Definition of duration
Duration is defined in the relevant literature as the "average commitment period of the acquisition payout" or also the "average self-liquidation period". A bond investment and the associated cash flow begins with the subscription or purchase of the bond and the payment of the purchase price (with accrued interest, if applicable) to the seller.
This is followed by cash inflows in the form of interest payments and finally the redemption of the bond. The duration measures how long it takes for these cash inflows to amortise the initial payout. For a zero coupon bond, the duration is therefore equal to the remaining maturity of the bond. In the case of coupon bonds, the higher the interest payments are in relation to the stake and the earlier they occur, the more the duration deviates in the direction of the acquisition date. In the simple duration variant, the interim payments are discounted at a uniform interest rate.
Investors should adjust the average duration of a bond portfolio to their individual time horizon. If the duration exceeds the investment horizon, there is the risk of price losses due to interim changes in the interest rate level. Interest rate risk, on the other hand, does not affect investors if the portfolio is held to maturity.
Variations of duration
The "effective duration" provides for a modified discounting of the interim inflows of funds compared to the conventional variant. These are not discounted with a uniform interest rate, but with the spot market interest rate applicable for the term until payment. Compared to simple duration, differences arise as soon as the interest rate curve is not completely flat.
Modified duration" is used in many search and sorting tools for the bond market. Modified duration indicates how the price of a bond changes when the general interest rate level changes by one basis point. It is therefore a sensitivity ratio. The ratio is only sufficiently informative for small interest rate changes.
The "key rate duration" does not examine the influence of interest rate changes on the bond price with regard to a complete shift of the entire yield curve around a constant interest rate. Instead, it assumes the shift of parts of the curve and examines the resulting impact on the price. The key rate duration therefore provides information on how the bond price develops if, for example, interest rates only change at the long end and the interest rate level at the short end remains constant.
Convexity
Duration has a very significant construction error: The larger the interest rate change under investigation in https://online-exness.com/login/ area, the less accurate its statement becomes. This is because its calculation assumes a linear, uniform relationship between the price and the yield of a bond. In fact, however, the relationship is not linear but convex (which corresponds to a curved curve in the graphical representation), which is hardly significant for very small interest rate changes. For interest rate changes of 1.00 per cent, deviations of 0.30 per cent of the nominal value are realistic.
If the effect of larger interest rate changes on the bond price is to be examined, convexity is used, which is also implemented in many search tools on the internet and can be applied to individual bonds or a bond portfolio just like duration. From a mathematical point of view, convexity takes into account not only the first but also the second derivative of the function that indicates the relationship between price and interest rate: The slope of the slope.
