convexity question

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financegal

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Non callablle Floating Rate Note(FRN): Maturity=9 years, coupon=LIBOR, convexity=0.48
Non callablle Inverse Floater (IF): Maturity=9 years, coupon=12%- LIBOR, convexity=111.20

PVBP of FRN is 0.4878


Brown is interested in these two bonds.. Assuming that interest rates increase substantially (over 100 basis points) Brown wonders which bond will have the greater price change. Which of the following most accurately describes the relationship between rising interest rates and price for these two bonds?

A) Both the FRN and the IF decrease in value but the FRN decreases in value more than the IF.

B) Both the FRN and the IF decrease in value but the IF decreases in value more than the FRN.

C) The FRN increases in value because the coupon increases as interest rates increase.

D) The IF increases in value since it is inversely related to interest rates.
 
I would have said B as well, because IF have higher convexity than FRN. (but that just seems too easy, so I don't think its right)
 
I ignored convexity, though that might very well be the easiest way to answer the question. Regardless here was the logic behind my picking B.

For the FRN:
Since the coupon of floating rate bonds vary in step with the interest rate, their price will remain pretty stable. Prices won't be completely flat though, due to accrued interest between reset dates (I'm assuming). Anyway, you don't need to know that to answer the question since it tells you the PVBP of FRN is 0.4878, implying the price does change slightly with interest rate movements.

For the IF:
Coupon payments are 12%-LIBOR, meaning the greater the LIBOR, the lower the coupon. If interest rates (LIBOR) increase, then not only will you be receiving lower coupon payments but the bond's cash flow will be discounted at an even higher rate. Both of which hurt bond price, hence the IF's price should decline more in a rising rate environment.

By the way, for a lot of the bond questions, you can create hypothetical numbers and plug them into your calculator to see the impact of changing coupons, interest, maturities, etc. I do that a lot when I'm unsure about my answer.
 
So it's the degree of convexity...that's weird, cuz I would've almost said A). cuz the convexity of that line is a lot closer to zero so the line is wayyy closer to being a straight line. That would mean price would be decreasing at a much faster rate than the IF.

I could be off on the wrong tangent here; anybody with the explanation?

*EDIT - just saw Dermot's explanation. Thanks!



Edited 1 time(s). Last edit at Thursday, May 4, 2006 at 01:46PM by zimzim78.
 
I would say B also, b/c the curve of the actual results is much more convex for IF than for the FRN. Therefore, the change in price given the change in IR will will be larger for FRN b.c. it's slope is flatter and less convex.
 
AJF - on the answer part, or I don't think I'm right at all part????

:)
 
:) the former

I wrote my answer without looking at yours, I maybe wrong as well. With these questions, I just practice the KISS method.

We need the almighty financegal to weigh in!
 
KISS method?

well atleast we know our answer is right, even though the reasoning maybe be wrong.
 
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