Key Rate Duration

[dinosaur]

I'm doing some ALM work on some A/L and have calculated the Effective Duration using 100 change. We want to see the key rate durations for the A/L (the individual pieces by maturity) and was wondering what interest rate I should use.

Do I still use the 2 * 100 bp change for an up and down or do I use the appropriate spot rates (change in)? The idea is that the components will sum to the Effective Duration but when I use the spot rate per my boss it doesn't match. It matches when I use the 100 bp change * 2 instead but I'm told this may not be right.

The change stems from when calculating the MV of A/L under different scenarios, that the rates to discount were approximated by the shift + the level spot rate. i.e. for a + 200 bp change, the MV was calculated using the level spot curve + 200 bp. I saw this and thought, that's not right, you need to discount at the new spot curve at + 200 bp to get the appropriate MV.

Any help would be appreciated!

[An Affair to Remember]

:)

[dinosaur]

The duration calc is based off the 100 bp change using the 1st formula above. We do multiple shifts to calculate the MV of A/L of +/- 50, 100, 200, 300 bp.

When calculating the MV on each scenario, I think you'd use the spot curve at each shift which won't be exactly the level +/- x bp.

Example:
Calculate the MV based on the +/- spot curve
Then calculate duration on the +/- 100 bp on MV
Next, calculate the Key Rate Duration (components of A/L and compare)

Let's say spot_120 (10 year) equals 5.60% up 100, 4.35% on level, 3.22% down 100.

Do I use 200 ( 2 * 100 change) or do I use 238 bp (5.60%-3.22%) when calculating the Key Rate Duration?

[An Affair to Remember]

No.

However, I interpolate the shift in between my key rates.

Maybe, that's what you are missing.

See Study Note 8V-115-00 Key Rate Durations: Measures of Interest Rate Risks by Thomas Ho (page 3)


Let say, you have key rate in 1 yr, 3 yr, 5 yr

What's your shift in 2 yr or 4 yr?

Or 1.5 yr, 2.5 yr, 3.5 yr 4.5 yr?

If you shift 1 yr rate by +100,
1.5 yr by +75
2 yr by +50
2.5 yr by +25
3 yr by +0

If you shift 3 yr rate by +100
1 yr by +0
1.5 yr by +25
2 yr by +50
2.5 yr by +75
3 yr by +100
3.5 yr by +75
4 yr by +50
4.5 yr by +25
5 yr by +0

If you shift 5 yr rate by +100
3 yr by +0
3.5 yr by +25
4 yr by +50
4.5 yr by +75
5 yr by +100
5.5 yr by +75
etc etc

I would interporate all your spot rates (in monthly interval).

[tope]

What is a key rate duration