## What is Effective Duration?

Effective Duration measures the duration of security with options embedded and helps in the evaluation of price sensitivity of hybrid securityHybrid SecurityHybrid securities are the combined characteristics of two or more types of securities, usually both debt and equity components. These securities allow companies and banks to borrow money from investors and facilitate a different mechanism from the bonds or stock offering.read more (bond and an option) to a change in the benchmark yield curve.

Effective duration approximates modified durationModified DurationModified Duration tells the investor how much the price of the bond will change given the change in its yield. To calculate it, the investor needs to calculate Macauley duration which is based on the timing of the cash flow.read more. But there is a difference in the denominator for calculation of both. The modified duration can be called a yield duration, while effective duration is a curve duration. This is so because the former is calculated using its own YTM, and the latter takes the market curve as a basis for calculation.

### Effective Duration Formula

The formula is given below:

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For eg:

Source: Effective Duration (wallstreetmojo.com)

Where,

- PV
_{– }= Present value of expected cash flows if the yield falls by r basis points. - PV
_{+ }= Present value of expected cash flows if the yield increases by r basis pointsBasis PointsBasis points or BPS is the smallest unit of bonds, notes and other financial instruments. BPS determines the slightest change in interest rate, to be precise. One basis point equals 1/100th part of 1%.read more. - PV
_{0 }= Present value of expected cash flows when no change in yield. - Δr = Change in yield.

### Examples of Effective Duration

#### Example #1

**A US-based pension scheme under the Defined Benefit Obligation (DBO) structure has liabilities to the tune of USD 50 million. The benchmark yield is standing at 1%. if the benchmark yield changes by 5 bps, then the liability amount changes from 48 million to 51 million USD. Calculate the effective duration of pension liabilities.**

**Solution:**

Given,

- PV
_{– }= USD 51 million - PV
_{+ }= USD 48 million - PV
_{0 }= USD 50 million - Δr = 5 bps = 0.0005

Calculation of Effective Duration will be –

Effective Duration Formula = (51 – 48) / (2 * 50 * 0.0005) = 60 Years

#### Example #2

**Suppose a bond, which is valued at $100 now, will be priced at 102 when the index curve is lowered by 50 bps and at 97 when the index curve goes up by 50 bps. The current measure of the index curve is 5%. Calculate the effective duration of the bond.**

**Solution:**

Given,

- PV
_{– }= $102 - PV
_{+ }= $97 - PV
_{0 }= $100 - Δr = 50 bps = 0.005

Calculation of Effective Duration will be –

Effective Duration formula = (102 – 97) / (2 * 100 * 0.005) = 5 Years

### Advantages

- Calculate accurate duration for asset-liability management.
- Works for hybrid securities.
- Based upon market yield instead of its own YTM.
- Helps in the calculation of the duration of complex items such as mortgage-backed securities.

### Disadvantages

- Complex calculation.
- Difficult to measure the variables in a practical scenario.
- An approximate measure of durationDurationDuration is a risk measure used by market participants to measure the interest rate sensitivity of a debt instrument, e.g. a Bond. It tells how sensitive is a bond with respect to the change in interest rates. This measure can be used for comparing the sensitivities of bonds with different maturities. There are three different ways to arrive duration measures, viz. Macaulay Duration, Modified Duration, and Effective Duration.read more.

### Limitations

The biggest limitation of effective duration measure is its approximation.

Take an example of an option embedded bond. The pricing of the bondPricing Of The BondThe bond pricing formula calculates the present value of the probable future cash flows, which include coupon payments and the par value, which is the redemption amount at maturity. The yield to maturity (YTM) refers to the rate of interest used to discount future cash flows.read more must be impacted by a number of factors:

- The period of availability of the call option.
- The call dates.
- The call price.
- Future interest rate direction and measure.
- Change in credit spreadCredit SpreadCredit Spread is the yield gap between similar bonds but with different credit quality. If a 5-year Treasury bond yields 5% and a 5-year Corporate Bond yields 6.5 percent, the gap over Treasury is 150 basis points (1.5 percent ).read more.
- The rate of the proxy instrument(s) for e.g., the index curve.

But while calculating duration, only a change in the last factor that is the increase or decrease in benchmark rate is considered. All other factors are assumed to be constant for the sake of calculation.

Further, the increase or decrease in rate is assumed to be constant in both the directions and a price is determined, whereas the change in interest rate might be varying and would impact the price differently.

Furthermore, if the interest rates are constant and the credit rating of the issuer gets upgraded, then the issuer would be able to get credit at a cheaper rate, and it would trigger a call execution and redemption. But such things are not taken into consideration at the time of calculation.

### Conclusion

Effective Duration is helpful in analyzing the sensitivity of hybrid instruments to the interest rate. Though the measure is an approximation, it is a widely used model for option embedded asset-liability management.

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