Key rate duration

[zxfmontreal]

When we are given an equally weighted treasury portfolio, let’s say:
Maturity: 3-month, 2-year and 5-year
Key rate durations: 0.06, 0.73, 0.34
The effective duration for the portfolio is the sum of 0.06+0.73+0.34
and not (1/3)*0.06+(1/3)*0.73+(1/3)*0.34
Why? When do we apply the weight to calculate the portfolio duration and when we don’t?
Schweser has an example of applying the weight in reading #46…

 

[zxfmontreal]

Anyone knows?
@S2000? What is your thought on this?

 

[Julia B]

Reading #46 on p. 318:
A portfolio’s key rate duration is the weighted average of the key rate durations of the securities in the portfolio. The key rate duration and the effective duration for each portfolio are calculated below:
Portfolio I
D(1) = (50/100) × 2 + (0/100) × 0 + (50/100) × 0 = 1 D(2) = (50/100) × 0 + (0/100) × 16 + (50/100) × 0 = 0 D(3) = (50/100) × 0 + (0/100) × 0 + (50/100) × 30 = 15
Effective duration = (50/100) × 2 + (0/100) × 16 + (50/100) × 30 = 16
So, both the key rate duration and effective duration are weighted.
I don’t have the Schweser books and hope someone else with the same study materials replies - very curious, maybe I am missing something.

 

[dcavici]

i think it is cause when you calculate the key rate durations, you already weighted them when you calculate the D1,D2,D3
The effective duration is just the simple sum of all of the weighted key weight durations.