A liability-driven mandate's monthly report has one job, which is to let a trustee who is not a bond specialist see whether the plan is on course and whether it can pay a margin call. Everything else is supporting evidence.
The two headline numbers are the funded ratio and the hedge ratio, in that order, each with its prior-month value and its policy target beside it. The plan in Worked Example 2 reports 85.000000% funded and 67.542254% hedged after the overlay, against 18.855634% before it. Those two numbers, tracked monthly, are the entire strategic picture: one says how big the hole is, the other says how stable it is.
What else goes in the monthly pack?
Beneath them, a usable pack carries six things.
- Surplus at risk, stated in currency for a stated rate move. On this plan a one standard deviation move of 90 basis points against the unhedged BPV is $99.554400 million, or 4.148100% of the liability, against $248.886000 million with no overlay at all. The overlay bought $149.331600 million of that.
- The key-rate profile of assets and liabilities side by side, bucket by bucket, because a matched total duration hides the structural risk that only the bucket comparison reveals.
- The collateral position: headroom in basis points, the size and composition of the liquid buffer, and the largest single-day call the book has faced in the last twelve months.
- The dispersion and convexity check, restated, because a rebalancing trade that fixed duration can break condition three without anyone noticing.
- The rebalancing log: every trigger breached, whether it was acted on, and the cost.
- A single reconciliation line proving that the reported asset BPV equals the sum of the sleeve BPVs including the overlay, because a hedge ratio computed off an incomplete asset BPV is the commonest error in this entire report.
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What goes in an index-based mandate's pack?
An index-based mandate's pack is different in content and identical in spirit. It carries realised tracking error against the ex ante estimate, the cell-by-cell weight and duration mismatches, the number of holdings against the index's issue count, and the transaction cost incurred against the index's own assumed turnover. The equivalent single check is that the reported active duration ties to the sum of the cell-level duration contributions.
A pack that carries all of this fits on two pages. A pack that carries none of it fits on one, and that is usually why it does.
{
"skill": "Decomposing a sampled bond portfolio's tracking error by cell and testing whether more holdings pay for themselves",
"use": "Have an assistant build the cell-level tracking-error decomposition from a holdings file and an index constituent file, then run the marginal analysis that says how much tracking error the next twenty holdings would remove and what they would cost.",
"tools": ["Chat assistants with code execution - Claude, ChatGPT, Gemini", "Python: pandas for the holdings-to-index join, NumPy for the variance arithmetic", "The index provider's own constituent and factsheet files as the primary source"],
"prompt": "Here is a portfolio holdings table and an index cell table, each carrying cell name, weight, spread duration, number of issues and an assumed idiosyncratic return volatility per bond, plus a portfolio and index modified duration and an assumed rate volatility. Compute the three tracking-error components separately: the duration-mismatch term, the sum over cells of the spread-weight-mismatch terms, and the sum over cells of the idiosyncratic terms scaled by one over the square root of the names held. Report each component in basis points a year, report total tracking error, and report each component's share of total VARIANCE rather than of total tracking error. Then recompute the total if the number of holdings in every cell doubles, and report the reduction.",
"verify": "Check the component shares are shares of variance and not of standard deviation, because adding standard deviations is the single commonest error in this calculation and it overstates the total by a large margin. Reproduce one cell's idiosyncratic contribution by hand from weight, volatility and holding count before trusting any of the rest. Confirm the portfolio and index weights each sum to 1.0000 and that the cell definitions on both sides are the same partition, since a join that silently drops a cell produces a lower tracking error and a wrong one. Trace every index weight, issue count and duration to the provider's own published factsheet with a date, never to the model's recollection of what the index contains. Then sanity-check the answer against the mandate: a sampled aggregate tracker reporting 4 basis points of tracking error on 26 holdings has an error in it somewhere.",
"diy": "You must be able to write the three-term decomposition from memory, say why the idiosyncratic term scales with one over the square root of holdings, and compute one cell's contribution with a calculator. An assistant will produce a tracking-error number for any holdings file you give it, including one where the sample has no exposure at all to a cell worth 12% of the index, and the number it prints will not look wrong. The cell-by-cell reconciliation is what catches that, and it is a by-hand skill.",
"market": "US"
}