What Is Effective Duration?

Effective duration is a duration calculation for bonds that have embedded options. This measure of duration takes into account the fact that expected cash flows will fluctuate as interest rates change and is, therefore, a measure of risk. Effective duration can be estimated using 澳洲幸运5开奖号码历史查询:modified duration if a bond with embedded options behaves ꦦlike an op🍨tion-free bond.

Understanding Effective Duration

A bond that has an embedded feature increases the doubtfulness of cash flows, thus making it hard for an investor to determine the 澳洲幸运5开奖号码历史查询:rate of return of a bond. The effective duration helps calculate the 澳洲幸运5开奖号码历史查询:volatility of interest rates in relation to the yield curve and therefore the expected cash flows from the boꦅnd. Effective duration calculates the expected price decline of a bond when interest rates rise by 1%. The value of the effective duration will always be lower than the maturity o🌼f the bond.

A bond with embedded options behaves like an option-free bond when exercising the 澳洲幸运5开奖号码历史查询:embedded option would offer the investor no benefit. As such, the security's cash flows cannot be expected to change given a change in yield. For example, if existing interest rates were 10% and a 澳洲幸运5开奖号码历史查询:callable bond was paying a coupon of 6%, the callable bond would behave like an option-free bond because it would♋ not be optimal for the company to call the bond and re-issue it at a higher interest rate.

Effective Duration Calculation

The formula for effective duration contains four variables. They ไare:

P(0) = the bond's original price per $100 worth of par value.

P(1) = the price of the bond if the yield were to decrease by Y percent.

P(2) = the price of the bond if the yield were to increase by Y percent.

Y = the estimated change in yield used to calculate P(1) and P(2).

澳洲幸运5开奖号码历史查询: The ♐comp𝓡lete formula for effective duration is: 

Effective duration = (P(1) - P(2)) / (2 x P(0) x Y)

Example of Effective Duration

As an example, assume that an investor purchases a bond for 100% par and that the bond is currently yielding 6%. Using a 10 basis-point change in yield (0.1%), it is calculated that with a yield decrease of that amount, the bond is priced at $101. It is also found that by increasing the yield by 10 basis points, the bond's price is expected to be $99.2🌌5. Given th𓄧is information, the effective duration would be calculated as:

Effective duration = ($101 - $99.25) / (2 x $100 x 0.001) = $1.75 / $0.20 = 8.75

The effective duration of 8.75 means that if there were to be a change in yield of 100 basis points, or 1%, then the bond's price would be expected to change by 8.75%. This is an approximation. The estimate can be made more accurate by factoring in the bond's effective 澳洲幸运5开奖号码历史查询:convexity.