Simple random and stratified random sampling

CFA level I / Quantitative Methods: Application / Sampling and Estimation / Simple random and stratified random sampling

A simple random sampling where we draw the sample randomly from the population such that each element of the population has an equal probability of selection, may not be the best approach in all situations.

Another frequently used alternative is stratified random sampling. In it, the population is divided into strata (subpopulations) based on one or more classification criteria. Then simple random samples are drawn from each stratum in size proportional to the relative size of the stratum in the population. Then these samples are pooled to from a stratified random sample.

It is better than a simple random sampling as it guarantees that population subdivisions of interest are represented in the sample. The estimates of parameters produced from stratified sampling have a greater precision i.e. smaller variance or sampling error as compared to the simple random sampling.

Example 1: Stratified random sampling

A bond portfolio manager wants to index from a universe of bonds. (Indexing is an investment strategy to construct a portfolio to mirror the performance of a specified index.) The manager decides to use stratified random sampling to choose the bonds in her portfolio. She classifies bond in two main categories: Government bonds and non-government bonds. Each main category has three further subcategories based on the maturity of the bonds - maturity up to 1 year, maturity from 1 year to 10 years, maturity longer than ten years. Each subcategory is further diving into three categories based on the annual coupon rate: coupon rate less than 3 percent, coupon rate from 3 percent to 6 percent, coupon rate greater than 6 percent.

(a) How many strata are there in this sampling plan?
(b) What is the minimum number of bonds the indexed portfolio can have as per this sampling plan?
(c) Is the sample chosen by this sampling criterion a random sample?

Solution:

(a) We have two issuer classifications, three maturity classifications, and three coupon classifications. In total, the plan has 2*3*3 = 18 different cells.

(b) Each stratum (cell) must have at least one bond. So, the indexed portfolio must include at least 40 bonds.

(c) The stratified random sampling doesn't strictly involve random sampling. But since the purpose of the sampling here is to index a portfolio rather than making an inference about a population parameter, lack of randomness is not a problem.


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