Description
Multiply gross wealth factor by (1-fee)^periods and return the lost gross-factor amount using expm1 for stability.
A simple return is a change relative to an initial value, while a gross return is a wealth multiplier and a log return uses a logarithm of that multiplier. Dividend, split, fee and currency conventions change what is included.
Multiply gross wealth factor by (1-fee)^periods and return the lost gross-factor amount using expm1 for stability.
When to use this tool
Use Compounded Fee Effective Spread when you need a stated return-basis conversion or contribution.
How to use the tool and how it works
- Enter grossReturn, feeFractionPerPeriod, periods. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read netGrossReturn, effectiveFeeSpread. Use the output convention below.
Require nonnegative grossReturn, feeFractionPerPeriod in [0, 1), and nonnegative integer periods. Multiply gross wealth factor by (1-fee)^periods and return the lost gross-factor amount using expm1 for stability.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| grossReturn | Nonnegative gross wealth factor, not a simple return fraction. | Required. Finite number; minimum 0. |
| feeFractionPerPeriod | Fee Fraction Per Period | Required. Finite number; minimum 0; strictly below 1. |
| periods | Periods | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| netGrossReturn | Net Gross Return | Required. Finite number. |
| effectiveFeeSpread | Gross factor lost to the modeled repeated fee, not an annualized fee percentage. | Required. Finite number. |
{
"input": {
"grossReturn": 1.1,
"feeFractionPerPeriod": 0.1,
"periods": 2
},
"output": {
"netGrossReturn": 0.8910000000000001,
"effectiveFeeSpread": 0.20900000000000002
}
}Limitations and assumptions
- GrossReturn is a wealth multiplier, not a simple-return fraction. Fee spread is gross minus net factor, not an annualized percentage or an actual fee quote.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Reconstruct the full investment cashflow and adjustment history for performance analysis. Align horizons, quote direction and numeric return scales, and include relevant fees and taxes explicitly.
References
Similar or alternative tools
- Fee Gross Net Reversal Factor
Return (net+fixedFee)/(1-rate), gross-minus-net fee and reciprocal gross-up factor.
- Transaction Fee Rebate Net Charge
Subtract rebate and flag credit when the net is negative.