27
Feb
How to calculate forward rate given series of spot rates - 6 min screencast
by David Harper, CFA, FRM, CIPM
Assume the 2 year spot rate is 6% and the 1.5 year spot rate is 5%. We want to solve for the six-month forward rate starting in 1.5 years. That is 1f3 or 0.5f1.5.
To solve, we just have to assume indifference between the two "investing opportunities." We should expect the same outcome (at the end of two years) faced with two choices:
- Invest at the two-year spot rate, for two years
- Invest at the 1.5 year spot rate, for 1.5 years, then "roll-over" into the six month forward
Here is the screencast:
Comments
Hi David,
Firstly, thank you for your tutorial, I have found it quite helpful. However, I do have a question that I am hoping you may be able to help with. I will give an example becuase I doubt my ability my explain the problem well enough.
Maturity (Years) Yield
5 8%
3 6%
2 5%
In order to calculate the 3 year forward rate 2 years from now:
(1.08)^5 = (1.05)^2 (1+2f5)^3
The answer I have is f= 11%. However when I do the calculation, I get cube root of 1.332724 which is much closer to 10%. Can you provide some insight on this. Also the formula I have uses n and n-1. Clearly the 5 and 2 used in this example do not jive with this n and n-1. Should the 1 actually be a variable number depending on the information provided? Also given this information could I find the 2 year forward rate 2 years from now? If so how can I do so?
Thank you again,
Mike Strong
Hi Mike, thanks for liking the tut.
Compound frequency can make a bit of a difference, but not enough to get to 11%. I tried semiannual and continuous. I get your answer. 11% looks wrong to me b/c (1+5%)^2*(1+11%)^3 implies 8.56% 5-year spot. So, I’d get your answer. And the n/n-1 doesn’t mean anything to me, sorry.
Re 2F2, you couldn’t get this because currently it varies with the 4-year spot. With these assumptions, I see infinite 2F2
Sorry can’t crack that code for you…David
Hi David,
Thank you very much for responding to my post so quickly. I believe that I have a better understanding of this now. I am sorry for not being clear regarding to the n and n-1. I was referring to the formula:
(1+ n-1Rn) = (1+ 0Rn)^n / (1+ 0Rn-1)^n-1
I was wondering if rather than always using n-1, is it possible to generalize this to n-t? Where t = (n – the holding period for the forward rate in question). Per the original question, n = 5 and t = 2. This is what I meant by there was no n-1 information used in this example. Do you think I am safe to rewrite this formula substituting n-t for all n-1? Thank you again for your help.
-Mike Strong
Hi David Harper and Mike B Strong,
Thanks guys for having the audacity to raise the question and also for the videocast.. was really helpful for my university exam (at Cass)... was a bit stuck on how to calculate these manually w/o the assistance of Excel.. brilliant!
Mandeep Singh
Hi David,
thanks for the tutorial, it is very helpful. But i am having a difficulty to find a next six month spot rate for japanese yen. do you know where i can get it? i mean like a more precise one.
Thanks.
dro
I want answer of this question
Spot (USD/EUR) : 0.8385/.8391
3months forward : 20/30
Spot (USD/GBP) : 1.4548/1.4554
3months forward : 35/25
Find the three month (EUR/GBP) outright forward rate
You are a recent graduate working with a large financial consulting firm as part of their graduate program. You have spent the previous couple of weeks participating in the graduate program training seminar. For your first project you have been put onto a team working with Fantra’s (a global soft drink manufacturer) financial team. As an introductory exercise, to get you warmed up, your boss has provided you with the following data and asked you to calculate the one year forward rate 2 years from now
one period spot rate i0,1 6.1% pa
one period forward rate i1,2 9.65% pa
three period spot rate i0,3 7.9% pa
i2,3=?
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