grayfox wrote:So you bought a 10-year (120 months) zero at a discount price in month 1 and sold one month later at the current price. I ignored that it would actually be a (119 month) bond and slightly higher in price. (Edit: Actually, I probably should have just calculated the discount price for the 119 month, and assumed the YTM was the same as the 120 month.)

E.g. $1000 10-Year Zero Coupon Treasury

1979.01 BUY YTM = 9.10 Price = $418.55

1979.02 SELL YTM = 9.10 Price = $418.55

Nominal return = 0.000%

This calculation ignores interest entirely. The reduction to 119 months is essential and it produces 1 month's worth of 9.10% interest. Like so:

1979.02 SELL YTM = 9.10 Maturity = 9.917 Price = $421.59

Nominal return = 0.72%

Maybe that's what you meant by your edit. For the record, I like the zero coupon method, it reinvests automatically, so to speak. However, zero coupons have a much longer duration than coupon bonds in time of high yields, for example:

boknows wrote:Over the entire year of 1979:

E.g. $1000 10-Year Zero Coupon Treasury

1979.01 BUY YTM = 9.10 Price = $418.55

1980.01 SELL YTM = 10.8 Price = $415.02

Total Return = -0.8425%

I get:

1980.01 SELL YTM = 10.8 Price = $397.32

Total Return = -5.07%

This is because the duration of a 10 year coupon bond of 9.1% is about 7 years, so the losses for the zero coupon with duration 10 years are greater and no longer balanced by the interest.

boknows: I think your method is mostly right, but it does ignore two things:

1) price appreciation to maturity, as hinted by your fellow posters elsewhere. A 10 year @9.1% @$100 in 1979 becomes a

**9 year** @10.8% @$90.51 in 1980, plus interest 9.1%, for a total return of -0.39%.

2) the yield curve. When you sell a 10 year bond after 1 year, it's a 9 year bond with a slightly different YtM. In 1980 the curve happened to be very flat, but at other times the curve is steeper. This actually involves getting yield curve data which is not easy.

FIRECalc probably assumes that the price depreciations self-correct in short order due to these two effects (e.g. yield curve flattening is an important reason why bond returns are close to the interest rates, as opposed to higher due to rolling yield), so it just uses the interest. I don't think it's a terrible assumption for all but the shortest intervals.