Based on the new idea "recursive method": how to track the duration of the daily frequency tracking mechanism

The duration of bond base is an important indicator to observe the behavior of bond market institutions. The most classic of the traditional duration measurement models is the "regression method". Different regression methods have been derived according to different treatment of model multicollinearity, but it is not easy to build a regression model with both accuracy and stability. In practice, the "regression method" still occasionally deviates from the actual direction when tracking the frequency, and the tracking at the daily level is more unstable.

    In this paper, we will provide a new duration measurement method, namely the "recurrence method". Its idea is direct and simple, and the measurement results can also be stable from a daily perspective, so it can track the direction of duration changes more stably.

    1、 Basic idea and algorithm of "recursive method"

    The basic idea of the "recursive method" is to use the net purchases of bonds with different maturities of the fund to calculate the duration. The Fund adjusts the duration of the portfolio by buying and selling bonds in the secondary market. The net purchase of long-term bonds or the net sale of short-term bonds can lengthen the duration of the portfolio, and vice versa. Since the staged sub indexes of different bond waiting periods provide duration values of different periods, the change in duration can be calculated by using the net buying volume of bonds of different periods of the fund on the current day, and then the duration of the fund on the current day can be obtained by recursion of the duration of the previous day, which is the basic idea of the "recursion method".

    In order to recursively calculate the duration, it is also necessary to synchronously recursively calculate the size of fund bond holdings. The total bond position size can be recursively calculated by the net bond purchases of the fund every day. In order to pursue the refinement of the model, the maturity of bonds in the hands of the fund every day also needs to be taken into account, and the maturity can be estimated by assuming the distribution of the duration of bonds held by the fund.

    The initial value of duration recurrence is derived from the quarterly report of the fund. The quarterly report of the fund will disclose the product duration and bond positions. The end of the quarter can be selected as the initial time point, and the total position size of the fund bonds and the median duration of the bond base can be used as the initial value to obtain the duration series of the fund recursively.

    2、 "Recursive method" model evaluation

    "Recursive method" is more robust at the level of daily frequency tracking duration. The "recurrence method" duration measurement result and the 10-year treasury bond interest rate have a good negative correlation. Since 2019, the correlation coefficient between the two is -0.67, while the correlation coefficient between the "regression method" duration result and the 10Y treasury bond in the same period is -0.19, which reflects that the error of the "recurrence method" result is or less. In addition, at the daily level, the "recurrence method" is more robust, while the "regression method" is more volatile, which can be reflected more intuitively from the comparison of their respective difference absolute value series.

    The "recurrence method" can grasp the change direction of duration, but there will be errors between the absolute value and the real duration.

    The change direction of the fund duration measured by the "recursive method" is consistent with the direction of the fund's buying and selling of long-term and short-term bonds, which ensures that the change direction of the duration results measured by the "recursive method" at local time points is consistent with the true value.

    However, due to the possible deviation between the assumptions of the model and the reality, the duration results may differ from the true values in value.

    The "recurrence method" expands the capability boundary compared with the "regression method", but it also has its limitations. Compared with the "regression method", the "recursive method" can be used to calculate the duration of the goods base and other types of institutions, such as agricultural commercial banks, urban commercial banks, insurance, etc., but it cannot be used to calculate the duration of the debt base sub categories, nor can it be used to calculate the duration divergence.

    Risk tip: there is deviation between the model assumption and the reality, the model parameter setting is not optimal, and the model oversimplifies the real situation