Constructing a pre-entry risk filter on price-ratio grids

A filter that waits for both columns

A pre-commitment risk assessment can be built from three indicators: the chance the position is profitable relative to initial capital, the probability-weighted expected percent result, and the dispersion of that result.

Those indicators are produced by combining a table of percent profit versus future price with a projected probability distribution of those prices.

Editorial interpretation: treat the finished indicators as a risk-of-ruin-filter. That is a constructed go-or-no-go check that bounds planned exposure after payoff and probability have been combined, before capital is committed.

Why the random variable is a weekly price ratio

The random variable is the weekly price ratio rather than the raw point change, because a 10-point move is a 100 percent wealth change in a 10-dollar stock and only a 10 percent change in a 100-dollar stock when equal dollar amounts are committed.

A 10 percent rise is expressed as a 1.10 ratio for either security, and the implied future price is the product of that ratio and the purchase price.

The shared axis is a price-ratio-grid: evenly spaced weekly price ratios used for both the payoff table and the probability column.

Three worksheets, one shared grid

The construction is split into a profit-sheet that maps terms and holding period to a percent-profit column, a distribution-sheet that maps price-history variance to a future-price distribution, and an integration-sheet that merges the two columns.

Building the profit-sheet

The profit-sheet turns quantity, price, terms, cash cost, and holding period into percent profit at each ratio step.

Short exposure is entered as a negative quantity. When no expiration applies, a 52-week holding period is used. Cash cost includes the original outlay plus margin interest, and profitability is measured against that original value on a 0.05 ratio grid.

Convertible payoffs can be mapped by iteratively choosing a gamma until the model price is close enough to the observed convertible price, then varying future stock price in that model to obtain the convertible value at each ratio.

Building the distribution-sheet

The distribution-sheet turns a year of weekly closes into variance, projects that variance over the holding period, and emits a probability column.

It uses 52 weekly closes to form successive price ratios, their natural logs and squares, then a variance projected across the holding period.

A biased-ratio shift then places the peak of the projected distribution at a ratio of 1.0 so short-horizon drift is removed before the probability column is formed.

Reading the integration-sheet

The integration-sheet combines the percent-profit column with the matching probability mass to form the three risk indicators on a 0.05 ratio step.

Probability-of-profit is the share of the projected ratio distribution in which the position finishes above the original cash outlay. Expected-profit is the probability-weighted average percent outcome of the position across the ratio grid. Sigma-in-the-profit is the dispersion of those percent outcomes around the expected value, used as a variability check.

Shared projections and grid spacing

The distribution-sheet should be run first so several security combinations from the same company can share one volatility projection.

Widening the step to 0.10 reduces processing time but coarsens the grid and reduces accuracy.