Hi I have a confusion in Q5 CT1 exam April 2010 . The fundamental concept is that given the same price, increase in coupon rate will cause YTM to increase or decrease. I can't agree on the examiner report that says that case 1 : coupon rate is 7%, Price is 108.1, YTM =4.73% Question ask what will YTM behave if coupon rate is increased to 9%, keeping price same. It will increase right. Calculation shows YTM =6.65% but the report is saying that YTM would decrease "Thus, increasing the coupon rate will increase the weight applied to the cash flows at the early durations and, as the forward rates are lower at early durations, the gross redemption yield on a security with a higher coupon rate will be lower than above." Where am I wrong?
As I interpret it in this part the price would change to reflect the 9% coupons. This is more of a question on the effect of the term structure of interest rates. If you were to do further calculations you would calculate a price for a 9% coupon bond and then you would solve for the IRR. You would find that it's slightly lower. In this case you should find that the report is accurate. Hope this helps
Sorry couldn't get it. How would the IRR be lower? can u give an example to elucidate? For coupon rate of 9% and using the same price as 108.1, YTM is coming out to be 6.629% which is higher than with 7% coupon and price as 108.1 (4.73%).
You wouldn't use the same price though because of no arbitrage, the price for a 7% coupon and a 9% coupon bond can't be the same (under same interest rate structure and term). If the coupon was 9% the price of the bond under that interest rate structure would be different ~115.23. If you look at the attached file I've worked the IRR out in each case. View attachment CT1 bond soln.xlsx
To explain the concept they're questioning: In a flat yield curve environment - i.e. if the forward rates were all 4.5% (or x% in general), then the GRY on both bonds would be 4.5% (assuming they were priced using this constant interest rate). If you use the spreadsheet I attached below then you can see this by setting all of the forward rates to a constant. Both IRR's (GRY's) will equal the constant. You can then play around with the term structure of the interest rates to see the effect it has on two different bonds. Setting the first 3 years forward rates to 0%, 1% and 2% for instance would be an exaggerated case of the term structure in the question. You would see a more pronounced difference in the GRYs. The reason this occurs is due to the time weighting of the payments. More of the total payment in the 9% coupon bond occurs while the interest rate is lower. This is what the ER is saying. If you had a 9% coupon bond that was not redeemed at par but instead at 100*9/7 (i.e. scaled up in the same way as the coupons), the time weighting of the cashflows would be the same and the bond would have the same GRY. Hopefully between this and the calculation you will get it..
