# Why YTM is higher than current yield in discount bond

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

• 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
• 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