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CMA Final · Strategic Financial Management · Interest Rate Derivatives

In the money market the 6-month spot rate is 6% p.a. and the 12-month spot rate is 7% p.a., both quoted as simple annual rates. What is the implied 6-month forward rate, 6 months from now (6x12), expressed as a simple annualised rate?

The implied 6x12 forward rate is about 7.77% p.a. Dividing the 12-month growth factor 1.07 by the 6-month factor 1.03 gives 1.038835, so the second half-year earns 3.8835%, which annualises to 7.77%. The simple 8% shortcut ignores compounding.

  1. A7.77%Correct
  2. B8.00%
  3. C7.00%
  4. D6.50%

Explanation

No-arbitrage requires (1 + 0.07 × 1) = (1 + 0.06 × 0.5) × (1 + f × 0.5). So 1.07 / 1.03 = 1.038835, and f × 0.5 = 0.038835, giving f = 7.767%, or about 7.77%. The 8.00% option comes from the shortcut 2 × 7% − 6%, which ignores compounding of the first-half interest.

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