You are given the following data on different rates with the same maturity(1.5years) , but quoted on a different basis and different compounding frequencies :

• continuously compounded rate: 2.00% annualized rate
• continuously compounded return on maturity: 3.00%
• annually compounded rate: 2.10% annualized rate
• semi-annually compounded rate: 2.01% annualized rate

you want to find an arbitrage opportunity among these rates.
is there any one that seems to be mispriced?

Based on the periods of compounding, the rate that is mispriced is the annually compounded rate.

First find out the effective rates of all the rates.

Continuously compounded rate:

= e ^ (Annual rate x period of compounding) - 1

= e⁰.⁰² ˣ ¹.⁵ - 1

= 0.0305

= 3.05%

Continuously compounded return on maturity:

= e ^ (Yield x period of compounding) - 1

=  e⁰.⁰³ ˣ ¹ - 1

= 0.0305

= 3.05%

Annual compounding :

= ( 1 + (Rate of compounding / Number of compounding periods in year))^number of compounding periods - 1

= (1 + 2.10%)¹.⁵ - 1

= 0.0317

= 3.17%

Semi-annual compounding:

= ( 1 + (Rate of compounding / Number of compounding periods in year))^number of compounding periods - 1
= (1 + 2.01%/2)³ - 1

= 0.0305

= 3.05%

Mispricing occurs at Annually compounded rate.

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