Hi all I need to confirm one thing. In May 2010, IAI paper, qus. 8: Here is a capital loss but the worst case scenario is not considered and the later possible date is choosen for redemption. Is it because here it is the INVESTOR who is choosing the redemption date instead of borrower. And the investor will wish to defer the capital loss as much as possible. And if the option of choosing redemption date is of the borrower, then we need to consider the worst case and will choose the earliest possible date. Please anyone rectify if I'm getting anything wrong here. Thanks
When redemption is at the option of the borrower, then you should consider the worst case from the point of view of the investor (as it's the investor who decides how much they are willing to pay). The worst case for the investor is a capital loss being received at the earliest date, and the capital gain being received at the latest date. It's questionable what is the right thing to do in the scenario when redemption is at the option of the investor. Note the wording of syllabus objective (xi)2 for the UK exams (I think the IAI syllabus is the same): "Calculate upper and lower bounds for the present value of a fixed interest security that is redeemable on a single date within a given range at the option of the borrower" So, it appears to me that this question is beyond the CT1 syllabus, and I'm not completely convinced by the answer given. Here's what I think: We can never be certain of getting a particular yield on an optional redemption date bond, as the yield earned depends on when redemption occurs, which we don’t know. In this question, if we assume the earliest redemption date (15 years), I get a price of 101.34. If we assume the latest redemption date (20 years), we get a price of 101.54. The price increases with duration, as there is a capital loss. You could calculate the price at intermediate durations – this should give steadily increasing values from 101.34 to 101.54. The investor wants a yield of 8%. If they choose to pay 101.54, then if the bond is redeemed after 20 years, they get a return of exactly 8%. If the bond is redeemed earlier, then they get a return of less than 8%, which is a problem. So they cannot pay 101.54 and always get a yield of 8% - if they paid that price, there would be occasions where the yield is less than 8%. If the investor pays 101.34, then if the bond is redeemed after 15 years, they get a return of exactly 8%. If the bond is redeemed later, then they get a return of more than 8%. And that’s fine. So 101.34 is the highest price they can pay to be certain of obtaining a yield of 8% on their investment. If they paid more, then we could find a redemption date on which they have a yield of less than 8%. Based on this, I'd say the answer was 101.34 (ie the answer you'd get based on assuming the worst case for the investor). The counterargument to this is that, as the investor has the option, they would never choose to redeem the bond at a date that was disadvantageous to them. So if they paid 101.54 (based on an 8% yield and redeeming after 20 years), then they would never choose to redeem early and so never receive less than an 8% yield. So, as I said, it's questionable what's right here.
Thankyou so much for explanation.Yes, I can't see this case in the chapter. But it is from a past IAI paper. So, how we should deal with this in exam? What the examiners expect from us to do in this type of qus ? If the option of redemption is of the borrower, we should consider the worst case scenario. But if it is chosen by the investor , then should be calculate price like calculated here? i.e. latest redemption date in case of capital loss and earliest date for capital gain? Please suggest the correct treatment from exam point of view.
As I've said above, I don't think there is a clear correct answer to this question, so it's very difficult to tell you what to do in an exam. All I can really say is that based on this one question, I'd probably try to take the same approach as the published solution if it was asked again.
