Hi All, Question 3.23 from the Part 3 Q&A bank is currently causing me some pain. Question 3.23 A man bought a 5-year forward contract on 1 May 2006 to buy 400nominal of stock that pays coupons of 4% pa payable quarterly on 31 March, 30 June, 30 September and 31 December. The stock is also expected to yeild 4.5% pa effective if purchased on 1 May 2006 and held forever. i) Calculate the forward price for the contract, given the risk free rate of interest is 5% The current issues I am having are: 1) How the annuity for the coupon payments is derived. The coupons payments are made quarterly which would indicate a immediate annuity paid pthly, since the payments are made at the end of the quarterly period. Essentially since we are getting the first coupon payment at 30/06/06 and the present value is being taken from the 01/05/06. Would this not be considered to be a annuity immediate pthly? It appears that the solution uses a annuity due paid pthly, and I hoping on some clarification on this. 2) The derivation of the formula for the price of stock (K = (S-I)e^(risk free interest *T) I have not seen this formula in the course notes or the flashcards at this stage. I may have missed it. If anyone can shed some light on this it would be most welcomed.
The problem is that they are paid quarterly (ie 3months) but the first payment is in 2 months. So to deal with questions like this we need to calculate the PV of the annuity on a nice date and then shift it. So if we calculate it on 30/6/6 that would be an annuity due - as the first payment is due straight away (at the start of the period). And then we shift it back 2 months to 1/5/6. hence multiply by v^(2/12). this is the approach taken. Alternatively we could calculate it's value on 1/4/6. In which case the first payment is at the end of the 3 month period - so it would be an annuity in arrears. We then shift it forward 1 month to 1/5/6. hence multiply by (1+i)^(1/12). Page 11 of Chapter 13.
Hi John, Thanks for your reply to my post. It makes sense as to the approach taken to solve it. If we are using such an approach in the exam, is it advisable to write this out to explain it? Or would you consider that to be a waste of time?
Confused with (ii) part of 3.23 Why in (ii) part while calculating I' in A due n, n is taken as 2.75 that is 2yrs 9 months and then discounted back to 1 month as from 1sep2008 to 1may2011 there are 2yrs 8 months , while in part (i) while calculating I in A due n, n is taken as 5 exactly, not done 5yrs 2 months ? Is this because in (ii) part a specific date is given 1 sep 2008 ? Thanks in advance
IAI May 2012 Applying the same concept in IAI CT1 paper of May 2012 Q.11 part (a) in calculating the price: Why while calculating coupons payments are multiplied by (1+i)^(2/12) and not multiplied instead by v^(2/12) as we cimsider that we have accumulated till 8yrs and then shifted back to 2 months to get 7yrs 10 months ? Please see question paper and solutios from IAI website. Please solve my problem as soon as possible.
If you've accumulated till 8 yrs and then shift back 2 months, you reach 8 yrs 2 months. Since we want a period of 7 yrs 10 months, we move forward by 2 months, and hence (1+i)^(2/12). You can choose the method which suits you best for such sums, there are a number of ways to do this
