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?

  • the YTM includes the fact that the bond's principal is paid back on maturity, the other two don't. Commented Sep 26, 2014 at 9:18
  • principal is discounted by YTM and coupon is not discounted in current yield. How could we know the yield after discount is large than current yield? Commented Sep 26, 2014 at 12:59

1 Answer 1


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.

  • In this case YTM is (50/950 + 1000/950) -1 so it's easy to understand YTM is larger than current yield. But what if it matures in two years? I cannot generalized to two years because the computation is more complicated and I cannot make sure YTM is larger than current yield. Commented Sep 26, 2014 at 13:10
  • I updated/edited to address multiple years. Commented Sep 26, 2014 at 13:38
  • It seems that the key point is that no matter how long the maturity is, the discounted principal still will contribute to a positive yield. This pluses the contribution of current yield will hold current yield < YTM always true. Commented Sep 26, 2014 at 14:18

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