I learned that in discount bond,
coupon rate < current yield < YTM
and the relationship will always hold.
I can figure out why
coupon rate <
current yield. But just cannot don't understand why does
current yield <
YTM hold anyway?
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Say you buy a bond that currently costs $950, and matures in one year, at $1000 face value. It has one coupon ($50 interest payment) left.
The coupon, $50, is 50/950 or 5.26%, but you get the face value, $1000, for an additional $50 return. This is why the yield to maturity is higher than current yield.
If the maturity were in two years, the coupons still provide 5.26%, and the extra 1000/950 is another 5.26% over 2 years, or (approx) 2.6%/yr compounded, for a total YTM of 7.86%.
This is a back-of envelope calculation, the real way to calculate is with a finance calculator. Entering PV (present value) FV (future value) PMT (coupon payment(s)) and N (number of periods). With no calculator or spreadsheet, my estimate will be pretty close.