Constant investment size in stock system evaluation

The fill rule belongs in the procedure

Walk-forward analysis is the out-of-sample scoring of entry, exit, and abstention rules as one procedure, using rule inputs, market state, and execution constraints such as how large each fill is. System optimization is a search over rule inputs inside a test protocol. The size rule is an execution constraint that belongs inside that protocol.

Robustness testing checks whether an evaluated signal still stands when a test assumption changes, including whether share count is held fixed while prices span a wide range. An equal-share fill gives every signal the same number of shares regardless of the name's price or the date in the sample. Constant investment size keeps the dollar stake of each signal fixed, so share count equals that stake divided by the price in force at the signal.

Equal-share fills create a price-level artifact

Equal share counts on a two-dollar name and a hundred-dollar name make a one-dollar move post the same dollar result even though the percent moves differ by a factor of fifty. The same percent move under equal share counts produces a dollar result fifty times larger in the hundred-dollar name than in the two-dollar name.

That gap is a price-level artifact: a test result driven by where the sample sits in price, not by the percent move the rule captured.

Constant investment size holds the stake fixed

Setting share count to a one-thousand-dollar stake divided by price makes a fifty-percent move post the same dollar result at two-dollar, twenty-dollar, and hundred-dollar prints. The score then follows the percent move the signal captured rather than the print level of the name.

Split-adjusted prints and the share formula

A split-adjusted series is a price history scaled by later split ratios so the series does not drop by the split factor on the split date. A split-adjusted print equals the actual print divided by the cumulative split ratio. Two later two-for-one splits turn a twenty-dollar actual print into a five-dollar adjusted print.

Using the adjusted print in the constant-stake share formula overstates share count by the split ratio and understates the price change by the same ratio, so the product that is dollar result is unchanged.

The four-to-one split case

In the worked four-to-one split case, a twenty-percent rise produces a two-hundred-dollar result from actual past prices, adjusted past prices, and the later forty-dollar print when the stake is held at one thousand dollars.

A long-history crossover sample

On a long-history twelve-and-one-hundred-twenty-bar crossover, constant-share scoring treats an early low-price winner as a small per-share gain while constant-dollar scoring keeps the large percent gain visible. Constant-share scoring on split-adjusted history underweights early low-price years and overweights later high-price years, so the same later trade can dominate the total under one size rule and not the other.

What the test should keep

Stock-system tests should keep split-adjusted prices and replace the implicit constant-share fill with a constant investment size so the evaluated procedure matches how the signals would be sized in use.