This is a question in 2015 level 1 notes, study session 17 - Basics of Derivative Pricing and Valuation:
The difference between a fixed-for-floating swap and an equivalent series of forward contracts is that: A. the payment dates would be unlikely to match B. all the fixed-rate payments in a swap are equal C. the floating-rate payments in a swap are unknown The answer given by the notes is B and its explanation is as following:
“The difference between a fixed-for-floating swap and a series of forward contracts is that all the fixed-rate payments in a swap are equal. A swap can be replicated by a series of forward contracts that expire on each of the swap’s payment dates, but the fixed rates on these forward contracts are not necessarily equal.” However, in the notes, it says ”Therefore, we can describe an interest rate swap as equivalent to a series of forward contracts, specifically forward rate agreements, each with a forward contract rate equal to the swap fixed rate. Isn’t it contradicatory to answer explanation above? I think the correct answer should be A. Please enlighten me if I’m wrong.
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The fixed-rate payment on a (market) FRA is the implied forward rate for the loan period. Unless the yield curve is flat, the implied forward rates for a series of (market) FRAs would not all be equal, so the fixed-rate payments would not be equal. Note that they are all equal for a plain vanilla interest rate swap.
When they describe a plain vanilla interest rate swap as, “equivalent to a series of forward contracts, specifically forward rate agreements, each with a forward contract rate equal to the swap fixed rate,” they’re talking about off-market FRAs: FRAs in which the initial value (of each) is not zero. (I know: they don’t say that they’re off-market FRAs; there are many subtleties such as this which the curriculum omits to mention.) The sum of all of the initial values of the off-market FRAs will be zero (because the initial value of the swap is zero), but the initial value of the individual FRAs will not all be zero: some will have a positive initial value while others will have a negative initial value.
Answer A is incorrect: as FRAs are custom agreements, you can set the payment dates to anything you wish, so you can certainly match the payment dates of a swap.
Answer C is incorrect: for both the swap and the series of FRAs the floating rates are not known initially.
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Thanks for your thorough explanation, my friend! This question has been bothered me for days and now I am clear 