Dollar Duration and Rebalancing Ratio

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FinNinja

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Dollar Duration is introduced within the Immunization strategies portion of the Fixed Income reading. But why would you want to rebalance to the ORIGINAL dollar duration in an Immunization strategy?
#1. Rebalancing occurs after a movement in time or interest rate. Assuming int rates remain constant your rebalancing ratio will always call for additional investment into your portfolio securities because duration falls as time passes. The percentage that duration falls actually increases as time passes so you would always be adding increasingly larger amounts into your portfolio in order to keep dollar duration constant.
for example: you have a zero coupon bond mkt value of $1,000 maturing in 5 years. duration is 5, dollar duration is 50. after 1 year your duration is now 4, dollar duration is 40. to rebalance you need to increaseyour position by 20% to $1,200. if you wait one more year your duration is then 3, dollar duration is 36 and your rebalancing ratio is 33.33%. after another year the rebalancing ratio becomes 50%, and after another year it becomes 100%. eg larger and larger investments into the securities haled to keep the original dollar duration.
#2 In an Immunization strategy one of the main tenents is to keep duration = liability time horizon, so why are we setting duration back to the original duration after 1 year? isn’t the liability time horizon less now by 1 year? If our liability in the previous example was 5 years away initially, after one year it would be 4 years away. Wouldn’t we want to adjust the portfolio duration to match the new liability time horizon?
 
It depends on the application isn’t it ? If you have a continuous liability ALM case ( such as steady rate of retirement for several years , or a certain pre-foreseen number of Life Insurance contracts maturing every year) , you do have a horizon but the horizon resets every year. . So you want to keep the DD balanced and not let it run down , to be able to fund future liabilities .
If it is one-shot case such as a big loan that needs to be paid off and never again , your scenario would look logical. Typical ALM is not like that.
 
they mention something called “controlling position” in the heading on the reading - but never define it in the CFAI curriculum. The Controlling position is the ORIGINAL DOLLAR DURATION - and you need to rebalance back to that, per my understanding.
Additionally - your assumption is that the Assets and the Liabilities move lock in step with either change in maturity or change in interest rates, and that assumption is definitely NOT TRUE.
 
beieve controlling postion would be to use the bond with highest duration to rebalnce
cheaper than buying or selling % of all bonds to rebalance
 
you make a good point, alimesoda.
however - you would need to buy the full amount needed (and provided by [Orig DD/new DD - 1] ).
 
janakisri wrote:
It depends on the application isn’t it ? If you have a continuous liability ALM case ( such as steady rate of retirement for several years , or a certain pre-foreseen number of Life Insurance contracts maturing every year) , you do have a horizon but the horizon resets every year. . So you want to keep the DD balanced and not let it run down , to be able to fund future liabilities .
If it is one-shot case such as a big loan that needs to be paid off and never again , your scenario would look logical. Typical ALM is not like that.
Click to expand...
This is a good point, I guess I was over simplifying and not thinking of ALM as a continual process. Thanks!
 
Hopefully CPK’s computer is switched off and he won’t notice my response…. :-)
Where I get confused is if you assume that liability duration remains constant, wouldn’t it be more cost effective to simply rotate some of those shorter bonds into longer duration bonds, or extend duration with a forward contract? Further, why doesn’t the text address the cost of the funds used to rebalance?
janakisri wrote:
It depends on the application isn’t it ? If you have a continuous liability ALM case ( such as steady rate of retirement for several years , or a certain pre-foreseen number of Life Insurance contracts maturing every year) , you do have a horizon but the horizon resets every year. . So you want to keep the DD balanced and not let it run down , to be able to fund future liabilities .
If it is one-shot case such as a big loan that needs to be paid off and never again , your scenario would look logical. Typical ALM is not like that.
Click to expand...
 
Nope it isn’t - it never is :)
controlling position seems to be the key word there….
liability duration IS NOT REMAINING CONSTANT. It is also changing. But at a different rate from the Asset Duration. So you need to push the duration of your assets back up to where it was - so the “width” of assets duration >= Width of Liabilities Duration.
 
Hank Moody wrote:
wouldn’t it be more cost effective to simply rotate some of those shorter bonds into longer duration bonds, or extend duration with a forward contract? Further, why doesn’t the text address the cost of the funds used to rebalance?
Click to expand...
I agree with this, but I think the book is more just showing how to adjust the dollar duration and not necessarilly where it is applicable. Adjusting duration by way of curve adjustments in the secondary market or using futures are both discussed in other areas of the material. This may just be a natural area to include this strategy as well.
 
By using bond with highest duration you use less cash to match original
Dollar duration
 
Why do we need to rebalance DD to original – I think it is desired by PM – why it would desire to keep it same. I think in the beginning PM has set the initial immunized target rate of return keeping in view the term structure of interest rate. Text Says, target rate will differ from YTM unless the term structure is flat. DD will tell us the change in portfolio given 1% in interest rate. Now due to movement in yield curve & also due to passage of time, DD has changed (i.e. lowered). If PM is willing to keep the original DD, this means that he is predicting fall in interest rate. so by keeping DD same (higher relative to now) portfolio will gain more. If the prediction is increase in Interest rate than I don’t think that PM would like keep DD as same. Text says that goal is to keep DD same but does not talk about the expceted change in interest rate.
Other thing – distribution of assets duration should be greater than distribution of liabilities (higher width) - is a way to immunize the multiple liabilities. Why higher range – basically shortest duration of asset should be equal to less than the shortest duration liability (so that we either have money in hand before or on the date of liability) & highest duration of the asset should be greater or equal to highest duration of liability (if longest maturity asset matures before longest maturity liability it will be prone to reinvestment risk). SO here they are talking about the duration range not DD. It should not be linked with DD rebalancing.
Yes the liabilty is from continuos ALM perspective otherwise we will keep on investing to keep DD as duration changes by virtue of passage of time. average Liabilty horizon shall remain same
 
Using controlling Position (i.e. Bond with Highest duration) you would require less cash to rebalance to original portfolio.
As given in ex 7
Original DD equals dollar 111,945
New DD equals dollar 82,579
So Increase in DD req to adjust it to original DD : 111,945 minus82579 equal to 29,366
Bond 1 has the highest duration which can be used as controlling position
So desired DD for Bond 1 to rebalance equal to 43,466 plus 29,366 equal 72,832
MV of bond 1 to get Dollar duration 72,832
MV equal 72,832 divide (4.246 x 0.01) equal 1,715,308
Additional investment required in Bond 1 equal 1,715,308 minus 1,023,704 equal
6, 91,604 which is less than the cash required 1,079,012 had we used all the bonds given in portfolio to rebalance.
 
I dont know why I was unable to use dollar sign, asterix sign, Hash sign while posting above reply. I tried 3 times couldnt. Lastly i changed them to words then only i could post. Any idea why?
 
rahuls wrote:
Why do we need to rebalance DD to original – I think it is desired by PM – why it would desire to keep it same. I think in the beginning PM has set the initial immunized target rate of return keeping in view the term structure of interest rate. Text Says, target rate will differ from YTM unless the term structure is flat. DD will tell us the change in portfolio given 1% in interest rate. Now due to movement in yield curve & also due to passage of time, DD has changed (i.e. lowered). If PM is willing to keep the original DD, this means that he is predicting fall in interest rate. so by keeping DD same (higher relative to now) portfolio will gain more. If the prediction is increase in Interest rate than I don’t think that PM would like keep DD as same. Text says that goal is to keep DD same but does not talk about the expceted change in interest rate.
Click to expand...
an immunized portfolio provides at least the immunized return for parallel shifts in the yield curve, up or down.
 
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