[Verse 1] Portfolio managers face a puzzle grand Thousands of bonds across the land Full replication costs too much to bear So we slice and dice with systematic care Stratified sampling breaks the index down Industry sectors, ratings, maturity crown Each bucket gets its representative few Mirror the whole with a selected crew [Chorus] Sample smart, optimize tight Fewer holdings, same insight Strat-i-fied, cat-e-gories Match the risk, keep the stories Cell by cell, we build it right Index tracking, feather light [Verse 2] Duration buckets, one to thirty years Credit quality from triple-A to tears Geographic regions, currencies too Each stratum needs its chosen few Market cap weighted, keep proportions true If corporate bonds make up twenty-two Then sample twenty-two percent that way Systematic rules guide every play [Chorus] Sample smart, optimize tight Fewer holdings, same insight Strat-i-fied, cat-e-gories Match the risk, keep the stories Cell by cell, we build it right Index tracking, feather light [Bridge] Optimization algorithms scan Minimize tracking error, that's the plan Quadratic programming finds the sweet spot Maximum correlation, minimum cost When new bonds enter, old ones leave Rebalancing keeps us on our sleeve [Verse 3] Transaction costs drop when holdings shrink But tracking error makes managers think Trade-off between efficiency and match Like threading needles through dispatch Monthly monitoring, quarterly review Keep sample fresh and performance true [Outro] From thousands down to hundreds clean Best replication ever seen Stratified sampling shows the way Index performance every day
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