Four-sleeve Monte Carlo annual-loss bounds

A book of random variables

A mixed-instrument book is framed as seeking the best available risk-reward tradeoff among random variables, not as a requirement to pursue high returns.

A usable risk sample is described as a track record that covers several market conditions and contains enough trades for profit-factor and win-rate estimates to be statistically meaningful. Systems with several free parameters are assigned a trades-per-parameter floor of 30 historical trades per parameter, so a two-length moving-average crossover is given a minimum of 60 trades to limit optimization fit.

A single equity path is not a risk test

A lone equity path is rejected as a risk test because repeated tests of the same rules can still produce large equity-curve differences. Risk-of-ruin is described as higher before an account has built a cushion.

Monte-carlo-resampling of daily profits

Monte-carlo-resampling converts a trade history into daily profits, draws those daily profits with replacement 260 times to form one synthetic year, and repeats that year 5,000 or 10,000 times to build an outcome distribution.

That resampled annual distribution is treated as approximately normal, so expectation and the one-sigma and two-sigma points can be read from it as a sigma-band. In the fully invested single-name illustration, breakeven-or-better sits outside the lower one-sigma point while the chance of a yearly loss remains high.

Four independent-sleeves and the loss tail

Raising the number of independent simultaneous holdings by a factor of four is stated to halve the variance of the annual distribution, because doubling independent samples reduces variance by the square root of two. Independent-sleeves are parallel, unsynchronized holdings that each take their own signals so daily results are not locked to a single name.

Splitting the same capital across four unsynchronized, independently signaled holdings is presented as generally adequate to cut the chance of an annual loss in a well-specified system. Eight holdings would halve variance again but meet diminishing returns and capital limits, and expected profit is not said to rise.

Time at risk and the drawdown-limit

A cyclic-hold that averages about 10 days from trough to peak is contrasted with trend following as a way to keep average time at risk shorter. Trend following is characterized by tentative entries, quick exits on failed onsets, a higher profit-factor, and a lower win rate.

A drawdown-limit is a pre-trade and in-trade bound on time at risk, simultaneous exposure, and the chance of early ruin, set before the next order is placed.