It can be seen that under the same conditions, bonds with small correction duration are more resistant to the risk of interest rate rise than bonds with large correction duration; But correspondingly, when the interest rate drops to the same extent, the ability to obtain income is weak.
It is the above characteristics of duration that provide reference for our bond investment. When we judge that the current interest rate level is likely to rise, we can focus on investing in short-term varieties and shorten the bond duration; When we judge that the current interest rate level is likely to decline, we should lengthen the duration of bonds and increase the investment in long-term bonds, which can help us get a higher premium in the rise of the bond market.
It should be noted that the concept of duration is widely used not only in bonds, but also in bond portfolios. A long-term bond and a short-term bond can be combined into a medium-term bond portfolio, and increasing the investment ratio of a certain type of bond can tilt the duration of the portfolio to the duration of this type of bond. Therefore, investors can accurately judge the future interest rate trend when operating large funds, and then determine the duration of the bond portfolio. After the duration is determined, they can flexibly adjust the weight of various bonds, which will basically achieve the expected results.
Duration is a method to measure the average duration of bond cash flow. Because the sensitivity of bond price will increase with the increase of maturity time, duration can also be used to measure the sensitivity of bond to interest rate changes, and duration can be calculated according to the weighted average of each coupon interest or principal payment time of bond.
The duration is calculated just like the weighted average. The variable is time, the weight is the cash flow of each period, and the price is equivalent to the sum of the weights (because the price is calculated by discounted cash flow method). In this way, the calculation formula of duration is a weighted average formula, so it can be regarded as the average time to recover costs.
Determining the duration, that is, affecting the sensitivity of bond prices to changes in market interest rates, includes three elements: maturity, coupon rate and yield to maturity.
：
Different bond prices have different sensitivities to changes in market interest rates. Bond duration is the most important and main criterion to measure this sensitivity. Duration is equal to the price change caused by the change of interest rate by one unit. If the market interest rate changes 1% and the bond price changes by 3%, the duration is 3.
The calculation method is as follows:
If the market interest rate is y, the cash flow (X 1, X2, ..., Xn):
d(y)=[ 1*x 1/( 1+y)^ 1+2*x2/( 1+y)^2+...+n*xn/( 1+y)^n]/[x0+x 1/( 1+y)^ 1+x2/( 1+y)^2+...+Xn/( 1+Y)^n]
Namely: d = (1* pvx1+... n * pvxn)/pvx.
Among them, PVXi represents the present value of the first cash flow, and D represents the duration.
For example, suppose there is a bond whose cash flow in the next n years is (X 1, X2...Xn), where Xi represents the cash flow in the first stage. Assuming that the interest rate is Y0, the interest rate rises to Y immediately after investors hold cash flow. Q: How long should they hold it so that its maturity value is not lower than the value with the interest rate of Y0?
The above questions can be quickly answered by the following theorem.
Theorem: PV (Y0) * (1+Y0) QQ is the required time and duration.
The proof of the above theorem can be obtained by taking the reciprocal of the y derivative and making it take the local minimum at Y=Y0.