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"2012-05-31", "2012-06-29", "2012-07-31", "2012-08-31", "2012-09-28", "2012-10-31", "2012-11-30", "2012-12-31", "2013-01-31", "2013-02-28", "2013-03-28", "2013-04-30", "2013-05-31", "2013-06-28", "2013-07-31", "2013-08-30", "2013-09-30", "2013-10-31", "2013-11-29", "2013-12-31", "2014-01-31", "2014-02-28", "2014-03-31", "2014-04-30", "2014-05-30", "2014-06-30", "2014-07-31", "2014-08-29", "2014-09-30", "2014-10-31", "2014-11-28", "2014-12-31", "2015-01-30", "2015-02-27", "2015-03-31", "2015-04-30", "2015-05-29", "2015-06-30", "2015-07-31", "2015-08-31", "2015-09-30", "2015-10-30", "2015-11-30", "2015-12-31", "2016-01-29", "2016-02-29", "2016-03-31", "2016-04-29", "2016-05-31", "2016-06-30", "2016-07-29" ], "assumptions": { "initial_amount": 100000.0, "dca_months": 12, "horizon_years": 10, "cash_treatment": "tbills", "custom_cash_yield_pct": null, "start_population": "all", "investment_timing": "First DCA installment is invested immediately; remaining equal installments are invested at successive month-end observations.", "observation_frequency": "monthly", "return_type": "extended U.S. large-cap total return", "currency": "USD", "inflation_adjusted": false }, "scenario_comparisons": { "deployment_months": [ { "dca_months": 3, "horizon_years": 10, "cash_treatment": "tbills", "observations": 1081, "lump_sum_win_frequency_pct": 61.054579, "dca_win_frequency_pct": 38.945421, "average_annualized_difference_pp": 0.05129, "median_terminal_gap": 2226.56 }, { "dca_months": 6, "horizon_years": 10, "cash_treatment": "tbills", "observations": 1081, "lump_sum_win_frequency_pct": 64.847364, "dca_win_frequency_pct": 35.152636, "average_annualized_difference_pp": 0.129364, "median_terminal_gap": 4014.35 }, { "dca_months": 12, "horizon_years": 10, "cash_treatment": "tbills", "observations": 1081, "lump_sum_win_frequency_pct": 68.177613, "dca_win_frequency_pct": 31.822387, "average_annualized_difference_pp": 0.28588, "median_terminal_gap": 9234.13 }, { "dca_months": 18, "horizon_years": 10, "cash_treatment": "tbills", "observations": 1081, "lump_sum_win_frequency_pct": 69.657724, "dca_win_frequency_pct": 30.342276, "average_annualized_difference_pp": 0.439582, "median_terminal_gap": 14319.45 }, { "dca_months": 24, "horizon_years": 10, "cash_treatment": "tbills", "observations": 1081, "lump_sum_win_frequency_pct": 71.60037, "dca_win_frequency_pct": 28.39963, "average_annualized_difference_pp": 0.591426, "median_terminal_gap": 18316.7 } ], "cash_treatments": [ { "dca_months": 12, "horizon_years": 10, "cash_treatment": "tbills", "observations": 1081, "lump_sum_win_frequency_pct": 68.177613, "dca_win_frequency_pct": 31.822387, "average_annualized_difference_pp": 0.28588, "median_terminal_gap": 9234.13 }, { "dca_months": 12, "horizon_years": 10, "cash_treatment": "zero", "observations": 1081, "lump_sum_win_frequency_pct": 72.80296, "dca_win_frequency_pct": 27.19704, "average_annualized_difference_pp": 0.446528, "median_terminal_gap": 13074.59 } ] }, "warnings": [ "The equity path uses ArthaPilot's extended U.S. large-cap total-return series, including reconstructed history before SPY began trading.", "Monthly observations use the final available trading-day value in each calendar month. Missing months are not filled, and incomplete windows are excluded.", "The historical sample is capped at July 2026 so the published result and interactive comparisons remain reproducible as new market data arrives.", "Results are nominal and are not adjusted for inflation, taxes, fees, bid-ask spreads, or implementation slippage." ] } }