# P1.T3.22.29. Properties of Interest Rates

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Describe Treasury rates, LIBOR, Secured Overnight Financing Rate (SOFR), and repo rates, and explain what is meant by the risk-free rate. Calculate the value of an investment using different compounding frequencies. Convert interest rates based on different compounding frequencies. Calculate the theoretical price of a bond using spot rates.

Questions:

22.29.1. Although the London Interbank Offered Rate (LIBOR) was the recognized benchmark (aka, reference rate) for short-term loans between highly-rated global banks, it began to be formally phased out in 2021 due to reliability concerns in the wake of investigations during the so-called LIBOR scandal(s). The Federal Reserve convened the Alternative Reference Rates Committee (ARRC). The ARRC subsequently recommended that LIBOR be replaced by the Secured Overnight Financing Rate (SOFR).

In regard to SOFR, each of the following statements is true EXCEPT which is false?

a. SOFR is based on actual repo transactions
b. SOFR is a backward-looking compound average rate
c. SOFR is the sole, mandatory replacement for LIBOR in all major currencies
d. SOFR is a risk-free rate (RFR) and therefore does not contain a credit spread

22.29.2. We are told to assume that an interest rate is 9.00% per annum with quarterly compounding. Each of the following statements is true EXCEPT which is false?

a. The effective annual rate is higher than 9.00%
b. The equivalent rate with continuous compounding is higher than 9.00%
c. The equivalent rate with monthly compounding (i.e., 12 periods per year) is lower than 9.00%
d. The stated (aka, quoted, nominal) rate is given as 9.00% such that the periodic rate is 2.25%

22.29.3. The current risk-free term structure includes the following zero-coupon interest rates 4.0% at one year, 5.0% at two years, and 6.0% at three years. These are given as per annum rates with annual compound frequency. A four-year risk-free bond pays an annual coupon of 3.0%; i.e., it pays a $3.0 coupon at the end of each year. (Treasury bonds pay every six months, but for convenience, we will imagine an annual-pay Treasury note). If the theoretical price of this four-year bond is$95.70, which of the following is nearest to the implied four-year zero rate?

a. 4.14%
b. 5.25%
c. 6.36%
d. 7.47%