One report says a strategy wins in more than 80% of months. Another shows a lower win rate but a positive total return. Lin is tempted to choose the first: winning more often sounds like a more reliable way to invest. What information would let her check that intuition?
A backtest report is a collection of calculations and assumptions. Read the underlying period returns, account rules, costs, and benchmark together. A headline cannot establish whether the comparison is fair, whether losses were tolerable, or whether the result is likely to persist. The SEC's investor guidance likewise distinguishes hypothetical backtests from actual performance and asks readers to inspect costs, methodology, selection, and benchmarks.1
What you will be able to do
- Reconcile cumulative return and a benchmark from complete net period returns.
- Read win rate, volatility, drawdown, exposure, turnover, and three ratios without swapping their definitions.
- Save a report-reading card that separates supported comparisons from missing evidence.
Build the comparison before ranking it
This independent synthetic C6 supplement contains six calendar months, M1 through M6. It does not extend G14's annual example or report the real C2 SPY study. Each account starts with $1,000, uses dollars, and has no external flows or borrowing. Personal taxes, dividends, and cash interest are excluded.
Account A puts all its money into fictional asset X at the start of each month and sells everything at month-end. B does the same with fictional asset Y. The next month starts again; ignore any gap between one month's sale and the next month's purchase. Each month contains exactly one completed round trip.
For each account, the complete assumed monthly trading cost is 0.2% of that month's starting equity, charged at month-end. It includes this example's commissions and slippage. Subtract that cost once, not again after using the net return. This supplied cost model is not an actual broker quote or a model of unlimited trading capacity.
The benchmark starts each month with half its equity in X and half in Y, then liquidates both at month-end, under the same proportional cost assumption. Its net monthly return is therefore the arithmetic average of A's and B's monthly net returns. This is a defined comparison portfolio, not a benchmark suitable for every risk profile.
| Month | A gross | A net | B gross | B net | Benchmark net |
|---|---|---|---|---|---|
| M1 | 1.2% | 1% | 3.2% | 3% | 2% |
| M2 | 1.2% | 1% | −0.8% | −1% | 0% |
| M3 | 1.2% | 1% | 3.2% | 3% | 2% |
| M4 | 1.2% | 1% | −0.8% | −1% | 0% |
| M5 | 1.2% | 1% | 3.2% | 3% | 2% |
| M6 | −7.8% | −8% | −0.8% | −1% | −4.5% |
All six observations are required. They are month-end observations; no within-month path is supplied. You cannot assume that an account never fell further between those endpoints.
Winning often does not ensure a positive total return
Compound A's net returns rather than adding them. Five gains of 1% turn $1,000 into $1,051.0100501. The final 8% loss leaves $966.929246092, a cumulative return of approximately −3.31%. Five of six months are positive, so its positive-month rate is 83.33%, despite the overall loss.
B alternates a 3% gain and a 1% loss. Each two-month factor is 1.03 × 0.99 = 1.0197. Repeating it three times leaves $1,060.271915373, a return of approximately 6.03%. Its positive-month rate is only 50%. The frequency of gains leaves out their size and the size of losses.
In this deliberately restricted example, each month has one complete trade, so the positive-month rate equals the winning-trade rate. That equivalence does not hold for a general strategy with multiple trades, positions spanning months, or unrealized changes. Label the unit counted in the numerator and denominator.
The benchmark compounds 2%, 0%, 2%, 0%, 2%, and −4.5%, ending at $1,013.45364, or 1.35% above its start. A's cumulative return is about 4.65 percentage points below the benchmark; B's is about 4.68 points above it. Those are descriptive return differences, not evidence of persistent risk-adjusted alpha.
Do not average A's and B's ending values to reconstruct this monthly rebalanced benchmark. That average is approximately $1,013.60058, a different result. It represents splitting the initial money between two subaccounts and allowing their relative weights to drift. Our benchmark resets its X/Y weights to half and half each month. Average the matching monthly returns, then compound that sequence.
Keep full precision through the calculations. Dollar amounts or percentages rounded for display should not become the next month's calculation inputs.
Separate an observed return from an annualized rate
The accounts ran for six months, not a year. Under a convention of 12 monthly periods per year, their annualized compound rates are the six-month wealth factors squared, minus one. That produces approximately −6.50% for A and 12.42% for B.
These are scaled rates, not additional months of observed performance and not forecasts of the next six months. An annualized result can be useful for a consistent comparison, but the six-month sample remains short.
Monthly sample standard deviation uses the deviations from the mean monthly return and divides their squared sum by 5, because there are six observations. A's monthly standard deviation is approximately 3.6742% and B's is 2.1909%. Multiplying each by the square root of 12 gives annualized volatilities of about 12.73% and 7.59%.
This square-root scaling is a reporting convention with assumptions about the return process. Serial dependence and changing variance can undermine a simple interpretation; compound-return aggregation adds complexity.2 Annualizing does not convert six observations into a long record.
Read the ratios with their inputs attached
For Sharpe, specify a monthly model risk-free reference of 0.1%, in the same currency. This teaching input is separate from the assumed zero interest on account cash and is not a current Treasury rate.
A's mean monthly net return is −0.5%; subtracting 0.1% gives mean differential return of −0.6%. B's mean net return is 1%, giving 0.9% after the reference. Divide each differential mean by its monthly sample standard deviation and multiply by the square root of 12. The annualized historical Sharpe ratios are approximately −0.57 for A and 1.42 for B. Substituting annualized compound return for this period arithmetic mean would change the calculation.
For Sortino, set the monthly target to zero, independently of the 0.1% Sharpe reference. Keep negative monthly returns and replace positive ones with zero. Average their squares across all six months, then take the square root.3 A has one −8% shortfall, giving monthly downside deviation of about 3.2660%. B has three −1% shortfalls, giving approximately 0.7071%.
Divide mean monthly return relative to the zero target by that downside deviation, then multiply by the square root of 12 under the same stated reporting convention. Annualized Sortino is approximately −0.53 for A and 4.90 for B. Do not silently replace the zero target with the Sharpe reference or divide only by the number of negative months.
For Calmar, divide annualized compound return by the positive magnitude of maximum drawdown observed over this same six-month, month-end window.3 A's maximum drawdown is 8%; B's is 1%. The ratios are approximately −0.81 and 12.42.
B's large Calmar number comes partly from a small drawdown denominator over a short observed window. It does not establish a long-term low-risk strategy. These calculations do not use a separate three-year drawdown history or unseen daily values.
| Measure | A | B |
|---|---|---|
| Six-month net cumulative return | −3.31% | 6.03% |
| Annualized compound rate, 12-month convention | −6.50% | 12.42% |
| Positive months / all six months | 83.33% | 50% |
| Annualized sample volatility | 12.73% | 7.59% |
| Annualized Sharpe, monthly reference 0.1% | −0.57 | 1.42 |
| Annualized Sortino, monthly target 0% | −0.53 | 4.90 |
| Maximum drawdown, observed month-ends | 8% | 1% |
| Calmar, same six-month window | −0.81 | 12.42 |
The ratios answer different questions. Comparing a Sortino number with a Sharpe number as though they shared a common scale is not meaningful. Zero denominators require an explicit undefined-result policy; “infinite” is not a substitute for evidence. A negative Sharpe ratio also needs care: greater variability can move a negative value closer to zero without making the underlying loss attractive.
Look behind the ratio table
Both accounts are fully invested in a risky asset at each month's start and hold no cash then. Each also has 100% single-asset concentration. Their exposure to different fictional assets can explain different outcomes without establishing skill. B's higher net return in this sample does not isolate why it performed better.
Under this chapter's one-sided purchase-turnover convention, monthly purchases divided by starting monthly equity equal 100% in each month. Adding those six monthly figures gives 600% over six months. This is not an annual turnover figure using average net asset value, and counting both purchases and sales would use another convention. Define the denominator before comparing reports.
At M6, both accounts remain below their M5 peaks. Earlier 1% declines in B were recovered in the next positive month, but its final decline has no recovery date within the supplied data. Keep the peak, trough, and recovery date separate. Do not invent a future recovery date or treat the worst observed month, −8% or −1%, as a limit on future losses.
Real implementation would still require evidence about trading capacity, depth, actual costs, taxes, and intramonth losses. Also ask how many versions were tried, how this period was selected, and what exposures the strategy carried. A report can calculate its statistics correctly while leaving these research questions unresolved.
A defensible conclusion is narrow: under the supplied six-month data and cost assumptions, B has the higher net cumulative return and listed ratios, with a smaller observed maximum drawdown. A's higher positive-month rate does not imply a positive cumulative return. Neither short, concentrated record proves persistent performance.
Explain one result and audit an incomplete report
Explanation. Why does A lose money despite five positive months?
Reference answers · reveal
Answer. The five 1% gains compound to about 5.10%, but the subsequent 8% loss applies to that enlarged account. The final wealth factor is 1.01 to the fifth power, multiplied by 0.92, which is below one. Counting wins discards the magnitudes.
Repair a label. A report divides six-month cumulative return by annualized volatility and labels the result “Sharpe.”
Answer. The numerator is neither the mean monthly differential return nor a matching annualized differential mean. Use the complete monthly net sequence, subtract the monthly reference, calculate its sample standard deviation, and apply the stated annualization convention. Do not fix only the label while leaving mismatched units unexplained.
Transfer. A report claims to cover six months but supplies only three rows: 3%, 3%, and 3%. It reports a 100% win rate, zero volatility, and an infinite Sharpe ratio. Can you accept the six-month comparison?
Answer. No. Request all six dated observations, the reason the other rows are missing, and whether losing periods were omitted. Do not fill blanks with zeros. Even a complete three-period series with constant returns has a zero sample standard deviation; that does not make the strategy risk-free. If these rows were selected from B's positive months, they cannot stand in for B's full six-month history.
Save a report-reading card
Record A's and B's full return sequences, dates, currency, net/gross status, cost model, benchmark construction, exposures, and turnover convention. Include cumulative and annualized return, sample standard deviation, the Sharpe reference, the Sortino target and all-period denominator, the drawdown window, and whether recovery is observed.
Independently recalculate at least two metrics from the inputs and state your rounding policy. Finish with three sentences: what comparison is supported, what apparent advantage could mislead, and what material you would request next. A finished card should preserve enough information for another reader to challenge your conclusion without reverse-engineering a chart.
Read the report as a chain: complete inputs and common assumptions first, calculations second, limited inference last. A strong-looking statistic cannot repair missing observations or supply a mechanism for future returns.
References
- SEC Investor Bulletin: Performance Claims, September 15, 2022, costs, methodology, backtesting, cherry-picking, and benchmarks.
- William F. Sharpe: The Sharpe Ratio, “Time Dependence.”
- PerformanceAnalytics: SortinoRatio, DownsideDeviation, and CalmarRatio. Specify targets, the full-series versus subset downside denominator, annualization, and the drawdown window.
Editorial status
AI-assisted draft synchronized to the accepted second-round Chinese source. Numerical examples are synthetic. See the author review. A separate AI reviewer has completed an independent full-text review. Human financial review and target-reader testing have not been performed and are not scheduled for this edition.