Finance

# Effective Duration

Effective Duration (Words <500)

The duration calculation for bonds that have embedded options is known as effective duration. It helps in evaluating the price sensitivity of hybrid security to change the benchmark yield curve. This measure of duration takes into consideration the fact that expected cash flows will fluctuate as interest rate changes and therefore is a measure of risk.

Formula and Calculation:

There are four variables in the effective duration formula:

P (0) – Bond’s original price

P (1) – Bond’s price if yield decreases by Y%

P (2) – Bond’s price if yield increases by Y%

Y – Estimated change in yield

Effective Duration = (P (1) – P (2)) / (2 * P (0) * Y)

Example:

1. An India-based retirement scheme has liabilities of Rs 100 million. The yield is standing at 5% and the yield changes by 10 bps, the liability changes from 98 to 102 million. Calculate effective duration.

P (0) – 100

P (1) – 98

P (2) – 102

Y – 0.001

Effective Duration = (P (1) – P (2)) / (2 * P (0) * Y)

= (98-102) / (2* 100 * 0.001)

= (3)/ 0.2

= 90

Effective Duration = 90 years

1. For example, assume that Adam purchases a bond for 200% par and that the bond is currently yielding 2%. Using a 100 basis-point change in yield (0.01%), it is calculated that with a yield decrease of that amount of the bond is at \$204.02. It is also found that by increasing the yield by 100 basis points the bond’s price is expected to be \$195.98. Given this information, the effective duration would be calculated as:

Effective duration = (\$204.02 – \$195.98) / (2 x \$200 x 0.01) = \$8.04 / \$4 = 2.01 years

Benefits & Limitations:

Benefits:

1. Calculates accurate duration for asset-liability management.
2. It works for hybrid securities.
3. It is calculated on the basis of market yield rather than its own YTM.
4. Helpful in the calculation of the duration of complex items such as mortgage-based securities.

Limitations:

1. The calculation gives an approximate measure of duration.
2. In practical scenarios, it is difficult to measure the variables.
3. The calculations are very complex.

Conclusion:

Effective duration calculates the expected price decline of a bond when there are changes in the interest rates by 1%.

It is a useful tool for analyzing the sensitivity of hybrid instruments to interest rates. Even though the calculation gives approximate results, it is a widely used model for option embedded asset-liability management.

Author: Urvi Surti