Building A Credit Bond Index Fund Using A Stratified Sampling Approach
— with ChinaBond Commercial Paper AAA Index

Abstract: The research explores using a stratified sampling approach to build a credit bond index fund with ChinaBond Commercial Paper AAA Index as the replication target. A wide range of stratification dimensions were considered. The approach was optimized to successfully achieve effective replication of the index. More research could follow: firstly, how to reduce duration jumps from rebalancing at the beginning of month; secondly, how to raise the minimum transaction volume while not impeding the replication performance; thirdly, how to effectively apply the approach for different portfolio sizes.

Keywords: Stratified sampling, tracking errors, performance deviation and credit spreads.

I. Methodology for Stratified Sampling Approach and Selection of Dimensions

The objective of our research is to replicate a credit bond index, ie. to minimize tracking errors and performance deviation, while trying to gain excess return.

The stratified sampling approach for an interest rate bond index is relatively simple because there is only one risk factor: the interest rate. Generally, index constituents can be divided into several buckets by maturity. The weighted average duration of each bucket is calculated separately and the constituent bonds within each bucket are further divided into two groups: one above and one below the bucket’s weighted average duration. From each group we can then select liquid bonds to represent the group and assign group weightings to those bonds to create the replicating portfolio. Credit bond indices are more complex as more factors need to be considered. We classify the factors to be considered for credit spreads into macro economy, sector and entity dimensions. The specific analysis factors and indicators are shown in the following table:

Table 1: Analysis Indicators of Credit Spreads

Through consideration of the above factors, we preliminarily choose dimensions of Sector, Rating and Duration for stratified sampling of credit bond indices, using ChinaBond Commercial Paper AAA Index as an example, as shown in the following figure.

Figure 1: Dimensions in Stratified Sampling of Credit Bond Indices (Preliminary)

Whether a layer of stratification is needed depends on whether there is significant credit spread differentiation. From the above dimensions, for general stratified sampling the first tier can consist of Sector, Rating and Duration.

Sector can be subdivided into the second tier, which consists of Finance, Real Estate, Urban Construction and Others, and can be further subdivided into the third tier under special circumstances (for example, if the portfolio size is relatively large). Generally, no more granular division is needed in Sector, but it can be so if necessary. Finance can be broken down into banking and non-banking. If necessary, banking can be subdivided into state-owned, joint-stock, and urban and rural commercial banks; and non-banking can be subdivided into insurance, securities, trust, etc. Since the maturity of the commercial papers is less than 1 year, the differences between state-owned, joint-stock, and urban and rural commercial banks are not significant. Real Estate can be subdivided into state-owned enterprises and private enterprises, and the spreads of the two types of enterprises are significantly different. Urban Construction can be subdivided by region, but subdivision by province may lead to too many divisions. We can group provinces by credit spreads (median) into 6 ranges, such as below 30bp, 30bp-60bp, 60bp-100bp, 100bp-150bp, etc. Those not belonging to the three categories (Finance, Real Estate, and Urban Construction) are classified as Others.

Ratings are mainly made up of three categories: implied ratings (primarily ChinaBond Market Implied Rating), external ratings and internal ratings. Since markets are more objective in judging and more effective in reflecting issuer credit risks, implied ratings generally play a key role. External ratings are mainly issuer credit ratings from rating agencies and, in general, commercial papers only have issuer ratings but not issue ratings due to short durations. Internal ratings are conducted by fund managers and chiefly comprise issuer ratings (including 15 grades, from C to AAA), credit outlook of issuer ratings (including four grades: positive, stable, negative and watchlist) and issue ratings. Most fund managers rely on internal ratings to evaluate an issuer’s default risk while also using implied ratings as references. The perceptions of fund managers and researchers, who personally participate in research or corporate interviews, also give additional input for decisions as to whether to invest in the bonds.

Maturity, as proxy for duration, can be initially subdivided into four ranges: 0 to 3 months, 3 to 6 months, 6 to 9 months, and 9 to 12 months. If the number of index constituent bonds is limited, a simple subdivision into two maturity ranges (less than 6 months and more than 6 months) can also be considered. The reason being that, the average difference between the yields of the 3-month, 6-month, 9-month and one-year commercial papers is only about 10bp, and if bonds are already classified by sector, the yield difference between buckets will be even lower, so such granularity is not necessary.

The key to a stratified sampling approach is to facilitate portfolio operations and improve portfolio liquidity, so essentially it is about selecting bonds with strong liquidity. There is no point in sampling the bonds that cannot be traded in the market.

II. Optimization on Stratified Sampling Approach

There are several customary considerations when designing a credit bond index fund and deciding which index to track. First, the index name should be easy to understand, allowing customers to visually know about the investment targets. Second, there must exist real customer demand. Demand comes from three channels: internet channel (who value stable returns and small drawdown but do not necessarily have credit risk expertise), bank retail channel (wealth management alternative choice, meeting demand overflow from bank wealth management) and institutional channel (who have certain expertise and place importance on credit risk). Third, investability is essential, meaning it is not difficult to replicate the index and the index portfolio itself has high stable returns and low credit risks.

This report attempts to construct a credit bond portfolio which tracks ChinaBond Commercial Paper AAA Index through a stratified sampling approach. The index is compiled by ChinaBond Pricing Center Co., Ltd. and belongs to ChinaBond Aggregate Indices family. The constituent bonds of the index include short-term commercial papers and super short-term commercial papers that are publicly issued and circulated in China, with issuer rating of AAA and ChinaBond Market Implied Rating of not lower than AA. In addition to its aggregate value, the index also contains sub-indices of the following six maturity ranges: 0-3 months, 3-6 months (including 3 months), 0-6 months, 6-9 months (including 6 months), 9-12 months (including 9 months) and 6-12 months (including 6 months).

To replicate ChinaBond Commercial Paper AAA Index with stratified sampling, we need to select appropriate dimensions. The primary logical order is rating, maturity and sector. If the portfolio size is small and cannot be further subdivided, the buckets can be defined only with rating and maturity. If the size is as large as over ten billion yuan and so there is sufficient capacity for more layers, the subdivisions can be carried out based on all three dimensions of rating, maturity and sector. The buckets are optimized with regards to liquidity, single-bond weighting and duration deviation.

For bond fund portfolios generally, the minimum size is 200 million yuan, the ideal size is 500 million yuan, a portfolio consists of 20 to 50 individual bonds and a single transaction in the interbank market tends to start with minimum face value of 10 million yuan. Thus our research aims to minimize the portfolio’s duration deviation from the index (i.e. min|portfolio duration - index duration|), while agreeing on the following constraints:

1. The initial portfolio size is 500 million yuan and a leverage ratio of no more than 120% is allowed.
2. The minimum face value¹ of an individual bond is 1 million yuan.
3. The portfolio is rebalanced once a month and the maturities of the selected bonds are not less than 1 month.
4. Index constituents are initially screened by internal ratings², so those not allowed or not covered by internal ratings (563 bonds, or 18.5%) are excluded. Among the investable bonds (2459 bonds, or 81.3%), we perform stratified sampling.
5. Cash does not exceed 5% of the portfolio.
6. If there are insufficient bonds in a bucket, a single bond closest to the bucket’s  duration will be directly selected as the sample.

Because the portfolio size is small, only buckets defined by rating and maturity are used in sampling, ie. the index constituent bonds are grouped based on their ChinaBond Market Implied Ratings and then on maturities³. In order to reduce the number of buckets by Market Implied Rating, AAA+, AAA and AAA- are combined as AAA, and AA+ and AA are combined as AA, as shown in Figure 2.

Figure 2: Stratified Sampling of ChinaBond Commercial Paper AAA Index (Optimized)

After completing the stratification according to the above framework, we give priority to retaining the bonds that already exist in the portfolio and add other bonds into the portfolio as alternatives to achieve the goal of minimizing duration deviations. For the added bonds, priority is given to the most liquid bonds (as reflected by the highest turnover rate) in each bucket in the previous month.

Once the general strategy of sampling replication is determined, it will not be changed, but in practice, as the fund size changes, granularity can be adjusted. If the size is small, the granularity will be coarser. If the size is large, it will be finer. 

III. Strategy Back-testing Results and Conclusions

The stratified sampling strategy was constructed, adjusted, optimized, and back-tested in accordance with the frameworks in the first and second parts of this report. The strategy back-testing period is from January to December 2021. The portfolio statistics after rebalancing at the beginning of each month are shown in Table 2. The back-testing results of tracking effects can be seen in Figure 3.

Table 2: The Portfolio Characteristic Values at the Beginning of the Month

The final calculations show that the annualized tracking error of the portfolio was 0.2185% and the average daily return deviation was 0.002%, both of which were kept at very low levels. The annualized return of the portfolio was 3.33%, outperforming the index benchmark by 25bp, and thus verifying the effectiveness of the strategy.

Figure 3: Back-testing of Tracking Effects

In summary, the replication strategy of stratified sampling constructed in this report can effectively track ChinaBond Commercial Paper AAA Index. Firstly, the tracking error and return deviation were significantly lower than the usual requirements of fund contracts (annualized tracking error is 3% and daily return deviation is 0.25% or less); secondly, an excess return of 25bp is achieved, which meets the further demands of bond index fund clients seeking excess return and relative ranking; finally, the portfolio duration is around 0.27 years, close to the index duration of 0.28 years.

There are three directions for subsequent improvement and optimization: firstly, we will consider how to reduce duration jumps from rebalancing at the beginning of each month; secondly, we will study how to raise the minimum face value of a single bond transaction as much as possible without harming the replication effects, so as to get close to the actual transaction constraint in the inter-bank bond markets; thirdly, we plan to explore how to fine tune the optimization for effective application of the strategy  when the portfolio size is increased to, for example, 1 billion yuan, 5 billion yuan, 10 billion yuan or even 20 billion yuan.

¹ Under normal circumstances, the minimum unit of trading in the interbank market usually starts at a quantity of 100,000 pieces, but considering the portfolio size setting and the possible fine-tuning mechanism in the actual investments, we choose to set 10,000 pieces as the minimum trading unit.
² The internal ratings here refer to the fund managers’ internal rating results.
³ Allowing for the positive correlation between duration and maturity, and by combining the stability of maturity, this paper selects maturity as the subdivision dimension.