key rate duration!

is key rate duration = % invested in 2 year bond * the time period? so if we have 35 mil invested in 2 year bonds and 15 invested in 5 year bonds, and the 2 yr rate increases by 50bps, other rates are constant, what is the key rate duration? in cfai page 266 bonds q28

I spent 20 mins reading page 247& 248. Still don’t quite get what is key rate duration of portfolio, but I was able to solve the problem. Anyways here is what I follow: Key rate duration of 2yr strip: 2 Key rate duration of a 5yr strip: 5 Rate duration of zerocoupons/strips = maturity time. Now when you have zero coupons, rate duration = key rate duration as well. All these means is that for 100 bps (1%) change in spot curve at a rate let’s say at 2%, you’d get effective change in value of your bond, that’ll be equivalent to the Key rate duration at that point which is 2%. Now that is simply if you just had invested in 2yr strips. However if your port contains more than just 2 yr strip, then for 1% change in 2yr key spot rate, your port value just won’t change for 2%, because you have other stuff in your port that’ll either pull the effective change down/up. Infact to compute the actual change in your port value, you need to compute the portfolios key rate duration which is equal to weighted avg of all key rate durations in your port, weighted by the $ invested in those durations. So for your question. if 2 yr int rate goes up by 1%, your port value declines by 2%(35/50) = 1.4% if 2 yr int rate goes up by .5% your port would decline by 1.4% *.5 = .07.

Remember that effective duration = sum weighted average of all the key rate durations. That helped me conceptually

a key rate duration is just the duration for a give bond that shows how that bond’s value in a portfolio will change given a change in interest rates.

thanx! got it