Friday, August 27, 2010

Perpetual Bonds

A nice piece today from one of my favorite Finance bloggers, Felix Salmon. Felix talks about perpetual TIPs and whether the government should issue them. Perpetual TIPs would be inflation linked bonds that never mature. Sort of like inflation linked preferred stock. The example given is for a bond paying an annual coupon of $120 in a world of 2% inflation and 2% real return.

The nominal return (from the Fisher equation) would be (1.02)(1.02)-1 = 4.04%

We could value the perp TIP in two ways.
First treat it like a growing perpetuity (that grows at the rate of inflation):

Price = cpn(1+i)/(R-i)
where i=inflation, and R=nominal rate. In this case the price would be:
6000 = 120(1.02)/(0.0404-0.02)

Alternatively we could value it in real terms and ignore inflation because inflation affects both the growth rate of the cash flow and appears in the nominal discount rate:

Price = cpn/r
where r = real rate of interest.
6000 = 120/0.02 = 6000.

The problem with a perp TIP though is that the duration (sensitivity to interest rate movements would be quite high. A 100 b.p. increase in the real rate would cause you to loose 1/3 of the value of the TIPs.

From a retirement point of view, I think Duration matched TIPS portfolios make more sense. This is an idea promoted by Zvi Bodie and apparently implemented at Boston U. With those I could buy a portfolio of TIPs that would be immune to interest changes provided I held them for the correct holding period.