In the literature I am reading "Deconstructing the yield curveCrump & Gospodinov Deconstructing the yield curve, FED REPORTS"Federal Reserve Bk of NY, Staff Report 884 (2019), I came across the definition for a one period holding return of a bond as:
The one-period holding return on a bond of maturity n$n$ from time t to t + 1 is defined as
-
r(n)t,t+1 ≡ p(n−1)t+1 − p(n)t
$$ r^{(n)}_{t,t+1} \equiv p^{(n−1)}_{t+1} − p^{(n)}_{t} $$
I am unable to type superscript or subscript. But theThe idea is that the price is defined as
p(n)t = $p^{(n)}_t = $ the time t log price of a zero-coupon bond which pays $1 at time: (t+n) t + n.
givenGiven this, the one period return from time t to t+1 is
- r(n)t,t+1 ≡ p(n−1)t+1 − p(n)t
$ r^{(n)}_{t,t+1} = p^{(n−1)}_{t+1} − p^{(n)}_{t} $
r(n)t,t+1 ≡$ =$ price at time:(t+1+n-1) - price at time:(t+n)
r(n)t,t+1 ≡$ =$ price at time:(t+n) - price at time:(t+n)
r(n)t,t+1 ≡$=$ p(n)t − p(n)t
r(n)t,t+1 ≡$ = $ 0
I am wondering if I am missing something to understanding the return? because this would always result in 0.
