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

Continuously compounded zero rates are 2.0% for 1 year, 2.5% for 2 years, and 3.1% for 3 years. A trader believes the actual 1-year rate in two years' time (the year 2 to year 3 period) will be 4.0% continuously compounded. Ignoring costs, which statement is correct?

The forward rate is 4.3%, computed as 3.1% times 3 minus 2.5% times 2. Because the trader expects only 4.0%, locking in the higher 4.3% by lending forward is attractive. Borrowing at 4.3% would be disadvantageous if the rate ends at 4.0%.

  1. AThe forward rate is 4.3%; the trader expects a lower rate than implied and would prefer to lock in the forward by lending forwardCorrect
  2. BThe forward rate is 4.3%; the trader expects a lower rate than implied and would prefer to borrow at the forward rate for that period
  3. CThe forward rate is 3.1%; the trader expects a higher rate and would borrow forward
  4. DThe forward rate is 2.8%; the trader expects a higher rate and would lend forward

Explanation

Forward = 3.1*3 - 2.5*2 = 9.3 - 5.0 = 4.3%. The trader expects 4.0%, below the forward rate. Locking in 4.3% by lending forward (via a FRA to receive fixed) benefits from the lower realized rate. Borrowing at 4.3% would be a loss when rates turn out to be 4.0%. The 3.1% and 2.8% options misapply the forward formula.

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