Two fixtures, two questions
The compounding card uses three invented returns: +10%, -10% and +5%. Starting at wealth one, the chain is 1.1, 0.99 and 1.0395. The terminal return is 3.95%, not the arithmetic sum of five percent. The drawdown card uses a different declared fixture of +10%, -20%, +15% and -5%. These are not two measurements of one undisclosed historical series; each card's exact inputs remain attached to its result.
The first fixture teaches multiplicative wealth accounting. The second teaches peak-relative path loss. Keeping them separate avoids a common interpretation error: comparing a return number from one sample with a risk number from another as though they described a coherent investment record.
Include the starting balance
For the drawdown example, the complete wealth path is 1, 1.1, 0.88, 1.012 and 0.9614. The running peak reaches 1.1 after the first positive return. The fall to 0.88 is a twenty-percent decline from that peak. Later recovery does not erase the historical maximum, and the final observation remains below the same peak. The reported maximum drawdown is a nonpositive decimal, -0.2.
Order and observation frequency
Reordering a fixed list of simple returns leaves their compounded terminal product unchanged. It can change where peaks occur and therefore change the maximum drawdown. The terminal statistic alone cannot reconstruct the experience between the first and last observations. This is why the drawdown export includes the entire calculated wealth and loss paths rather than only one scalar.
These paths are observed only at the supplied endpoints. An intraday loss between two month-end marks is not present and cannot be recovered from those monthly returns. External cash flows also require a different accounting treatment. The example does not infer either missing price points or deposits from a smooth-looking path.
Complete loss and annual equivalents
A -100% return takes the nonnegative-wealth chain to zero. Subsequent positive percentage returns keep it at zero unless an external contribution is explicitly introduced, which this card does not support. Values below -100% are rejected. Separately, the compounding card annualizes its three-period fixture using twelve periods per year. That equivalent rate is a mathematical transformation of the toy sample, not a forecast, a year of observations or a claim about a provider's returns.
| Fixture | Output | Value |
|---|---|---|
| 10%, -10%, 5% | Terminal wealth | 1.0395 |
| 10%, -10%, 5% | Compounded return | 0.0395 |
| 10%, -20%, 15%, -5% | Terminal wealth | 0.9614 |
| 10%, -20%, 15%, -5% | Maximum drawdown | -0.2 |
Reproduce the referenced calculations
Primary references
These sources support methods and conventions. The example values are original constructions, not observations extracted from these documents.
Related investigations
Validation examplesCompound returns and external cash flows
Distinguish chained investment returns, account balance growth and money-weighted experience using a fully specified hypothetical cash-flow timeline.
Risk measurementDrawdown depends on the observed path
Trace maximum drawdown through ordered wealth observations, distinguish depth from duration and show how coarser sampling can conceal a larger interim loss.
Implementation contractsMissing data and alignment: decide what was actually observable
Keep missingness, stale observations, asynchronous timestamps and covariance sample selection visible in a calculation's input history.