Value Fixed Rate Leg (Swap)

CFA Level II
#1

I know how the equation to value a fixed rate leg of the swap but the logic behind it I can’t quite wrap my mind around. Value Fixed Rate = Fixed Rate * (Sum Discount Factors) + Last Discount Factor. It might be because we’re so close to the end, but I am having trouble understanding the logic regarding this formula. Any help would be greatly appreciated.

#2

This formula gives you the present value for $1 of notional. Think of it as a fixed-rate bond paying:

coupon, coupon, . . . coupon, coupon + par

For $1 par, this is:

fixed rate, fixed rate, . . . fixed rate, fixed rate + 1

So the sum of the discount factors times the fixed rate is the fixed-rate part, above, and the last discount factor is the 1 part.

#3

All you’re doing is calculating the fixed payments and discounting them back to PV. Because we are using $1 notional principal, payment is simply the interest rate (1 * interest rate). It is nothing more than a simple TVM calculation.

#4

Thank you both for your answers! That actually makes a lot of sense and greatly helps me memorizing the formula - something that I had trouble doing prior - because I didn’t understand the intuition behind it. Awesome! Thanks again.

#5

You’re quite welcome.