Size-matched buy-and-hold evaluation for stock systems

Profit is not the evaluation

A mechanical trading system is a fully specified signal process whose entries, exits, and stand-aside decisions can be reconstructed from rule inputs, market state, and execution constraints. Walk-forward analysis treats those entry, exit, and abstention rules as one replayable procedure and scores them as market state is revealed, rather than as a single static fit.

A mechanical stock procedure that finishes with a profit can still fail evaluation if an untimed buy-and-hold book would have done better over the same window. The buy-and-hold benchmark is a passive always-long comparison book used to test whether a stock procedure adds timing value beyond simply owning the issue.

Hold the stake in dollars, not shares

Fixed contract sizing is a pre-trade exposure rule that keeps each new position at a stated dollar or contract stake so later prices cannot silently enlarge the book. Fixed contract sizing at a constant dollar stake is treated as preferable to a constant share count, because an unchanging share count warps later trades as prices change.

Constant-dollar trade size, illustrated here with a 1000-unit stake, sizes every signal as stake divided by price. Each new mechanical long, short, or stand-aside decision is then taken at that same dollar contract.

Why an unadjusted hold is the wrong twin

A constant-dollar mechanical book cannot be compared to a buy-and-hold book that keeps the first trade's share count, because a large price rise inflates the holder's average size while each system signal stays at the original stake.

In the supplied illustration, a move from 5 to 50 price units turns a 1000-unit, 200-share hold into 10000 units, while the mechanical book continues to size each signal at 1000 units. Unadjusted buy-and-hold comparisons tend to overstate the passive book against a constant-dollar mechanical system, because a held stock position often grows in value while system trade size stays fixed.

Two alignments

The two alignments are presented as a correction, especially for long-only systems.

An equity-compounded share count scales the base stake-over-price lot by current equity relative to starting equity so the mechanical book tracks its own results. When start equity is 1000, shares equal (1000 divided by price) times (1000 plus net profit) divided by 1000. That equity-compounding alignment becomes unusable if losses exceed the 1000-unit start, because the equity ratio and implied share count turn negative. With a 1000-unit start, the matching compounded percent return is defined as 100 times net profit divided by 1000.

A size-matched comparison keeps the buy-and-hold book always long but resets its share count to the mechanical book's 1000-over-price size at every signal. Remaining differences then come from timing, not scale.

A size-matched long and short sequence

In the worked sequence, both books held 159 shares in October 1975. After the mechanical book exited the long and shorted 125 shares in January 1976, the buy-and-hold size was cut to 125 shares so the books stayed size-matched.