Present Value Discount Factos

Let’s say the rate for a 2-year is 5%.

Why isn’t the discount factor:

1 / (1.05)^2

How come instead they use:

1 / (1 + (.05 x 2))

Doesn’t that ignore the effects of compounding???

I don’t have a good answer of why but you’re always deannualizing the rate, in this case I’m assuming it’s 720/360 days

I get confused all the time. I’m sure one of them is correct but be mindful that the results aren’t that different.

how about the forward rate discount factor and converting that into different ytm/spots in fixed income…FML

So I think of it this way

1 * (1+ .05)^2 is basically 1 * (1.05) * (1.05) no compounding


1 * (1+ .05*2) is basically no compounding

RULE of THUMB: Always use the second one when dealing with LIBOR (Swaps, FRA, etc…)

It’s about nominal vs effective rate.

  1. For nominal (LIBOR, etc) : 1 + i * days / 360

  2. For effective (risk-free interest rates, etc) : (1 + i)^(days/365).

If you are working through derivatives and given Libor or something similar, use the first

If you are given a risk-free rate without any additional info, use the second. (example binomial tree, etc)