Over a horizon shorter than the bond's maturity, the yield is not the return, and two more terms appear.
Rolldown example: a five-year Indian G-sec
Rolldown is the price gain a bond earns by ageing down a sloped curve while the curve stays put. Take a five-year Indian G-sec issued at par with a 6.30% annual coupon on a curve whose four-year point sits at 6.18%. A year later the bond is a four-year bond repriced at 6.18%, which lifts it to 100.414105, so the one-year total return is the 6.30 coupon plus 0.414105 of price, or 6.714105%: 41 basis points more than the yield.
Cross-check it a second way. The bond's modified duration at the four-year point is 3.446059 years, and duration times the 12 basis point slope gives 0.413527 points of price gain. The two routes differ by 0.000577 points, about six hundredths of a basis point, and the difference is convexity. Any rolldown calculation disagreeing with the duration shortcut by more than a basis point or two has an arithmetic error rather than a convexity effect. Rolldown is also what makes an inverted curve expensive to hold: there the term is negative and the yield overstates the expected return.
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How do you forecast the short-rate path?
The short-rate path matters because a constant-maturity bond index never holds a bond to maturity, so its return depends on where policy goes. A Taylor-type rule gives a disciplined starting point:
i = r* + π + 0.5 × (π − π*) + 0.5 × (output gap)For India with a neutral real rate r* of 1.20%, current inflation of 4.90%, a 4.00% target and a positive output gap of 0.50 points, the rule prescribes 6.80%. Against a policy rate of 5.50% (the repo rate after the Reserve Bank's 7 October 2026 hike from 5.25%; as of October 2026, check against the monetary policy statement), that reads as 130 basis points of accommodation. For the United States with r* at 0.80%, inflation at 2.60%, a 2.00% target and a negative gap of 0.40 points, the rule prescribes 3.50% against an illustrative 3.75% policy rate (the target range has been 3.75% to 4.00% since the Federal Reserve's 16 September 2026 hike), which reads as 25 basis points of restriction.
How wide is the error band on a Taylor rule?
Now the part most presentations of the Taylor rule omit: propagate the uncertainty in the rule's own inputs. Sensitivity to r* is one to one, to inflation 1.5 because inflation enters twice, and to the output gap 0.5. With an honest plus or minus 0.75 point range on India's neutral rate, plus or minus 0.20 on measured inflation and plus or minus 1.00 on the real-time output gap, the prescription carries a band of 1.00 × 0.75 + 1.5 × 0.20 + 0.5 × 1.00 = 1.55 points either side. The United States earns tighter ranges on the first two inputs, plus or minus 0.50 on the neutral rate and plus or minus 0.15 on measured inflation, against the same plus or minus 1.00 on the real-time gap, for a band of 1.00 × 0.50 + 1.5 × 0.15 + 0.5 × 1.00 = 1.225 points.
Read those next to the stances they are supposed to diagnose. India's 130 basis point accommodation sits inside a band 1.19 times its own size. The US 25 basis point restriction sits inside a band 4.9 times its size, so the rule cannot tell you whether US policy is tight or loose at all. A Taylor rule organises a discussion about policy well and settles it badly.