Hi asja,

From our learning XLS @

http://www.bionicturtle.com/premium/spreadsheet/5.b.3._tuckman_key_rates/
where I simply followed Tuckman's motivating example of a 30-year mortgage:

(per the video tutorial), each key rate is "shocked" with a +1 bps shift (and the neighboring rates), so if you consider 5-year shift, we are taking a flat 5% yield curve and shocking up all the rates from 2 years to 10 years (linear interpolate from +0 to +1 bps from 2 to 5 years, and interpolate from +1 bps to +0 from 5 to 10 years). So, this is as if the yield curve were a string and we pulled up the 5 year rate slightly....

Then the $10.65 key rate 01 is just like a DV01, it is the dollar change for the 2 year key rate shift. But while DV01 assumes a parallel shift of the entire yield curve, the KR01 gives the dollar change for just the shock to the segment (in this case, from 2 to 10 years).

And the key rate duration = KR01 / Initial bond price * 10,000

Note this is equivalent to: mod duration = DV01/Price * 10,000

so in key rate duration, we have an analog to modified duration; i.e., what is the % change in the bond price given a one unit shift in the key rate

Also could you explain the advantages/disadvantages of key rate exposure technique in mult-factor hedging? why is the face value than the current market value of a hedging bond used?

The key advantage is: it gives the chance to be more realistic than single-factor duration, and implicity then, allows some consideration for non-parallel shifts. From Sanjay Nawalkha (emph mine):

"key rate durations

**can manage interest rate risk exposure arising from arbitrary nonparallel shifts** in the term structure of interest rates. ... The key rate duration model describes the shifts in the term structure as a discrete vector representing the changes in the key zero-coupon rates of various maturities. Interest rate changes at other maturities are derived from these values via linear interpolation. Key rate durations are then defined as the sensitivity of the portfolio value to the given key rates at different points along the term structure. These duration measures can be used in

**decomposing portfolio returns, identifying interest rate risk exposure, designing active trading strategies, or implementing passive portfolio strategies such as portfolio immunization and index replication**. Similar to the duration vector models, an appealing feature of the key rate model is that it does not require a stationary covariance structure of interest rate changes (unless performing a value at risk or VaR analysis). Hence, it doesn’t matter whether the correlations between changes in the interest rates of different maturities increase or decrease or even whether these changes are positively or negatively correlated. Also, the model allows for any number of key rates, and therefore, interest rate risk can be modeled and hedged to a high degree of accuracy"

why is the face value than the current market value of a hedging bond used? because Tuckman quotes DV01 per 100 face value

David

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