ghariton wrote:So the reason for multiplying by the inflation index is to have the duration measure the impact of changes in the nominal rate of interest on the value of the real bond -- not changes in the real rate.
I feel sure there's an error here, but won't have time to take apart the math until Monday.
ghariton wrote:This has been discussed elsewhere on this forum, but none of us could figure out how a reported duration can exceed the maturity of a bond. Even for a strip, which is completely back-end-loaded, the duration equals the maturity (or maturity divided by gross return).
By back-loading, I mean (following the example of the linked paper by Christiensen et al.
) the importance of the changes in the expected value of the coupons and principal, i.e., for a nominal 5% bond (assumed to pay annually for simplicity) the cash flows are $5, $5, ..., $105, but the coupons recieved from a real bond will increase with inflation (call it 2%), $5, $5.10, $5.20, ..., $105*factor. This had importance consequences in their calculation of the Break-Even Inflation Rate - they had to solve for this factor reiteratively until they found a BEIR that worked for bonds of the same duration when the modified duration of the RRB is determined by changing the cash-flows by the BEIR.
ghariton wrote:which is the formula James is using.
Well, yeah, but only because when I looked at the figures I thought 'gee, it looks like the geometric difference between the duration of the RRB expressed in real terms and that reported by Globe Investor is the Index Factor!'. When I performed the calculations, it worked! I am by no means convinced that this method makes sense.
I look at it like this: You calculate the Real Price using the real coupon and the real yield, according to convention
IIAC wrote:Aside from the indexing provision, RRBs are identical to conventional semi-annual pay bullet bonds that repay 100 per cent of principal at maturity. Thus, the clean price, given yield to maturity for a RRB, is calculated in a similar fashion. The price resulting from this calculation is known as the “real price.”
A change in inflation will not affect the real price; only a change in real yield will.
You get the Nominal Price by multiplying the Real Price by the Index Ratio:
IIAC wrote:Settlement amounts for transactions in RRBs are based on the nominal price and nominal
accrued interest, which are calculated as follows:
Nominal.PriceDate = Real.Price * Index.RatioDate
Now, since you're getting the Real Price by treating the thing as a normal bond, you can also get the Real Macaulay Duration and the Real Modified Duration using the same assumptions (which doesn't mean it's right - it just means you can). It appears from my reconstruction of the GlobeInvestor numbers that this is exactly what they have done.
But the Real Modified Duration of the RRB expresses the percentage change in Real Price that will result from a change in the Real Yield. And further, the percentage change in the Nominal Price will be exactly the same as the percentage change in the Real Price, no matter what the value of the Index Ratio. That is to say, the Nominal Modified Duration should be equal to the Real Modified Duration.
So I don't get understand the Globe Investor calculation. And, to my chagrin, I'll be too busy to look at your math carefully until Monday.