# Exact definition of effective daily federal fund rates

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.

• Aren't FF futures based on the average fed funds rate for the delivery month? If so I don;t see how you can get the FF rate compounded daily by trading FF futures. – noob2 Sep 26 '18 at 3:20
• @noob2, indeed, we cannot track exactly... yet, I consider longing FF futures as borrowing at daily risk free rate to buy a 30 day bond. SHV is like using my cash to invest in 3 month bond (suppose i can buy and sell at midpoint every day without fee, that is somewhat like daily compounding already). Let's phrase it differently, suppose daily federal fund rate = 30 day rate = 3 month rate for the whole year, by investing in SHV, do I get (A) or some version of (B)? – user40780 Sep 26 '18 at 22:58