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FRM Part I · FRM Exam Part I · Properties of Interest Rates

Continuously compounded zero rates are 3% for 1 year, 3.6% for 2 years and 4.2% for 3 years. A trader believes the 1-year rate in two years' time will be 5.0% (continuous). Relative to the market forward rate for year 3, what does the trader expect, and what is the market forward?

The market forward rate for year 3 is 5.4%, from 3 times 4.2% minus 2 times 3.6%. Since the trader expects only 5.0%, the trader would lock in the higher 5.4% by lending (receiving the FRA rate), because borrowing at 5.4% would be unfavorable.

  1. AForward is 5.4%; trader expects the rate to be lower than forward, so would lend via the FRACorrect
  2. BForward is 5.4%; trader expects the rate to be lower than forward, so would borrow via the FRA
  3. CForward is 4.2%; trader expects the rate to be higher than forward, so would borrow via the FRA
  4. DForward is 5.4%; trader expects the rate to be higher than forward, so would borrow via the FRA

Explanation

Forward for year 3 = 3*4.2% - 2*3.6% = 12.6% - 7.2% = 5.4%. The trader expects 5.0%, below 5.4%, so locking in the 5.4% rate by lending (receiving fixed) via an FRA gains. Borrowing at 5.4% would lose if the rate is 5.0%.

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