CA Final · Advanced Financial Management · Interest Rate Risk Management
A bank quotes simple annual money-market rates of 6.00% p.a. for 6 months and 7.00% p.a. for 12 months. Ignoring bid-ask spreads, what is the fair 6 x 12 FRA rate (annualised, simple interest)?
The fair 6 x 12 FRA rate is about 7.77% p.a. It is the rate that makes investing for 12 months equal to investing for 6 months and then rolling over at the forward rate, so 1.07 divided by 1.03 gives the six-month growth factor, which annualises to 7.77%.
- A7.77%Correct
- B8.00%
- C7.00%
- D6.50%
Explanation
No-arbitrage requires (1 + 0.07 x 1) = (1 + 0.06 x 0.5)(1 + f x 0.5). So 1.07/1.03 = 1.038835, giving f x 0.5 = 0.038835 and f = 7.767%, about 7.77%. The 8.00% figure comes from the shortcut 2 x 7 - 6, which ignores interest on interest. The 7.00% figure just repeats the 12-month rate.
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