Explanation
For a bond trading at a premium (above par value):
- Current Yield = Annual Coupon Payment / Current Market Price
- Coupon Rate = Annual Coupon Payment / Par Value
When a bond trades at a premium:
- Current Market Price > Par Value
- Since the denominator in the current yield calculation (market price) is larger than the denominator in the coupon rate calculation (par value)
- The current yield will be less than the coupon rate
Example:
- Par value =
$1,000
- Coupon rate = 5% → Annual coupon =
$50
- Market price =
$1,100 (premium)
- Current yield =
$50 / $1,100 = 4.55%
- 4.55% < 5% (coupon rate)
This relationship holds true because the bond's price is higher than its face value, so the same coupon payment represents a smaller percentage return relative to the higher purchase price.
