1) I was trying out some examples of horizon yield. But this solution seems wrong to me. How can the value of the reinvestments on coupons for 4 years be $38.3356? It should involve one less $8 payment from the 5th year (full maturity) and hence should be 51.004 - 8 = $43.004. In fact, the 2nd timeline adds up to give the exact same value.
But proceeding forward to calculate the realized rate of return, the value is not coming out to be the original 12.18% with $41.004, but rather with $38.3356. How are these things happening?
2) What exactly is the difference between the realized rate of return and yield to maturity? Is it just a calculation coincidence that their values are the same here (12.18%), or are both terms the same thing?
Thanks in advance!
- 38.3356*1.1218 + 8 =43.004 + 8 = 51.004
You have to account for the magic of compounding. If I put the coupons in an account earning 12.18%, the balance in the account at the end of year 4 is 38.33576. Roll that up with another year of interest gets the balance up to 43.004 and then I deposit the last coupon for a grand total of 51.004.
- YTM gets the present value of the coupons and the face amount to equal the price at time 0. More often than not, the reinvestment rate for the coupons will not equal the YTM. For example, if I leave the coupons under my mattress at 0%, my realized return is sure not going to be 12.18%, but something lower (10.495% according to my BAII).
Really sorry for the late reply, wasn’t keeping well. Thank you for the explanation! It is clear now.
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