{ "version": "2026.1", "generated_at": "2026-09-08", "generated_by": "scripts/gen_part_time_income_study.mjs", "study": "part-time-income-early-retirement-2026", "url": "https://quantcalc.app/research/part-time-income-early-retirement-2026/", "license": "CC-BY-4.0", "method": { "engine": "QuantCalc C Monte Carlo engine (quantcalc-server 2.0.0) over the public simulate contract, with the planner's recurring income life event", "capital_market_assumptions": { "source": "JPMorgan LTCMA 2026", "as_of": "2025-11-01", "asset_classes": [ "US Equity", "International Equity", "Bonds", "Real Estate", "Cash" ], "expected_returns": [ 0.067, 0.074, 0.048, 0.065, 0.032 ], "volatilities": [ 0.152, 0.18, 0.05, 0.15, 0.01 ] }, "plan": { "current_age": 55, "retirement_age": 55, "end_age": 95, "horizon_years": 40, "spending_annual_real": 55000, "social_security_annual_real": 28000, "social_security_start_age": 67, "allocation": [ 0.5, 0.2, 0.3, 0, 0 ], "mix": "70/30", "inflation_rate": 0.025, "pension": 0, "taxes": "none applied to the income, benefits or withdrawals in this mode" }, "personas": [ { "key": "A", "starting_wealth": 1200000 }, { "key": "B", "starting_wealth": 950000 } ], "incomes_annual_real": [ 10000, 20000, 30000 ], "durations_years": [ 5, 10 ], "work_start_age": 55, "lump_arm": { "amount": 50000, "equals": "10000 × 5", "held_from_age": 55 }, "income_event": "sent exactly as the planner sends a recurring income life event (type income, annual amount, startAge 55, endAge 60 or 65, inflationCategory CPI, the planner's default for income); handlers.c converts it to a monthly amount over months [0, years × 12) and monte_carlo.c apply_life_events raises it with the plan's inflation rate, so it is a constant amount in today's dollars — the same convention as spending; the engine adds it gross to the cash flow, and no tax is applied to it or to withdrawals in this mode", "paths_per_arm": 10000, "pairing": "seed s with n ≤ 30 paths reads Sobol cache rows s..s+n−1 (random.c generate_sobol_normal offset = seed mod (rows − n + 1)); the 334 windows tile rows 0..9999 exactly", "paired_statistic": "per path: this arm's terminal real wealth − the no-work baseline's terminal real wealth on the same market path; reported as median, p10, p90, mean, the share of paths where this arm ends higher, and survival crossovers; income arms are additionally paired against the lump arm", "success_gain_per_10k_year": "(arm success rate − baseline success rate) in percentage points, divided by the number of $10,000-years of income (annual income ÷ $10,000 × years worked)", "dollars": "real (today's dollars); the engine deflates every reported value by its inflation path", "success": "a path counts as a success when the portfolio never reaches $0 before 95; the terminal value of a ruined path is $0", "checks": { "baseline_equals_itself": { "pA_base": { "max_abs_diff": 0, "share_tied": 1 }, "pB_base": { "max_abs_diff": 0, "share_tied": 1 } }, "starting_wealth_as_designed": true, "income_event_echo": [ { "arm": "pA_i10000_y5", "monthly_amount": 833.3333333333334, "month_start": 0, "month_end": 60, "inflation_category": "cpi" }, { "arm": "pA_i20000_y5", "monthly_amount": 1666.6666666666667, "month_start": 0, "month_end": 60, "inflation_category": "cpi" }, { "arm": "pA_i30000_y5", "monthly_amount": 2500, "month_start": 0, "month_end": 60, "inflation_category": "cpi" }, { "arm": "pA_i10000_y10", "monthly_amount": 833.3333333333334, "month_start": 0, "month_end": 120, "inflation_category": "cpi" }, { "arm": "pA_i20000_y10", "monthly_amount": 1666.6666666666667, "month_start": 0, "month_end": 120, "inflation_category": "cpi" }, { "arm": "pA_i30000_y10", "monthly_amount": 2500, "month_start": 0, "month_end": 120, "inflation_category": "cpi" }, { "arm": "pB_i10000_y5", "monthly_amount": 833.3333333333334, "month_start": 0, "month_end": 60, "inflation_category": "cpi" }, { "arm": "pB_i20000_y5", "monthly_amount": 1666.6666666666667, "month_start": 0, "month_end": 60, "inflation_category": "cpi" }, { "arm": "pB_i30000_y5", "monthly_amount": 2500, "month_start": 0, "month_end": 60, "inflation_category": "cpi" }, { "arm": "pB_i10000_y10", "monthly_amount": 833.3333333333334, "month_start": 0, "month_end": 120, "inflation_category": "cpi" }, { "arm": "pB_i20000_y10", "monthly_amount": 1666.6666666666667, "month_start": 0, "month_end": 120, "inflation_category": "cpi" }, { "arm": "pB_i30000_y10", "monthly_amount": 2500, "month_start": 0, "month_end": 120, "inflation_category": "cpi" } ], "duration_identity": [ { "persona": "A", "income": 10000, "identical_years": 5, "differ_from_year": 6, "live_paths_year6": 10000 }, { "persona": "A", "income": 20000, "identical_years": 5, "differ_from_year": 6, "live_paths_year6": 10000 }, { "persona": "A", "income": 30000, "identical_years": 5, "differ_from_year": 6, "live_paths_year6": 10000 }, { "persona": "B", "income": 10000, "identical_years": 5, "differ_from_year": 6, "live_paths_year6": 10000 }, { "persona": "B", "income": 20000, "identical_years": 5, "differ_from_year": 6, "live_paths_year6": 10000 }, { "persona": "B", "income": 30000, "identical_years": 5, "differ_from_year": 6, "live_paths_year6": 10000 } ], "zero_return_identity": { "row0": { "five_year_terminal_gap": 50000.00000000931, "ten_year_terminal_gap": 100000.00000001863, "lump_terminal_gap": 50000, "five_year_year1_gap": 10000.000000001863, "baseline_year1": 2944999.999999998 }, "baseline_terminal_row0": 1583999.9999999776, "baseline_terminal_expected": 1584000, "tolerance": 0.01, "volatility_floor": 0.0001, "max_gap_from_lump_rows_1_to_29": 46.004830556456 }, "linearity": [ { "persona": "A", "years": 5, "surviving_baseline_paths": 8933, "max_relative_deviation": 2.464886342065132e-13 }, { "persona": "A", "years": 10, "surviving_baseline_paths": 8933, "max_relative_deviation": 1.938117089079166e-13 }, { "persona": "B", "years": 5, "surviving_baseline_paths": 6736, "max_relative_deviation": 1.7035374197320887e-13 }, { "persona": "B", "years": 10, "surviving_baseline_paths": 6736, "max_relative_deviation": 1.1409585190560748e-13 } ], "never_lower_with_income": true, "determinism": { "arm": "pA_i10000_y5", "seed": 210, "n": 30, "identical": true }, "engine_ruin_count_matches_terminal_gt_zero": true, "batched_equals_single_call": { "arms": 16, "max_gap": 0 } } }, "cells": [ { "persona": "A", "starting_wealth": 1200000, "arm": "baseline", "income_annual_real": null, "years_of_work": null, "work_start_age": null, "work_end_age": null, "total_income_real": null, "ten_k_years": null, "lump_added_at_55": null, "is_baseline": true, "result": { "success_rate": 0.8933, "success_ci95": [ 0.887097108487552, 0.8992008272974366 ], "terminal_real": { "p5": 0, "p10": 0, "p25": 562053.3653452836, "p50": 1648751.6477969878, "p75": 3481045.5199848474, "p90": 6311412.378682064, "p95": 8549956.992550796, "mean": 2652375.4239962883 } }, "baseline_result": { "success_rate": 0.8933, "terminal_real": { "p5": 0, "p10": 0, "p25": 562053.3653452836, "p50": 1648751.6477969878, "p75": 3481045.5199848474, "p90": 6311412.378682064, "p95": 8549956.992550796, "mean": 2652375.4239962883 } }, "success_gain_pp": 0, "success_gain_pp_per_10k_year": null, "paired_vs_baseline": { "median_diff": 0, "p10_diff": 0, "p25_diff": 0, "p75_diff": 0, "p90_diff": 0, "mean_diff": 0, "share_higher": 0, "share_lower": 0, "share_tied": 1, "a_survives_b_fails": 0, "b_survives_a_fails": 0, "both_fail": 1067, "by_year": [ { "year": 1, "age": 56, "median_diff": 0, "p10_diff": 0, "p90_diff": 0, "mean_diff": 0, "share_higher": 0 }, { "year": 2, "age": 57, "median_diff": 0, "p10_diff": 0, "p90_diff": 0, "mean_diff": 0, "share_higher": 0 }, { "year": 3, "age": 58, "median_diff": 0, "p10_diff": 0, "p90_diff": 0, "mean_diff": 0, "share_higher": 0 }, { "year": 4, "age": 59, "median_diff": 0, "p10_diff": 0, "p90_diff": 0, "mean_diff": 0, "share_higher": 0 }, { "year": 5, "age": 60, "median_diff": 0, "p10_diff": 0, "p90_diff": 0, "mean_diff": 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