{ "version": "2026.1", "generated_at": "2026-09-07", "generated_by": "scripts/gen_bucket_study.mjs", "study": "bucket-strategy-vs-total-return-2026", "url": "https://quantcalc.app/research/bucket-strategy-vs-total-return-2026/", "license": "CC-BY-4.0", "method": { "engine": "QuantCalc C Monte Carlo engine (quantcalc-server 2.0.0), bucket withdrawal rule vs constant-real total return over the public simulate contract", "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": { "capital": 1000000, "retirement_age": 65, "end_age": 95, "horizon_years": 30, "spending_annual_real": [ 35000, 40000, 45000 ], "plan_mixes": [ { "key": "60/40", "allocation": [ 0.45, 0.15, 0.4, 0, 0 ] }, { "key": "80/20", "allocation": [ 0.6, 0.2, 0.2, 0, 0 ] } ], "inflation_rate": 0.025, "social_security": 0, "pension": 0, "taxes": "pre-tax" }, "bucket_arm": "Cash reserve of bucket_years × the year's planned spending carved out of the portfolio at retirement and invested in the roster's cash asset; spending drawn from cash first, then pro rata from the growth bucket; year-end refill per rule; growth bucket rebalanced annually to the plan mix.", "refill_rules": { "annual_if_positive": "refill to target at year end only if the growth bucket's nominal return that year was ≥ 0", "when_below_half": "refill to target at year end whenever the reserve is below half its target, whatever the year's return" }, "total_return_arm": "Constant-real withdrawal from a portfolio whose starting mix is the plan mix × (1 − share₀) plus share₀ in the cash asset, share₀ = bucket_years × annual spending ÷ capital, rebalanced annually; both arms hold the same initial cash.", "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: bucket terminal real wealth − total-return terminal real wealth on the same market path; reported as median, p10, p90, mean, and the share of paths where the bucket arm ends higher", "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 during retirement; the terminal value of a ruined path is $0", "checks": { "cash_identity": { "max_relative_gap": 5.327666569394003e-10, "success_rate_both": 0.0021, "note": "100%-cash plan mix: bucket arm and total-return baseline are the same portfolio, so per-path yearly values must agree" }, "determinism": { "arm": "s40000_m60-40_b3_annual_if_positive", "seed": 210, "n": 30, "identical": true }, "engine_ruin_count_matches_terminal_gt_zero": true, "batched_equals_single_call": { "arms": 54, "max_gap": 0 }, "share0_identity": true } }, "cells": [ { "spending_annual_real": 35000, "spending_rate": 0.035, "plan_mix": "60/40", "plan_allocation": [ 0.45, 0.15, 0.4, 0, 0 ], "bucket_years": 2, "refill_rule": "annual_if_positive", "initial_cash_share": 0.07, "bucket": { "success_rate": 0.9408, "success_ci95": [ 0.9360029452780613, 0.9452585093215397 ], "terminal_real": { "p5": 0, "p10": 127371.42613596372, "p25": 459643.9327650239, "p50": 981839.035877187, "p75": 1760703.790499715, "p90": 2790516.1645243247, "p95": 3599530.6578735923, "mean": 1301006.004518019 } }, "total_return": { "success_rate": 0.9461, "terminal_real": { "p5": 0, "p10": 140962.98362524915, "p25": 462616.5453731296, "p50": 957457.676242119, "p75": 1685748.167786532, "p90": 2621329.883567795, "p95": 3349335.5626895293, "mean": 1238727.193447153 }, "allocation": [ 0.4185, 0.13949999999999999, 0.372, 0, 0.07 ] }, "paired": { "median_diff": 25982.770177268074, "p10_diff": -16087.015051247698, "p25_diff": 0, 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