It might be a very simple question but for some reason I’m a bit confused.
Let’s say we enter a long SOFR vs fix interest swap at par. Say 5 year swap with annual coupons (the rfr is daily compounded and paid at each annual reset). The swap rate will be the average of forward rates weighted by the DFs (5 periods so 5 sets of DF*forward rate)
Zero coupon curve (and swap curve) is upward sloping.
At initiation the NPV of the swap is zero. If we assume the curve stays what it is then we would lose in MtM due to the rolldown as in 1 year for example our now 4y swap would be MtM at a lower swap rate than our fixed coupon rate.
Now if assume the forward rates are actually realised, the final NPV of the swap should end up being zero by definition. But what does ‘forward rates realised’ actually mean? Does that mean a swap rate constant as we go through time? Spot 5y swap rate = 4y swap rate in 1y = 3y swap rate in 2y, etc.?
If that’s the case, for example in 1 year, our now 4y swap rate would still be the same as our fixed coupon rate -> no mtm impact but if we look at the past cash flows and the first reset, we most likely paid more than we received. So the NPV (past cash flows + future mtm) should be negative at this time.
How would it go up to 0? It seems to me the swap rate of the smaller time-to-expiry swaps should go progressively up to compsentate.