My Finance

0. Introduction. Previously, we wrote a deterministic equation connecting the zero-coupon bond rates and the total returns for 10-year bonds. But we only approximated the zero-coupon bond rates with classic 10-year rates, for which we have much more data, back from 1927. And we need zero-coupon bonds to compute exact returns, not classic coupon Treasuries. Here, we explain and address this discrepancy.

1. Why we need zero-coupon bonds. Classic Treasury bonds pay semiannual coupons, so they pay 20 such coupons during their (for example) 10-year lifetime. We choose 10-year bond rates because they have the most data for them, going back to 1927 or even further. There are classic Treasury bonds with other maturities, for example 7-year or 30-year, but their data does not go back enough. Therefore, 10-year Treasury bond rates serve as the classic benchmark for long-term Treasury rates. They are free of default risk, but very much exposed to interest rate risk.

2. Data. Previously, it was not great with regard to zero-coupon bond rates data. We had Federal Reserve daily data from January 1990 until now, for maturities 1 year, 2 years, etc up to 10 years. But this is not nearly enough to make inference! Only 36 years. Instead, we found an article in Federal Reserve repository (it’s their own internal version of arXiv or SSRN) which includes data from 1961 for zero-coupon maturities from 1 to 7 years and from 1971 for 8, 9, 10 years.

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