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Interpreting the Effective Federal Funds Rate for Daily Accrual

Article Quant Q&A · Author: user40780
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Summary

The document asks how to translate a quoted effective federal funds rate into a daily return when estimating the growth of a cash deposit. It contrasts treating a 13% annual rate as an effective annual return, converted to an equivalent daily compound rate, with dividing the quoted rate by a 360-day convention and compounding that daily amount. Those conventions produce different estimates of both daily interest and the balance after a year, as the question’s examples illustrate.

The response tentatively favors the effective annual interpretation but explicitly expresses uncertainty and notes that the observed rate is an average and varies over time. It does not establish the precise official day-count or accrual convention, nor does it explain how a quoted overnight benchmark maps to returns on instruments such as futures or an exchange-traded fund. Treat the arithmetic as a framing of the question, not a definitive specification for instrument valuation; actual accrual depends on the benchmark definition and product terms.

Key ideas

  • The question distinguishes an effective annual rate from a quoted rate divided by a day-count basis.
  • Compounding a daily accrual can produce different annual growth depending on the convention used.
  • The reply tentatively selects one interpretation but does not give a definitive benchmark specification.
  • The effective federal funds rate varies, so holding it constant is a simplifying assumption.

Tags

Fixed incomeStatistics
Full text
# Exact definition of effective daily federal fund rates


# Exact definition of effective daily federal fund rates












based on https://fred.stlouisfed.org/series/DFF

I found that the effective federal fund rate reach to something like 13% in 1982. Based on my trading experience, I could earn this risk free rate compounding daily by investing in (CME_FF / SHV etc.). Suppose the federal fund rate does not change during 1982, which of the following is True?

(A) it means after 1 year, a deposit of 10000USD leads to 11300USD? This essentially means daily rate is 1.13^(1/365.25)-1 = 0.00033467, means 10000USD deposit earns 3.3467USD one day.

(B)or it means each day, the daily rate is 0.13/360=0.000361111, means 10000USD deposit earns 3.61111USD one day. This means after one year, my annual rate is effectively (1+0.000361111)^365.25 - 1= 0.140962248, meaning a deposit of 10000USD becomes 11409.622USD.

I am quite confused. Thank you.

## Answer by Bob (score -1, accepted)

https://quant.stackexchange.com/a/41933

I believe (but I am not sure) it is the first (A). However, noob2 comment makes sense to me. That is, it is an average and the actual rate will vary.

Bob

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