7.5 Yield Relationships: YTM and CY
So far, we have discussed the relationship between YTC and YTM. Here, we will add the Current Yield (CY), expressed in dollars, which is defined as:
CY = Coupon ÷ Price
The Current Yield ignores any discount or premium that may add to or detract from the bond’s overall return. CY is, in a way, analogous to a stock’s Dividend Yield (Dividend ÷ Price), which ignores any changes in price – even though price changes will affect the investor’s overall return. We shall assume no call penalties in the following explanatory examples. See the other comments below the table.
| Par Bond | Discount Bond | Premium Bond | |
| Coupon | 10% | 8% | 12% |
| YTM | 10% | 10% | 10% |
| Price | Par | 98% | 102% |
| CY | $10 ÷ $100 = 10% | $8 ÷ $95 = 8.42% | $12 ÷ $102 = 11.8% |
| Therefore | YTM = CY | YTM > CY | YTM < CY |
| Summary | YTC = YTM = CY | YTC > YTM > CY | YTC < YTM < CY |
The Current Yield does not take a bond’s price discount or premium into consideration.
- We have assumed no call penalty in the case of the Premium Bond.
- Since we have not specified a maturity, we can arbitrarily call the prices of the discount and premium bonds 95% and 102% respectively. In any case, the relationships are as depicted.
- As we already know, the relationships are reversed in comparing discount and premium bonds.
- In the “summary” line above, note that we had already established the relationships between YTC and YTM earlier.
- What does this assume about the relationship between the size of the call penalty (were there one, in the case of the bond premium), and the YTC-YTM-CY relationships? Indeed, the size of the call penalty is relevant.
