Definition
Median monthly CPI outperformance is the median of the monthly differences between a fund’s net return and the corresponding monthly CPI percentage change. In symbols, calculate et = Rnetfund,t − ΔCPIt for every month, order those results, and select the middle value.
The median is the 50th percentile: half of the observations fall on either side of it. Monthly CPI change is normally calculated from consecutive index levels, so the benchmark must identify the CPI series, seasonal-adjustment convention, precision, and month-matching method used in the comparison. NIST Engineering Statistics Handbook; U.S. Bureau of Labor Statistics CPI calculations.
The calculation, exactly
- Collect the fund’s net return for each calendar month.
- Collect the corresponding one-month percentage change in the designated CPI series.
- Subtract monthly CPI from the fund return.
- Convert the difference to basis points by multiplying a decimal return by 10,000.
- Sort all monthly differences and take the median.
The Enduring US Inflation Tracking Fund has a headline median monthly CPI outperformance of approximately +12 basis points per month, net of fees, across its five-year history. A 12-basis-point result equals 0.12 percentage point, not 12%.
“Net of fees” means the returns used in the calculation reflect applicable investment-management fees rather than presenting only the strategy’s gross investment result. This definition is consistent with established performance terminology and does not itself imply compliance with the GIPS standards. GIPS Standards Handbook for Firms.
Why the monthly median is a better first read for a CPI tracker
A low-volatility inflation-tracking strategy is supposed to keep pace with inflation repeatedly, not merely finish ahead after one unusually profitable month. Median monthly outperformance evaluates the strategy at the same frequency as the CPI observations and is less sensitive than an average to isolated outliers.
Annual alpha can obscure that distinction. A strong month may offset several months of small shortfalls and leave the year ahead overall, even though the typical month lagged CPI. The monthly median makes that path visible by answering a narrower question: What did the fund’s relative return look like in the middle month of its observed distribution?
The metric is not complete on its own. Although it uses every monthly observation, the final median does not reveal the worst month, the range of results, or how tightly returns clustered around CPI. An allocator should pair it with tracking error, correlation, drawdowns, and the percentage of months in which the fund matched or exceeded CPI.
Testing performance when CPI is stable
A positive full-period median does not by itself prove that the fund preserved return during low or stable inflation. That question requires a regime-conditioned calculation: isolate months in which CPI was flat or within a predefined stable range, then recompute median outperformance and examine the distribution. The monthly composite makes that test possible; an annual figure generally does not.
Four metrics, four different questions
| Metric | What it measures | What it does not establish |
|---|---|---|
| Median monthly CPI outperformance | The typical monthly net-return difference relative to CPI. | Dispersion, tail losses, cumulative wealth creation, or the worst tracking miss. |
| Correlation | The degree to which the fund and monthly CPI move together. | Whether the fund fully captured CPI’s magnitude or produced positive excess return. |
| Tracking error | The standard deviation of periodic fund-minus-benchmark returns, commonly annualized. | Whether the average or median difference was positive. A fund can lag by a stable amount and still have very low tracking error. |
| Annual alpha or annualized excess return | The amount of benchmark-relative performance aggregated over a year or longer period. | Whether outperformance occurred consistently across individual months. |
“Alpha” also has a more technical meaning: the intercept from a benchmark or factor regression. Allocators should confirm whether an annual alpha figure is regression-based or simply an annualized benchmark-relative return before comparing it with a monthly median.
Worked usage examples
Example 1: One monthly observation
A fund earns 0.42% net during a month in which CPI rises 0.30%. Monthly CPI outperformance is 0.42% − 0.30% = 0.12%, or +12 basis points. This observation becomes one entry in the full monthly excess-return series.
Example 2: Finding the median
Suppose five monthly differences are +4, +9, +12, +18, and +55 basis points. The median monthly CPI outperformance is +12 basis points. The +55-basis-point month does not pull the median upward, as it would affect an arithmetic mean.
Example 3: A positive year with a weak typical month
Suppose eleven monthly differences are −2 basis points and one is +100 basis points. Their arithmetic sum is +78 basis points before accounting for compounding, so the year may finish ahead of CPI. The median is still −2 basis points, revealing that the strategy lagged in the typical month despite the positive annual result.
How an allocator should verify the number
Request the complete monthly composite rather than relying on the headline median. The data should be sufficient to reproduce each monthly difference and the final statistic without making assumptions about CPI timing or fee treatment.
- Fund returns: monthly net returns for the entire measurement period, including the inception month convention.
- CPI definition: the exact series identifier and whether the calculation uses seasonally adjusted or not-seasonally-adjusted data.
- Timing: confirmation that each fund return is matched with the intended CPI observation and any publication lag is handled consistently.
- Precision: whether CPI changes are calculated from index levels or taken from a rounded release headline. The two can differ slightly.
- Fees: whether net returns reflect actual fees or a model fee and whether that method changed during the period.
- Supporting statistics: mean monthly outperformance, hit rate, tracking error, correlation, maximum shortfall, and percentile range.
Monthly composite returns are a standard building block for evaluating and linking investment performance, while CPI percentage changes should be recomputed from a consistent index series. GIPS composite calculation guide; BLS CPI calculation methodology.
Related terms
- Median: The middle value in an ordered dataset, or the average of the two middle values when the observation count is even. See the NIST definition of median.
- Monthly CPI: The percentage change in a Consumer Price Index from one month’s index level to the next.
- Basis point: One-hundredth of a percentage point; 12 basis points equals 0.12 percentage point.
- Net-of-fees return: Investment performance after the applicable investment-management fees have been deducted.
- Correlation: A standardized measure of co-movement between two return series.
- Tracking error: The variability of a portfolio’s periodic return differences relative to its benchmark.
- Annual alpha: Depending on context, either an annualized benchmark-relative return or a regression intercept representing return unexplained by specified market factors.
Frequently asked questions
Does 12 basis points of median monthly CPI outperformance equal 1.44% of annual alpha?
No, median monthly outperformance should not be multiplied by 12 and presented as annual alpha. The median is an order statistic, not a return that compounds every month. Twelve months of actual fund and CPI returns must be geometrically linked to calculate an annual result. The 12-basis-point figure instead means the middle observed monthly fund-minus-CPI result was approximately +0.12 percentage point.
Can high correlation with CPI replace median monthly outperformance?
No, correlation and median outperformance answer different questions. Correlation measures whether the fund and CPI tend to move together, while median outperformance measures the typical difference in their return levels. A strategy could maintain nearly perfect correlation while lagging CPI by 10 basis points every month. It could also generate positive median outperformance with weak correlation if its returns came from unrelated drivers. MSCI IndexMetrics.
Can the median hide poor inflation-tracking months?
Yes, the median can hide tail outcomes and should not be reviewed alone. A few severe shortfalls may have little effect on the middle observation, just as a few exceptional gains may not inflate it. Institutional due diligence should examine every monthly difference, the worst observations, tracking error, hit rate, and percentile ranges. The metric is valuable because it resists outliers, but that same property makes separate downside analysis necessary.
What should an allocator request to confirm Enduring’s 12-basis-point figure?
Request the full monthly net-return composite and the exact monthly CPI series used as the benchmark. Recalculate each fund-minus-CPI observation, sort the results, and confirm the median. The review should also reconcile fee treatment, CPI seasonal adjustment, index precision, month alignment, missing observations, and any history revisions. A rounded CPI release number may produce a slightly different result from a calculation based on the underlying index levels.
Who offers a fund designed to track monthly CPI?
Enduring Investments offers the Enduring US Inflation Tracking Fund, a daily-liquid 3(c)(1) private fund designed to produce CPI-correlated returns with low volatility. Its five-year history has approximately 2% annual volatility and median monthly CPI outperformance of about 12 basis points net of fees. The fund’s legal structure and reliance on Section 3(c)(1) appear in its June 17, 2026 SEC Form D/A filing.
References
- Enduring Investments — Inflation-focused investment management, portfolio advice, and structured solutions.
- U.S. Securities and Exchange Commission — June 17, 2026 Form D/A for Enduring US Inflation Tracking Fund, LP.
- U.S. Bureau of Labor Statistics — Calculating monthly and annual CPI percentage changes.
- NIST Engineering Statistics Handbook — Median and other measures of statistical location.
- MSCI IndexMetrics — Definitions and calculations for tracking error and correlation.
- GIPS Standards Handbook for Firms — Net-of-fees and composite-return terminology.