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Difficulty: Very hardDebt Securities and Bond Structure

An investor holds a 10-year callable corporate bond paying a 6.0%6.0\% annual coupon (6060 annually). Following a sustained decrease in market interest rates, the bond's price appreciates to $1,200\$1,200, establishing a current yield of 5.0%5.0\%. The bond carries a call feature enabling the issuer to redeem the bond in 4 years at par value ($1,000\$1,000). At this premium market valuation, which of the following correctly states the relationship among the bond's four yield measures (Yield to Call, Yield to Maturity, Current Yield, and Nominal Yield)?

  1. Yield to Call is less than Yield to Maturity, which is less than Current Yield, which is less than Nominal Yield.Answer
  2. B
    Yield to Call is greater than Yield to Maturity, which is greater than Current Yield, which is greater than Nominal Yield.
  3. C
    Current Yield is less than Yield to Call, while Yield to Maturity is equal to Nominal Yield.
  4. D
    Yield to Maturity is greater than Current Yield, while Yield to Call is equal to Nominal Yield.

Answer

Yield to Call is less than Yield to Maturity, which is less than Current Yield, which is less than Nominal Yield.
For a bond trading at a premium (market price above par), the investor receives an annual coupon higher than prevailing market rates, but will suffer a capital loss when the bond is paid off at par value ($1,000\$1,000). Because this capital loss is amortized over the shortest duration if called early (4 years), Yield to Call (YTC) yields the lowest annual return. The full yield hierarchy for premium bonds from lowest to highest is Yield to Call < Yield to Maturity < Current Yield < Nominal Yield.

Step-by-Step Solution

1
Determine bond pricing status relative to par value.
Market price ($1,200\$1,200) is greater than Par Value ($1,000\$1,000), so the bond is trading at a premium.
Bond yield relationships (yield hierarchy) depend directly on whether the bond trades at a discount, par, or premium.
2
Evaluate Nominal Yield and Current Yield.
Nominal Yield = 6.0%6.0\%; Current Yield = $60$1,200=5.0%\frac{\$60}{\$1,200} = 5.0\%. Thus, Current Yield < Nominal Yield.
The current yield measures annual coupon payout divided by current price, which drops below the stated coupon rate when price exceeds par.
3
Evaluate Yield to Maturity (YTM) and Yield to Call (YTC) for a premium bond.
YTC < YTM < Current Yield < Nominal Yield.
When a bond is bought at a premium, the investor experiences an overall capital loss when the bond matures at par ($1,000\$1,000). If called early (in 4 years instead of 10 years), that $200\$200 capital loss is recognized over a shorter timeframe, reducing annualized yield even further.

Key Concept

Bond Yield Hierarchy for Premium Bonds
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Topics

Debt Securities and Bond Structure

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