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8.7 Bond’s Effective Duration in Practice

8.7.1 Effective duration of a callable, putable, and Straight Bonds

  • The duration of a bond measures the sensitivity of the bond's full price to changes in the bond's yield to maturity or to changes in benchmark interest rates.
  • For bonds with embedded options, the only appropriate duration measure is the curve duration measure known as effective (or option-adjusted) duration.
  • Effective duration indicates the sensitivity of the bond's price to a 100 bps parallel shift of the benchmark yield curve assuming no change in the bond's credit spread.

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Notes:

  • DeltaCurve = the magnitude of the parallel shift in the benchmark yield curve (in decimal);

PV-= the full price of the bond when the benchmark yield curve is shifted down by DeltaCurve; PV+= the full price of the bond when the benchmark yield curve is shifted up by DeltaCurve; and PV0 = the current full price of the bond (i.e., with no shift).

In practice, the estimation procedure is usually as follows:

i. Given a price (PV0), calculate the implied OAS to the benchmark yield curve at an appropriate interest rate volatility ii. Shift the benchmark yield curve down, generate a new interest rate tree, and then revalue the bond using the OAS calculated in Step 1. This value is PV-.

iii. Shift the benchmark yield curve up by the same magnitude, generate a new interest rate tree, and then revalue the bond using the OAS calculated in Step 1. This value is PV+.

iv. Calculate the bond's effective duration.

Notes:

  • Without a market price, we would need an issuer-specific yield curve to compute PV0, PV- and PV+. The effective duration of a callable bond cannot exceed that of the straight bond.
  • When interest rates are high relative to the bond's coupon, the callable and straight bonds have similar effective durations.
  • When interest rates fall, the effective duration of the callable bond is lower than that of the straight bond. The effective duration of a putable bond cannot exceed that of the straight bond.
  • When interest rates are low relative to the bond's coupon, the putable and straight bonds have similar effective durations.
  • When interest rates rise, the effective duration of the putable bond is lower than that of the straight bond Notes:
  • When interest rates are high relative to the bond's coupon, the call option is out of the money, so the bond is unlikely to be called.
  • Recall that the call option gives the issuer the right to retire the bond at the call price and thus limits the price appreciation when interest rates decline. As a consequence, the call option reduces the effective duration of the callable bond relative to that of the straight bond.
  • When interest rates are low relative to the bond's coupon, the put option is out of the money, so the bond is unlikely to be put.
  • When interest rates rise, the put option moves into the money and limits the price depreciation because the investor can put the bond and reinvest the proceeds of the retired bond at a higher yield. Thus, the put option reduces the effective duration of the putable bond relative to that of the straight bond.

8.7.2 Use of One-Sided Durations and Key Rate Durations to Evaluate the Interest Rate

Sensitivity of Bonds with Embedded Options One-sided duration is an effective duration when interest rates go up or down. It is better at capturing the interest rate sensitivity of a callable or putable bond than the (two-sided) effective duration, particularly when the embedded option is near the money.

Key rate duration reflects the sensitivity of the bond's price to changes in specific maturities on the benchmark yield curve.Key rate durations help portfolio managers and risk managers identify the "shaping risk" for bonds – that is, the bond's sensitivity to changes in the shape of the yield curve (e.g., steepening and flattening).

Notes:

  • Effective durations are normally calculated by averaging the changes resulting from shifting the benchmark yield curve up and down by the same amount. The problem is that when the embedded option is in the money, the price of the bond has limited upside potential if the bond is callable or limited downside potential if the bond is putable. Thus, the price sensitivity of bonds with embedded options is not symmetrical to positive and negative changes in interest rates of the same magnitude.
  • The valuation procedure and formula applied in the calculation of key rate durations are identical to those used in the calculation of effective duration, but instead of shifting the entire benchmark yield curve, only key points are shifted, one at a time.

Lesson Wrap-Up

This lesson should leave you able to explain the bond's effective duration in practice in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain effective duration of a callable, putable, and straight bonds in your own words.
  2. Explain use of one-sided durations and key rate durations to evaluate the interest rate in your own words.
  3. State one exam-style risk, valuation, or market implication of the bond's effective duration in practice.