Austria's 100 year bond.

If you create a bond with a 2% coupon in a world where interest rates are 0.9%, you can bet that that bond is going to be very very volatile. 

Case in point - Austria's 100 year bond that matures in 2117.  (note: register for the economist and you can view a few articles for free).

My quick calculations show that this bond has a duration of about 56.  That's pretty high!  I'd be interested to know whether investors are buying this a straight bet on interest rates or whether they are using it as part of a portfolio.  You wouldn't need much of this bond to tilt the duration of your portfolio higher.

Here are my excel computations, with the predicted price change using duration alone (which is not terribly accurate in this case).  For bonus points - explain why this is the case...

Should the US issue 100 year bonds?

There's been some talk in the press about whether the US Treasury should issue 100 year bonds.  The idea is that by issuing long term bonds, the government would be able to lock in the current low interest rates.   The fundamental premise seems a little silly really.  First of all, the idea of locking in long term rates assumes that rates will, on average be higher than they are currently.   If this is so, then why would anyone buy these bonds off a low rate.   Put another way, to make this argument you have to assume that the Treasury has better rate forecasting ability than the market.

Another argument for these bonds is that there is demand for them from various institutional investors.  So why would investors demand long term bonds?   The most obvious reason is that long term bonds tend to have high duration.  This means that their prices are more sensitive to interest rate movements than shorter duration bonds.  Counter-intuitively, these long duration bonds are actually very useful for managing interest rate risk - particularly when used in immunization strategies.

So this all sounds good, but it turns out the the Federal Government already issues a longer duration bond than a 100 year bond.  The duration of a 100 year 4% coupon bond selling off a yield of 4% is actually about 25 years.   However, 30 year STRIPS, which are zero coupon bonds, have a duration of 30 years.  Therefore the duration argument doesn't really seem to make much sense.  The only small advantage to 100 year bonds is that they have higher convexity than the STRIPS.

You can check these numbers using the Bond function on wolfram alpha.

Bottom line, I don't think that 100 year bonds have much of an advantage over currently available bonds.