Okay, I've now read it twice.
So correct me if I'm wrong, but you want to calculate a total return series based on riding the yield curve and not constant maturity to determine the capital gains or losses for each year?
Just imagine you're in the late 1800's. There are no such things as CDs or bond funds. You want a bond portfolio. What do you do? You can simply build a bond ladder.
Let's say that you're really rich, so that you don't add or subtract any significant amount from the portfolio; you're mostly letting it ride. If you have a 10-year ladder, each year you collect coupons and maturing principals to buy a new 10-year rung in your ladder. This is exactly how our bond ladder/fund model works, too. The difference between our model ladder and fund is that the ladder keeps its rungs until maturity and the fund sells its shortest rung at when it reaches a specific maturity.
Of course, in real life, coupons are paid twice a year. Maybe you can buy two rungs per year starting 6 months apart, so your 10-year ladder has 20 rungs. Yes, we cheat: our model is simplified. It assumes simple annual coupons. If you want to model the semi-annual coupons in a spreadsheet, go ahead*. Nobody is stopping you. If you think that this makes a big difference, I have bad news for you: it doesn't. The imprecision of the historical annual yields we have for the late 1800's and first half of the 1900's is way worse than any small error in our calculations.
* [Added]: In the process, you'll lose the self correcting property, though, as we only have annual yields.
Our model exposes its modeled fund to a collection of bonds of various maturities. So, when a specific part of the yield curve is affected by a change, but other parts are less affected, the fund will have a partial exposure to that change, like what happens in real funds like TBM (Total Bond Market).
If so, my first thought is why bother imputing and/or interpolating bogus yields? Indexed bond funds are already constant maturity and the additional complexity isn't needed if you can just use a CMT and weight the series to get the exact duration needed to match a fund.
I think that your understanding of indexed bond funds is flawed. Index bond funds have a maturity cut out (TBM sells bonds when they reach 1-year to maturity). The weighting of various maturities is based on market weight
, not on trying to maintain a specific average maturity or duration.
And also, T-Bills don't pay a yield. You buy them at a discount to par and the yield is baked in at maturity. All other Treasuries pay interest twice a year not once.
Please take the time to model the difference in total returns between a T-Bill and a 1-year treasury with 2 coupons remaining with the exact same yield-to-maturity, and calculate the total 1-year return difference. If it strikes you as a significant difference, please come back reporting about it on this thread.