Quantitative Methods For a 6-month security that pays a coupon and face value at maturity, which of the following yield metrics would be the highest? Assume yield is positive. A. Bond-equivalent yield B. Holding period yield C. Effective annualized yield

Great explanation, @vincentt! Another way to answer this question is to assign a coupon and face value to the security and compute all 3 yield metrics. Let's say the security costs 100 and pays 110 (100 face and 10 coupon) in 6 months. The holding period yield would be: HPY = (P1 - P0 + D1) / P0 = (100 - 100 + 10) / 100 = 10% The bond-equivalent yield though is simply twice the semi-annual holding period yield, or 20%. The effective annual interest rate for this security would be the annualized holding period yield: r = (1 + 0.1)^2 - 1 = 21%

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This topic has 5 replies, 3 voices, and was last updated Sep-177:55 pm by AdaptPrep.

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- AdaptPrep
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  22 Sep 2017 at 8:04 am
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  Quantitative Methods
  
  For a 6-month security that pays a coupon and face value at maturity, which of the following yield metrics would be the highest? Assume yield is positive.
  
  A. Bond-equivalent yield
  B. Holding period yield
  C. Effective annualized yield
- fabian
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  23 Sep 2017 at 9:53 am
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- vincentt
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  23 Sep 2017 at 9:54 am
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  Lowest: Holding period yield => it’s not annualised (otherwise would be the same as C).
  Mid: Bond-equivalent yield => multiply by 2.
  Highest: Effective annualised yield => power of 2.
- fabian
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  23 Sep 2017 at 9:55 am
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  Awesome explanation @vincentt, thanks! I wasn’t sure myself.
- vincentt
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  23 Sep 2017 at 9:58 am
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  no prob at all @fabian‌ wasn’t sure if I’m supposed to explain the answer.
- AdaptPrep
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  24 Sep 2017 at 7:55 pm
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  Great explanation, @vincentt‌!
  
  Another way to answer this question is to assign a coupon and face value to the security and compute all 3 yield metrics.
  
  Let’s say the security costs 100 and pays 110 (100 face and 10 coupon) in 6 months.
  
  The holding period yield would be:
  HPY = (P1 – P0 + D1) / P0 = (100 – 100 + 10) / 100 = 10%
  
  The bond-equivalent yield though is simply twice the semi-annual holding period yield, or 20%.
  
  The effective annual interest rate for this security would be the annualized holding period yield:
  r = (1 + 0.1)^2 – 1 = 21%
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