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|Subject: Re: YTM vs. CAGR||Date: 12/2/2009 3:04 PM|
|Author: andpatt||Number: 29282 of 35498|
The purchase price is $387.50. Par is $1,000. The holding period is the same 15.8172 years. But this time, let’s subtract the purchase price from par and then divide the result by the holding period. That result is $38.72, or the implied annual gain on our purchase price. Now, divide that gain by the purchase price. That result is 0.09992258, which can be rewritten as 9.99%.
remember that the YTM is an anual yeild. the geometric average which you calculated as the CAGR is one soloution.
A algebraic average would be another, however your calculation of algebaic average is not quite right. Assuming the stright line apreciation you presented. the yield in the second year would not be 9.99 but rather 38.72/426.22=9.08% ... add these up and devide by 15.8172 and well the geometric average and geometric average are the same if there is no variance in the rates.
I believe the answer to your question of why the bonds are listed as they are is one of simple mathematics rather than the vagries of bonds and the special relationship bond investors have with inflation.
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