 This topic has 7 replies, 4 voices, and was last updated Sep18 by daharmattan1.

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I have difficulty in understanding this statement from Schweser material: “If portfolio duration is less than liability duration, portfolio is exposed to reinvestment risk”. Now I understand that if portfolio duration is smaller that means when rates go down, liabilities increase more in value than portfolio assets and so assets can not fulfill the liabilities. Also, since rates go down reinvestment income would go down in general. But how can we conclude that it is reinvestment risk that dominates. In general if there is a duration mismatch between assets and liabilities, there is a interest rates risk. I am not able to place reinvestment risk in this picture as well as not able to understand quantification of the same. Any thoughts please?

Use an example: Let’s say the portfolio’s duration is 5.0 (holding a single Bond) and the liability duration is 7.0 (with a single liability). In this case we might conclude that the Bond is due to mature in 5 years. However as the liability isn’t due until end of year 7 we have 2 years to fill, so we are subject to the risk that we will be unable to achieve the required return from the Bond (invested for 2 years from end of year 5 to end year 7). This is where reinvestment risk comes into play.
To extend the example, say that the liability is for $1m. We set aside $710k in a Bond trading at YTM of 5%. If this was held for 7 years it would offset the $1m. However as we only secured a term of 5 years we can only be assured that at the end of the term (5 years) the Bond will mature at $907k. If we can reinvest this into a new Bond for a term of 2 years paying 5% then we have successfully achieved a final value of $1m (and thus offset the liability).
On the other hand if interest rates fall and the YTM reduces to 4% for the 2year Bond, the final value will be $981k, leaving us short $19k. Of course rates could rise, in which case we could end up ahead (YTM of 6% for the 2year Bond would produce $1,019k).
**just to add, in the example (for simplicity) we are talking a single liability with starting duration of 7.0. Remember that as we get closer to the time payment is due or owed the duration will reduce (this goes for any asset or liability). Therefore by the end of year 5 the liability will have a duration of around 2.0 etc etc…


I realised after posting that reinvestment returns with work to offset gain/loss from price changes, that’s the whole purpose of immunisation but again how to place both of them together. Like in 1st case when rates go down, also value of liabilities goes up more than assets and reinvestment returns go down, so do we expect a shortfall for sure and vice versa? In 2nd case when rates go up and value of assets goes down more than liabilities, do we expect reinvestment returns to cover the shortfall as these should go up?
Probably I am blabbering or just over thinking. 
You are on the right track, though remember that the actual impact will depend to some extent on the structure of the liability. If we are holding Bonds to maturity then the price change due to interest rate changes is kind of irrelevant (as the plan all along is for the Bond to mature <at par> so we can clear the debt.
For example: If the liability has a fixed value (say $100), due to be paid at some point in the future (using previous example, let’s say at year 7) then it will be unaffected by changes in the interest rate, but the asset (Bond) will be affected if it has a maturity unequal to the 7 year of the liability.
Just to reiterate:
*immunisation is based on the assumption we are trying to perfectly offset $1 of liability at a certain date with $1 of asset at the same date.
*Reinvestment risk only comes into the picture when there is a mismatch
*If the asset (say zero coupon Bond) has been matched to the liability so that the Bond maturing (at par) meets the liability, then interest rate changes should not adversely impact the strategy. 




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