cash flow amount (including the reinvestment yield for the remaining period) equal to the first liability payment, and the last asset cash flow with a duration longer than the last liability payment (implying selling it on the market at the time of the obligation).
I’m not too bright on FI either, but hope this helps a little.
Macaulay duration is typically longer than modified duration. They would be equal only if the YTM were zero, and modified duration would be longer than Macaulay duration only if the YTM were negative.
Effective duration can be anything: negative, zero, positive, and if positive, less than Macaulay duration, equal to Macaulay duration, or greater than Macaulay duration. (Indeed, effective duration can be longer than the time to maturity; it is so for inverse floating-rate bonds.)
Macaulay duration is the weighted-average time to receipt of cash flows, where each weight is the present value of the cash flow at that time divided by the sum of the present values of all cash flows. It is not a measure of interest rate sensitivity of price.
Modified duration and effective duration are measures of interest rate sensitivity of price; the former assumes that the cash flows do not change when the yield changes, while the latter allows that cash flows might change when the yield changes.
All types of duration have time as their units, usually expressed as years.
How would you then interpret the mod or effective duration if the units is in years? Isn’t the unit of these durations % change in price from 1% change in YTM?
Therefore, the units on modified duration, effective duration, key rate duration, spread duration, empirical duration, and so on are % change in price for a 1% per year change in YTM.
so then what does the outcome represent for modified duration if the unit is in years? That the percentage change in price for a 1 percent change in YTM per year is increasing/decreasing the duration of my bond in years? i.e. it takes longer or shorter to recover the cash flows? Is this the intuitive interpretation?