# Understanding Risk-Free Rate Frequencies

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”?

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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%.

Simplify the complicated side; don't complify the simplicated side.

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Thanks. That’s was easy to digest!

My pleasure.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/