# Effective Duration

The sensitivity of a bond's price against the benchmark yield curve

## What is Effective Duration?

Effective duration is the sensitivity of a bond‘s price against the benchmark yield curve. One way to assess the risk of a bond is to estimate the percentage change in the price of a bond against a benchmark yield curve such as a government par curve.

The effective duration figure is used for hybrid securities, which can be divided into a bond and an option (callable bonds). Embedded bonds increase the uncertainty of cash flows and make it difficult for investors to measure the internal rate of return. This is where the concept of effective duration comes into effect.

### What is Duration?

In 1983, economist Frederick Macaulay discovered a way to determine the price volatility of a bond, which was called the “Macaulay Duration.” Although an effective tool, the strategy was not given much importance until the 1970s when interest rates became relatively unstable. During that time, many investors needed a tool that would help assess the volatility of their fixed-income investments. It led to the development of “modified duration,” which provided a better way to calculate changing bond prices.

Then in the mid-1980s, interest rates fell and investment banks created “effective duration” or “options adjusted duration,” which calculated price movements based on the call features of the bond.

### How to Calculate Effective Duration

When bonds offer an uncertain cash flow, the effective duration is the best way to calculate the volatility of interest rates. The formula is as follows:

Where:

• V–Δy  – The bond’s value if the yield falls by a certain percentage
• V+Δy – The bond’s value if the yield rises by a certain percentage
• V0 – The present value of cash flows (i.e. the bond’s price)
• Δy – The change in the value of the yield

### Example of Effective Duration

An investor buys a bond at par for \$100 with a yield of 8%. The price of the bond increases to \$103 when the yield falls by 0.25%. Alternatively, the price of the bond falls to \$98 when the yield increases by 0.25%. The effective duration of the bond will be calculated as:

In the example above, every 1% change in interest rates results in a change in the price of the bond by 10%.

Effective duration is a useful tool for holders of callable bonds because interest rates change and the bond can be recalled before it matures.

### Effective Duration vs. Curve Duration

Effective duration differs from modified duration because the latter measures the yield duration – the volatility of the interest rates in terms of the bond’s yield to maturity – while effective duration measures the curve duration, which calculates the interest rate volatility using the yield curve as a benchmark.

Using the YTM curve as a benchmark, effective duration considers the possible fluctuations in the expected cash flow of the bond. The cash flows remain uncertain due to the high volatility of the interest rates of the bonds. Since the internal rate of return is not well defined, strategies such as modified duration and Macaulay duration do not work.

### Importance of Duration for Investors

Duration is important to investors for numerous reasons. It is a helpful tool to assess the interest rate risk of a bond and can be used as part of risk assessment along with the credit risk and liquidity of the bond. In addition, it can also help the bondholder maximize profits if their predictions are accurate. If an investor believes that interest rates will fall, they will build their portfolio with a high duration to reflect this.

The effective duration shows how sensitive a bond is to changes in market returns for different bonds with the same risk. By accurately estimating the effect of a market change on bond prices, investors can construct their portfolio to capitalize on the movements of interest rates. Also, it can help them manage their future cash flows and protect their portfolios from risk.