2019issue C1028-32
The recovery budget, the share count, and the first stop from one ranked tail
The archive set an annual portfolio-loss cap from the gain needed to recover a decline, then used a percentile-return to place the stop-loss and to scale the share count so each name used one slice of that budget.
- A 20 percent decline requires a 25 percent subsequent gain to recover, and a 50 percent decline requires a 100 percent subsequent gain, so the annual cap was set from that recovery multiple rather than from a willingness-to-lose guess.
- A normal-model 1 percent daily value-at-risk was exceeded on about 1.8 percent of days in a 5030-day index sample, and the gap widened farther left; a percentile-return was used instead of a fitted curve.
- On the worked book, an 8 percent annual cap became an 8000 equity-book limit and 800 per name; the 0.4 percent percentile distance then capped one illustrated name at 71 shares.
- Risk of ruin was much lower at 10 positions than at two under most plotted win-rate and payoff pairs, and those risk controls were presented as independent of a winning-edge requirement.
The annual loss cap from a recovery multiple
A 20 percent account decline requires a 25 percent subsequent gain to return to the prior balance, and a 50 percent decline requires a 100 percent subsequent gain. In a two-year compound-return comparison, plus 50 percent then minus 50 percent finished at minus 25.0 percent, minus 50 percent then plus 75 percent finished at minus 12.5 percent, and two consecutive minus-4-percent years finished at minus 7.8 percent.
Using a 9 percent median annual benchmark, a later-year gain of that size was treated as able to offset an 8.25 percent decline, which was rounded to an 8 percent annual portfolio-loss cap. A 15 percent later-year gain was treated as able to offset about a 13 percent decline. That account-level annual loss cap is the total-portfolio-value-at-risk: it was set from a recovery multiple rather than from an arbitrary willingness-to-lose figure.
How the book was split and why position count mattered
Portfolio volatility was to be reduced with an adequate number of holdings, risk-based position sizing, risk-based stop-loss orders, and assets that are not highly correlated. Those controls were presented as independent of a winning-edge or payoff-edge requirement.
On a 100000-unit book with 10 percent held in cash and an 8 percent total-portfolio annual loss cap, the implied equity-book dollar limit was 8000, or 800 per name if that limit was split equally across 10 holdings.
With a 60 percent win rate and a 1-to-1 payoff, risk of ruin was about 1.70 percent at 10 positions versus 44 percent at two. With a 40 percent win rate and a 3-to-1 payoff the figures were 2.5 percent versus 41.6 percent. A 40 percent win rate at even odds produced ruin at every position count shown, while the other plotted combinations fell below 20 percent ruin once 10 positions were held. Risk of ruin is the chance that a string of losses exhausts trading capital, shown in the source to fall as independent position count rises under most win-rate and payoff pairs.
Where a normal value-at-risk understated the tail
Value-at-risk is a forecast of the loss associated with a chosen probability over a stated lookback and sampling interval.
On 5030 daily index returns ending 31 December 2018, a normal-model 1 percent daily value-at-risk of minus 2.79 percent (mean 0.0142 percent, standard deviation 1.2039 percent, z of minus 2.3263) was exceeded on about 1.8 percent of days, understating frequency by about 44 percent. The same model at 0.5 percent produced minus 3.09 percent, expected about 1.28 times per year, versus an observed 1.35 percent of days (3.38 times per year), understating frequency by about 62 percent. The normal tail was described as usable above roughly 5 percent probability and progressively worse farther left.
A percentile-return in place of a fitted curve
A percentile-return is a nonparametric ranking of historical returns used to read the tail without fitting a stable distribution. Implementation used a 256-day log return, a 0.4 percent percentile rank (about four years or 1000 daily prices recommended), annualization by the square root of 256 divided by the sample length, a 16-times factor for one-day returns, and a stated floor of 25 trading days for the estimation window.
The first stop and the share count
A nonparametric 0.4 percent annual percentile on one illustrated 80-unit name implied a 14 percent (11.20) per-share loss. Dividing an 800-unit position-loss budget by that distance allowed at most 71 shares (5714). Repeating the same budget across the other nine candidates kept total equity-book risk at 8000.
Volatility-position-sizing scales the share count so the dollar loss at that stop equals a fixed slice of the account-level loss budget. The stop-loss is a pre-entry exit placed at the price distance implied by the chosen value-at-risk level, then adjusted if volatility changes.
A stop at the 5 percent value-at-risk level was described as expecting about five exits in 100 days, or roughly once a month. A 0.4 percent level was described as expecting one exit in 250 trading days, or about once a year. On the 80-unit example the initial stop sat 11.20 below entry at 68.80 and could be recalculated after entry if volatility changed.