**Factors that Affect Duration**

**Zero Coupon Bond**: For a zero coupon bond, duration is the same as its maturity period. For a zero coupon bond, the fulcrum on the seesaw would be placed right under the bond’s future value money bag at the maturity period (right most end of the plank), balancing its load right under. This is because the complete cash flow for a zero coupon bond comes through at the time of maturity.**Vanilla Bond**: For a vanilla bond, the duration of bond is less than the maturity time. If we now again visualize the seesaw, then in the case of vanilla bond, the money bags would be placed all over the plank. Smaller moneybags representing smaller repayments / cash flows before the maturity time (right most end of plank) and a bigger money bag placed at the right most end indicating the last big payment at the end of bond maturity.- The fulcrum in this case will be positioned somewhere between the initial and final point of time (beginning and end of bond period). The fulcrum balances the plank at the point in time when the total cash flow till that time equals the bond price.

**Macaulay Duration**- This is the most common way of calculating a bond’s duration and it became popular starting 1970s. This duration derives its name from its creator – Frederick Macaulay. This duration is calculated as the sum of multiplications of cash flow present values and corresponding time in which they are paid, divided by the bond’s total price.

**Modified Duration**- This is a modified version of Macaulay duration and takes into account the interest rate changes. Changes in interest rates affect duration as the yield gets affected each time the interest rate varies. In regular bonds, the interest rates and bond price move in opposite directions. An approximate unit percent change in yield shares an inverse relationship with modified duration. This type of duration is very well suited for the purpose of gauging a particular bond’s volatility.

**Effective Duration**- In above formula, cash flows are considered to be constant. However, in case of bonds with redemption features and embedded bond options, cash flows also change as the rate of interest changes. For such bonds, the duration calculation has to take into account this variability. Effective duration does just that. It uses binomial trees to estimate the option adjusted spread. These calculations can get a bit complex.

**Key-Rate Duration**- Key rate duration calculates the eleven ‘key’ maturities’ spot durations. These maturities are positioned at 3 months, 1 year, 2 years, 3 years, 5 years, 7 years, 10 years, 15 years, 20 years, 25 years and 30 years on the spot rate curve. The key rate duration allows portfolio duration to be calculated for a change equivalent to 1 basis point in rate of interest, while keeping the yield for maturities other than those on the 11 points constant. This duration is most commonly used for portfolios, which comprise of securities with differing maturity periods. It should be noted that addition of the various key rate durations along the spot rate curve is the same as calculating effective duration.

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