 # sport rates

3 yr annual sport rate=7% 4 yr annual sport rate 7.5% 1 yr implied forward rate in four yrs is closest to a. 7% b.7.75% c. 9% d. 10% Please be gentle when solving and explain in detail this is one of my weak topics i just don’t get the story.

i believe to solve a 1yr forward in 4 years you need the 4th and 5th year spot rates…

3 yr spot = 7 4 yr spot = 7.75 1yr forward in 4 years is (1+r3)^3*(1+1f4) = (1+r4)^4 1+1f4 = 1.0775^4/1.07^3 ==> 1.1003 ans: choice D CP

Thought behind it: you have a 3 year asset --> u keep invested in it for 1 year --> which is the forward rate and with the no arbitrage principle --> you get the 4 year spot rate. CP

cpk123 Wrote: ------------------------------------------------------- > 3 yr spot = 7 > 4 yr spot = 7.75 > > 1yr forward in 4 years is > > (1+r3)^3*(1+1f4) = (1+r4)^4 > > 1+1f4 = 1.0775^4/1.07^3 ==> 1.1003 > > ans: choice D > > CP You made a slight mistake here…Should have used 1.075, not 1.0775 in the numerator. Answer is C.

Correct me if I’m wrong, but I assume you are finding the 1 year forward rate from year 3 to year 4. = [(1.075)^4 / (1.07)^3] - 1 = 9.0141% Answer is C? Drawing a cashflow timeline helps me to solve these types of questions. You are trying to find the 1 year discount rate between years 3 and 4. You already have the true discount rate (or what you call spot rates) between those two years. 1) If i was to deposit money for 3 years, my FV in 3 years would be Principal x (1+7%)^3. 2) If i was to deposit money for 4 years my FV in 4 years would be Principal x (1+7.05%)^4. Assume in scenario 1), if i had that FV amount at year 3 and i would want to deposit my money for one more year, my FV in year 4 must equal to 2). Therefore you use this equation: (1+7%)^3 times (1 + r )^1 = ( 1 + 7.05%)^4 re-arranging to solve for R you will get the answer shown above. hope this helps.

char lee- i shd have included 5 yr sport rate =8%

ahh that makes more sense. in this case it would be D). 10% [(1.08)^5 / (1.075)^4] - 1 = 0.100234 same concept in my last thread applies.

3 yr annual sport rate=7% 4 yr annual sport rate 7.5% 5 yr annual spot rate = 8% 1 yr implied forward rate in four yrs is closest to a. 7% b.7.75% c. 9% d. 10% 1f4 = (1.08^5)/(1.075^4) - 1 = 10.02% therefore (d)

for these kind of problems i would just do like 4* 7.75 - 3 * 7 = 10 (approximate value)

koppcha Wrote: ------------------------------------------------------- > for these kind of problems i would just do like > > 4* 7.75 - 3 * 7 = 10 (approximate value) why didn’t you use 5*8- 4*7.5?

I think i need to calculate 1f4 right not 1f5.

Char-Lee Wrote: ------------------------------------------------------- > 3 yr annual sport rate=7% > 4 yr annual sport rate 7.5% > 5 yr annual spot rate = 8% > 1 yr implied forward rate in four yrs is closest > to > > a. 7% > b.7.75% > c. 9% > d. 10% > > > > 1f4 = (1.08^5)/(1.075^4) - 1 = 10.02% therefore > (d) best way to do it…just memorize this concept

saurya_s Wrote ------------------------------ >koppcha Wrote: ------------------------------------------------------- > for these kind of problems i would just do like > > 4* 7.75 - 3 * 7 = 10 (approximate value) >why didn’t you use 5*8- 4*7.5? you are right i would have used this. Got confused

t = 1 m = 4 t = numerator m = denominator 1.08(5) / 1.075 (4) = 10%