# Forward Rates

Hi

Came across a practice question that provides two series of forward rates:

F(n-1,1) ….i understand this is (n-1) year forward rate, 1 year from today

F(1,n-1) …..1 year forward rate, (n-1) years from today

Not sure how to interpret and use above series to get holding period return given spot rates….

thanks..

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Can you post the question?

summary of ques is:

5 year spot rate = 7%

F(1,4) = 8.02%

F(4,1) = 11.10%

1 year holding period return is 3% as follows..

(1.07)5

(1.03)1 * (1.0802)4

i dont get why F(1,4) is used instead of F(4,1)

Your interpretation of the notation is backward.

F(1,4) is the annualized forward rate beginning 1 year from now and for a duration of 4 years (i.e., ending 5 years from now).  So F(1,4) is the four year forward rate, one year from today.

Edit: Corrected typo

iceman_1212 wrote:

So F(4,1) is the four year forward rate, one year from today.

It would be the one year forward rate, beginning in four years.

iceman_1212 wrote:
F(1,4) is the annualized forward rate beginning 1 year from now and for a duration of 4 years (i.e., ending 5 years from now).

So F(4,1) is the four year forward rate, one year from today.

These two sentences seem to contradict each other.

Check the 2019 Level II curriculum, volume 5, p. 7, paragraph 5:

F(T*, T) means the T-period forward rate starting at time t = T*.

So F(1, 4) means the 4-year forward rate beginning one year from today, and F(4, 1) means the 1-year forward rate beginning four years from today.

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O i get it …my bad…

thanks

S2000magician wrote:

iceman_1212 wrote:
F(1,4) is the annualized forward rate beginning 1 year from now and for a duration of 4 years (i.e., ending 5 years from now).

So F(4,1) is the four year forward rate, one year from today.

These two sentences seem to contradict each other.

Check the 2019 Level II curriculum, volume 5, p. 7, paragraph 5:

F(T*, T) means the T-period forward rate starting at time t = T*.

So F(1, 4) means the 4-year forward rate beginning one year from today, and F(4, 1) means the 1-year forward rate beginning four years from today.

Thanks for pointing out - have corrected the typo