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21 May 2008, 11:06
Kudos
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21 May 2008, 12:39
Kudos
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Well, I'm not a CFA and definitely not a math geek, but I'll give it a shot.
I'm not sure what the assumptions are for your questions. Generally, American style bonds pay out coupons twice per year, but the question says annual coupons so does that mean one payment per year? I'm going with once per year because its simpler.
Anyhow, for Q7, the equivalent rates for the zero coupon bonds are 4% for the 1 year, 6% for the 2 year and 7% for the 3 year. I'm a little unclear on the next step, but I think you should take either an average or a weighted average of the prices of the zero coupon bonds to get the market value of the coupon bond. I'm going to go with the average of $889.28 because I don't really care that much, but I think you might actually want to take a weighted average of the NPVs to get a present value equal to the 5% coupon; and again, payment frequency could be a factor here.
So, if the price (market value) of the 5% coupon bond is $889.28 (because you'd get the same from the zero coupon bonds), the YTM would be 9.41%. The key to this question is finding the current market price of the 5% coupon bond based on the current prices of the zero coupon bonds. Once you have the price, just plug in the values to find YTM.
----
For Q8, the YTM of the 7% coupon bond is 7.5% (it is selling at a discount so the YTM must be greater than the coupon). The YTM on the zero coupon bonds are 5.26% for the 1 year, 5.41% for the 2 year and 6.84% on the three year. Again, you need to match the duration of the 7% coupon bond (3 years) with the zero coupon bonds. You'll probably want to take a weighted average, but I'm just going to take the average which is 5.84%. So if you match the durations and the bonds have the same risk (we can only assume they do because no other info is given), then differences in YTM are an arbitrage opportunity.
So the 7% coupon bond has a YTM of 7.5% and the zero coupon bonds have an average YTM of 5.84%. You should sell zero coupon bonds and take the proceeds and buy the 7% coupon bonds until you get the NPV of $2000 you are looking for.
Note: I just wanted to point out again that I just took the simple average in both problems, but you probably need to take a weighted average to match durations and values.
I'm not sure what the assumptions are for your questions. Generally, American style bonds pay out coupons twice per year, but the question says annual coupons so does that mean one payment per year? I'm going with once per year because its simpler.
Anyhow, for Q7, the equivalent rates for the zero coupon bonds are 4% for the 1 year, 6% for the 2 year and 7% for the 3 year. I'm a little unclear on the next step, but I think you should take either an average or a weighted average of the prices of the zero coupon bonds to get the market value of the coupon bond. I'm going to go with the average of $889.28 because I don't really care that much, but I think you might actually want to take a weighted average of the NPVs to get a present value equal to the 5% coupon; and again, payment frequency could be a factor here.
So, if the price (market value) of the 5% coupon bond is $889.28 (because you'd get the same from the zero coupon bonds), the YTM would be 9.41%. The key to this question is finding the current market price of the 5% coupon bond based on the current prices of the zero coupon bonds. Once you have the price, just plug in the values to find YTM.
----
For Q8, the YTM of the 7% coupon bond is 7.5% (it is selling at a discount so the YTM must be greater than the coupon). The YTM on the zero coupon bonds are 5.26% for the 1 year, 5.41% for the 2 year and 6.84% on the three year. Again, you need to match the duration of the 7% coupon bond (3 years) with the zero coupon bonds. You'll probably want to take a weighted average, but I'm just going to take the average which is 5.84%. So if you match the durations and the bonds have the same risk (we can only assume they do because no other info is given), then differences in YTM are an arbitrage opportunity.
So the 7% coupon bond has a YTM of 7.5% and the zero coupon bonds have an average YTM of 5.84%. You should sell zero coupon bonds and take the proceeds and buy the 7% coupon bonds until you get the NPV of $2000 you are looking for.
Note: I just wanted to point out again that I just took the simple average in both problems, but you probably need to take a weighted average to match durations and values.
21 May 2008, 12:39
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Ryme,
On the first one I believe you need to calculate the no arbitrage price of the 3 year bond using spot rates (unless that's not something your class covers - if its not, let me know). I'm working on the solution now...
edit: pelihu is on the right track for no. 7. The yield for each zero coupon should be the spot rate for that year
On the first one I believe you need to calculate the no arbitrage price of the 3 year bond using spot rates (unless that's not something your class covers - if its not, let me know). I'm working on the solution now...
edit: pelihu is on the right track for no. 7. The yield for each zero coupon should be the spot rate for that year
