SandyRham wrote:
Unfortunately we are currently selling 10yr+ debt to pay today's obligations, and how much a 10yr+ government promise raises depends crucially on overall inflation over the next 10 years.
With inflation so low a tiny rise is a large ratio change and it is the change that reduces the govt. take for a given promise (secured by our taxes).
[My emphasis]
Sandy, a rather minor point but it niggles me.
The variable to look at here is not so much the rate of inflation,
r say, or the ratio of changes in it, but 1+
r, or rather it's inverse 1/(1+
r) and the ratio of change in that. This, and its relatives, are the elemental factors in any discounting calculation, not
r itself.
Here's an example. Take a 100 nominal of 10-year bond with an annual coupon of 3%. Let's say the current inflation rate, and its expection over the 10-year period, is zero, and also that the price of money over that term is, coincidentally, 3% per annum. Then the market price of the bond is 100.
Next assume the expectation for inflation suddenly jumps to 1% per annum over the term and the yield jumps accordingly to 4% (strictly it should be 1.03*1.01-1 = 4.03%, but let's not get hung up on second order effects). The price of the bond is now 91.89 (or 91.66 if 4.03% is used). So, the effect of an addition of 1% to the inflation rate is a reduction in the bond value/price to
91.89% of its former value. The ratio of the two inflation rates ('after' v 'before'), however, is infinite (or undefined if one picks nits).
By way of contrast, or rather not, now assume a similar scenario to the above for the same 10-year bond but with the yields before and after the inlationary jump of 1% being 9% pa and 10% pa respectively. (The price of money and rate inflation before the jump are such that the yield is 9%. Since we are ignoring effects of the second and higher orders the actual mix of these two doesn't matter.) The values/prices of the bonds are 61.49 and 56.99, respectively, representing a reduction in value to 56.99/61.49 =
92.67%.
This is not too dissimilar to the comparable figure of
91.89% in the first scenario.
The upshot is that it's not
δr/
r you should look at but (1+
r+
δr)/(1+
r) ≈ 1+
δr, or, for convenience just
δr if you really want to whip out the constant.
ADDED:I think I didn't make my point above very clearly. It's this. If bonds are weathering inflation of 6% p.a. and it increases by 1% to 7% then, other things being equal, that increase has the same effect (reduction) on bond wealth as it does when inflation jumps similarly by 1% from zero, or from any other starting point. Roughly.