Formula for valuing pay fixed, receive equity return swap

CFA Level II Portfolio Management
#1

Ok, so this probably really simple but right now just can’t see it.

The formula in the CFAI text for valuing this type of swap is (Equity return) - (final discount factor) - (orginal fixed rate)*(sum of discount factors at time t).

In the EOC questions (eg Q6, Reading 57), the PV of the fixed rate is calculated the same as a regular swap, and then subtracted from the equity return to get the MV.

What I can’t figure out is how the formula in the text is the same as the method used in the EOC questions. I know they arrive at the same answer but I just can’t see it.

Why subtract the third term from the final discount factor, and then subtract that from the equity return?

#2

I’d recheck that formula if I were you. I believe that it’s not equity return, but equity value ; i.e., notional × (1 + equity return).

The formula for valuing all derivatives (or anything else, for that matter) is:

Value = PV(what you will receive) − PV(what you will pay)

We value the fixed or floating leg as a bond – interest payments plus principal – so we have to value the equity leg as return plus principal.