6.07.2005

Q&A: What are some of the ways to duplicate a bond index?

A:
  • Pure bond indexing: try own all the bonds in the index in proportion to their market value weights.
    • it's difficult and costly to implement because a bond index typically consists of thousands of issues.
  • Simple sampling: the sample selected may not accurately reflect the risk factors of the index.
  • Stratified random sampling: divide the population of index bonds into groups with similar risk factors (e.g. issuer, duration/maturity, coupon rate, credit rating, call exposure, etc). Each group is called a stratum or cell.
    • Select a sample from each cell proportional to the relative market weighting of the cell in the index.
    • A stratified sample will ensure that at least 1 issue in each cell is included in the sample.

Bonus Points

  • In investment analysis, it is often impossible to study every member of the population. Sampling is the process of obtaining a sample
    • A simple random sample is a sample obtained in such a way that each element of the population has an equal probability of being selected.
    • A biased sample is one in which the method used to create the sample results in samples that are systematically different from the population.
    • it is the method used to create the sample not the actual make up of the sample itself that defines the bias. A random sample that is very different from the population is not biased: it is by definition not systematically different from the population. It is randomly different.
  • In stratified random sampling, the population is subdivided into subpopulations (strata) based on one or more classification criteria. Simple random samples are then drawn from each stratum (The sizes of the samples are proportional to the relative size of each stratum in the population). These samples are then pooled.
    • Stratified random sampling guarantees that population subdivisions of interest are represented in the sample. The estimates of parameters produced from startified sampling have greater precision -- that is, smaller variance or dispersion -- than estimates obtained from simple random sampling.

Category: Quantitative Analysis > Probability

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