How can “a one-month risk-free rate of 1%, quoted on an annual compounding basis” be understood in simple terms?
Along similar lines, how can one explain “a five-month risk-free rate of 2.5, quoted on a semi-annual compounding basis” or “a nine-month risk-free rate, quoted on a quarterly compounding basis”?
The frequencies make these statements very abstruse. Please help me understand how it works.
All of these quotes are nominal, annual rates. The first is 1% / 12 = 0.0833% per month, and the second is 2.5% / 2 = 1.25% every 6 months. If the third were quoted at, say, 3%, then it would be 3% / 4 = 0.75% every 3 months.
The effective rates are those nominal rates compounded for the quoted period of time. The first has an effective 1-month rate of (1 + 0.0833%)1/1 − 1 = 0.0833%. The second has an effective 5-month rate of (1 + 1.25%)5/6 − 1 = 1.0406%. The third has an effective 9-month rate of (1 + 0.75%)9/3 − 1 = 2.2669%.
Thanks. That’s was easy to digest!
My pleasure.