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Damodaran's historical data on 10-year T-note returns (found here) uses the following formula to calculate the 1-period total return on a T-note ($R_1$) given the 10-year constant maturity yield-to-maturity in the prior year ($Y_0$) and the current year ($Y_1$).

$R_1=(Y_0*\frac{1-(1+Y_1)^{-10}}{Y_1}+\frac{1}{(1+Y_1)^{10}})-1+Y_0$

Where can I find a derivation or description of this formula? It seems very odd to me that the only two data points I would need to calculate the total return to a T-note are the beginning and ending yield-to-maturities.

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  • $\begingroup$ Not sure how accurate that formula is, but over short intervals all you really need is the current yield and the previous period's yield. $\endgroup$
    – John
    Commented Aug 12, 2012 at 13:36
  • $\begingroup$ I get that you can do that for a given instrument, but the index isn't a given instrument. So you have to make assumptions about what year 11 looks like, etc. $\endgroup$
    – MikeRand
    Commented Aug 13, 2012 at 3:00
  • $\begingroup$ I think the assumption is that the index is continually rebalanced into a hypothetical 10-year security. $\endgroup$
    – John
    Commented Aug 13, 2012 at 14:46

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First term in parens is the annuity formula applied to a 10 year stream of coupon payments at rate y0, second term in parens is discounted one dollar of principal payable at ten year maturity. Then subtract $1 invested today and add a current cash coupon at rate y0.

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  • $\begingroup$ Silly question, but why wouldn't I look at a 9-year annuity (i.e. the original 10-year annuity less the 1 year of cash flow from year 1)? $\endgroup$
    – MikeRand
    Commented Aug 15, 2012 at 2:30
  • $\begingroup$ I have the same question, why is it still 10-year cash flow when you sell the bond at the end of the first year? Shouldn't it be 9 year remaining? $\endgroup$
    – user6926
    Commented Jan 9, 2014 at 2:22

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