Effective duration

Hybrid securities are types of securities which can be split up into a plain bond and an option. The embedded option in a hybrid however both drives up cash flow uncertainty and changes the cash flows in function of the interest rate. As a result, the duration can no longer correctly measure the interest rate sensitivity of a hybrid.The overcome this problem, the concept of effective duration is introduced.

Hybrids and uncertainty

The origin of additional cash flow uncertainty lies in the embedded option. In the case of callable bonds, the issuer could have the possibility to refinance at a cheaper rate thus calling back the outstanding bonds due to general economic circumstances impacting the market interest rate or company specific improvement such as credit rating improvements. Of course in the case of the putable bond the reverse is true. A deterioration in the company’s creditworthiness or interest rates increases could lead to investors exercising their embedded put option, thus invoking early reimbursement of the bond.


The effective duration measures the percentage change in the hybrid in function of a change in the benchmark rate, Δr, e.g. the return of a sovereign bond in which the headquarter is located. Additional information requirements are the bond’s current value (dirty price) P0, the value of the bond when interest rate increases, P and the value of the bond when interest rates fall, P+.

 EDUR = \dfrac{P_- - P_+}{2 \cdot \Delta r \cdot P_0}


Hybrid securities behave somewhat differently with respect to interest rate changes due to the embedded option. The interest rate sensitivity for hybrids can be assessed by using effective duration.