spot and forward rates between, forward, problems, like

lxwarr30

I've been working fixed income problems all day and it's going...okay, except I have a mental block about converting between spot and forward rates. Anyone have any words of wisdom? Problems like - what is the 1-year forward rate 2 years from today, blah blah. Even with the answer in front of me I don't get it.

suyash1989

Think of it in terms of future value. Lets say the 1-year rate is 1% and the 2-year rate is 2%.

So, the FV of $1 in 1 -year is 1.01 and the FV of $1 in 2-years is 1.0404.

Now what is the 1-2 year forward rate? It's just the rate that will grow 1.01 to 1.0404 in one year. That is, 1.0404/1.01 - 1.

Hope that helps anyway.

waldziuchna

theres a trick that Schweser uses....not sure if you have access to that

Wasteoftime

What's the Schweser trick? I do have access. Ohai, thanks - I sort of get it when you put it like that, but not completely.

ogoluwa

If you come to me today for a loan that will be paid back in 12 months, and you want your cash money right now, then I'll charge you the 12 month spot rate.

If you come to me today and tell me you're going to need a loan in two years, and the loan will be paid back in 12 months after you get your cash money (remember you'll get your money in two years), then we would use the one-year forward rate two-years from today.

There are lots of extra details (such as there isn't an actual loan) but that's the idea. Or are you just asking about the mechanics of the calculation?

And I like saying cash money

joemoran

Conceptually I get what we're trying to calculate but not actually how to calculate it. I could just memorize, I suppose, but I like to have a handle on what I'm actually doing. Plus all the subscript f's in the formula give me a headache. 1f0 1f2 all that. Boo.

thisisbrianly

This is what I remember offhand.... Someone, please correct me if I am wrong.

Draw a time line.
Say I have 2 yr spot rate (current rate for 2 yrs loan) and 3 yr spot rate (current rate for 3 yrs loan) and I need a 1 yr forward rate, 2 yrs from now.

0_____ 1 yr______2 yrs _____3 yr


Go from now (t = 0) to t = 2 you need the 2 yr spot rate which you have.
From 2 yr to 3 yr you need a 1 yr forward rate (the rate applicable 2 yrs from now)

The combined effect of these two should be the 3 yr spot rate. (If I invest for 2 yrs and then re invest for 1 yr, it should be equal to me investing for 3 yrs right now.)

So (1 + 2yrs spot rate)(1+ 1 yr fwd rate 2 yrs from now) = (1 + 3 yrs spot rate)

The subscripts are there to make it more manageable... They don't have much to do with the concept per se.



Edited 1 time(s). Last edit at Wednesday, March 30, 2011 at 05:11PM by anish.

draz

And 2 yr spot rate = 2f0 = 2 yr fwd rate from now (t = 0)



Edited 1 time(s). Last edit at Wednesday, March 30, 2011 at 06:14PM by optiix.

orang3eph

one thing that really helps me with these, is that the exponents on each side of the equation need to add up to the same number.
ie a^3 x b^4 = c^7 (because 3+4 = 7). or, a x b^6 = c^7 (because a is the same as a^1).

if they don't add up, your equation is wrong somehow, because the time periods don't match.

lc26mizzou

Thanks, everyone. I think I get it now. I'll practice again tomorrow with all this in mind. Much appreciated.