Q&A Bank Part 5 Q4

[Avviey]

Hi,

Part ii) of this question required you to estimate f and f*, so I wonder

1) how is f=7.73% generated? The average of 7.75% and 7.71% of the 1 year and 5 year spot rates respectively?

2) it says for Bond C: 10 [(1-e^-5*0.0773)/(e^0.0773-1)] +..... = 111.35. Where does this bold part come from? i know 0.0773 is the constant instantaneous forward rate for the period up to 5 years.

Part iv), the answer says " spot rate will be the same as forward rate during the first 5 years". i dont know the reason behind it.

I'd appreciate alot if someone can help together with my previous query.

Many thanks.

 

[Elroy]

Hi,

Part ii) of this question required you to estimate f and f*, so I wonder

1) how is f=7.73% generated? The average of 7.75% and 7.71% of the 1 year and 5 year spot rates respectively?

2) it says for Bond C: 10 [(1-e^-5*0.0773)/(e^0.0773-1)] +..... = 111.35. Where does this bold part come from? i know 0.0773 is the constant instantaneous forward rate for the period up to 5 years.

Part iv), the answer says " spot rate will be the same as forward rate during the first 5 years". i dont know the reason behind it.

I'd appreciate alot if someone can help together with my previous query.

Many thanks.

1) guess so... clearly f isn't constant.. so why not take the average. Not a lot of data so probably as good an approx as any.

2) this is your CT1 annuity factor for the coupons.

part iv) The reason is that there is no term structure before 5 years. If the forward rate is constant f, then ZCB is exp(-integral(f)dt) = exp(-tf). we get spote rate as ln(discountfactor)/t

Sorry if that doesn't make sense!

 

[Avviey]

Hi,

Thanks again for the attempt, not too convinced, anyone else can help?

for question 2), could you tell me the annuity factor for coupon from CT1?ie. an example will do. thanks alot again.

 

[Elroy]

Hi,

Thanks again for the attempt, not too convinced, anyone else can help?

for question 2), could you tell me the annuity factor for coupon from CT1?ie. an example will do. thanks alot again.

for part 2)

let i = e^(0.0773)-1

[(1-e^-5*0.0773)/(e^0.0773-1)]
=
(1-v^5)/i = annuity in arrears for n years = pv of coupons.




for part 4)
see: page 10 of chapter 11 of notes.

 

[Avviey]

Thank so much again.

for part 2), could you please give me an example for this annuity factor? sorry i still cant recall the formula.

for part 4), where on p10 of chapter 11 illustrate the point that spot rate will be the same as the forward rate? i assume the forward rate mentioned here is instantaneous forward rate rather than discrete forward rate?

Thank you.