{
  "version": "2026.1",
  "generated_at": "2026-09-08",
  "generated_by": "scripts/gen_sequence_defenses_study.mjs",
  "study": "bond-tent-vs-bucket-vs-guardrails-2026",
  "url": "https://quantcalc.app/research/bond-tent-vs-bucket-vs-guardrails-2026/",
  "license": "CC-BY-4.0",
  "method": {
    "engine": "QuantCalc C Monte Carlo engine (quantcalc-server 2.0.0): multi-period glide path, bucket withdrawal rule and Guyton-Klinger guardrails against a constant 60/40 level-spending control 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_allocation": [
        0.45,
        0.15,
        0.4,
        0,
        0
      ],
      "inflation_rate": 0.025,
      "social_security": 0,
      "pension": 0,
      "taxes": "pre-tax"
    },
    "arms": [
      {
        "key": "control",
        "kind": "fixed",
        "rebalance": "monthly",
        "label": "Constant 60/40 (control)",
        "bucket_years": null
      },
      {
        "key": "tent60",
        "kind": "glide",
        "rebalance": "monthly",
        "label": "Bond tent to 60/40",
        "bucket_years": null
      },
      {
        "key": "tent70",
        "kind": "glide",
        "rebalance": "monthly",
        "label": "Bond tent to 70/30",
        "bucket_years": null
      },
      {
        "key": "bucket3",
        "kind": "bucket",
        "rebalance": "annual",
        "label": "3-year cash bucket",
        "bucket_years": 3
      },
      {
        "key": "matched3",
        "kind": "matched",
        "rebalance": "annual",
        "label": "Matched-cash control for the 3-year bucket",
        "bucket_years": 3
      },
      {
        "key": "bucket5",
        "kind": "bucket",
        "rebalance": "annual",
        "label": "5-year cash bucket",
        "bucket_years": 5
      },
      {
        "key": "matched5",
        "kind": "matched",
        "rebalance": "annual",
        "label": "Matched-cash control for the 5-year bucket",
        "bucket_years": 5
      },
      {
        "key": "gk",
        "kind": "gk",
        "rebalance": "monthly",
        "label": "Guardrails (Guyton-Klinger)",
        "bucket_years": null
      },
      {
        "key": "control_annual",
        "kind": "fixed",
        "rebalance": "annual",
        "label": "Constant 60/40, annual rebalance",
        "bucket_years": null
      }
    ],
    "tents": [
      {
        "key": "tent60",
        "label": "Bond tent to 60/40",
        "steps": [
          [
            2,
            0.4
          ],
          [
            5,
            0.45
          ],
          [
            8,
            0.5
          ],
          [
            10,
            0.55
          ],
          [
            30,
            0.6
          ]
        ],
        "periods": [
          {
            "end_year": 2,
            "allocations": [
              0.30000000000000004,
              0.1,
              0.6,
              0,
              0
            ]
          },
          {
            "end_year": 5,
            "allocations": [
              0.3375,
              0.1125,
              0.55,
              0,
              0
            ]
          },
          {
            "end_year": 8,
            "allocations": [
              0.375,
              0.125,
              0.5,
              0,
              0
            ]
          },
          {
            "end_year": 10,
            "allocations": [
              0.41250000000000003,
              0.1375,
              0.44999999999999996,
              0,
              0
            ]
          },
          {
            "end_year": 30,
            "allocations": [
              0.44999999999999996,
              0.15,
              0.4,
              0,
              0
            ]
          }
        ],
        "mean_equity_share": 0.5583333333333333
      },
      {
        "key": "tent70",
        "label": "Bond tent to 70/30",
        "steps": [
          [
            2,
            0.4
          ],
          [
            5,
            0.475
          ],
          [
            8,
            0.55
          ],
          [
            10,
            0.625
          ],
          [
            30,
            0.7
          ]
        ],
        "periods": [
          {
            "end_year": 2,
            "allocations": [
              0.30000000000000004,
              0.1,
              0.6,
              0,
              0
            ]
          },
          {
            "end_year": 5,
            "allocations": [
              0.35624999999999996,
              0.11875,
              0.525,
              0,
              0
            ]
          },
          {
            "end_year": 8,
            "allocations": [
              0.41250000000000003,
              0.1375,
              0.44999999999999996,
              0,
              0
            ]
          },
          {
            "end_year": 10,
            "allocations": [
              0.46875,
              0.15625,
              0.375,
              0,
              0
            ]
          },
          {
            "end_year": 30,
            "allocations": [
              0.5249999999999999,
              0.175,
              0.30000000000000004,
              0,
              0
            ]
          }
        ],
        "mean_equity_share": 0.6375
      }
    ],
    "bucket": {
      "years": [
        3,
        5
      ],
      "refill": "annual_if_positive",
      "matched_control": "plan mix × (1 − share₀) plus share₀ in the cash asset, share₀ = bucket years × annual spending ÷ capital, rebalanced annually (backend/src/monte_carlo.h)"
    },
    "guardrails": {
      "guard_hi": 1.2,
      "guard_lo": 0.8,
      "adjust": 0.1,
      "cpr_min_years_remaining": 15
    },
    "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; the guardrails arms are also run as 10,000 single-path calls (n = 1 reads row s) to obtain each path's realised spending",
    "deciles": "paths ranked by the first-decade real CAGR of the constant 60/40 portfolio with no withdrawals (year-10 real wealth ÷ starting wealth, tenth root), split into ten groups of 1,000; decile 1 is the worst first decade — the sequence-of-returns study's definition",
    "paired_statistic": "per path: arm terminal real wealth − control terminal real wealth on the same market path; reported as median, p10, p90, mean, share of paths the arm ends higher and survival crossovers, at age 95 and by year",
    "realised_spending": "guardrails only: each path's average annual real spending over the 30 retirement years and its 30-year spending series, from one single-path engine call per path; level-spending arms spend the plan on every path",
    "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": {
      "flat_glide_identity": {
        "max_relative_gap": 0,
        "success_rate_both": 0.8712,
        "note": "a five-period glide path that is 60/40 in every period reproduces the constant 60/40 control path by path (monthly rebalance in both code paths)"
      },
      "determinism": {
        "arm": "s40000_gk",
        "seed": 210,
        "n": 30,
        "identical": true
      },
      "engine_ruin_count_matches_terminal_gt_zero": true,
      "batched_equals_single_call": {
        "arms": 28,
        "max_gap": 0
      },
      "start_identity": {
        "gk_vs_control_year1_max_relative_gap": 1.729694588122977e-15,
        "withdrawing_arms_below_no_draw_year1": true,
        "note": "guardrails cannot adjust before the first anniversary, so its year-1 wealth equals the control; every fully-invested monthly-rebalanced withdrawing 60/40 arm (control, guardrails) ends year 1 below the no-withdrawal arm on every path"
      },
      "bucket_study_reproduction": {
        "source": "research/data/bucket-strategy-study-2026-09.json",
        "source_run_at": "2026-09-06T22:39:23.695Z",
        "cells": [
          {
            "spend": 35000,
            "bucket_years": 3,
            "bucket_study": {
              "bucket_success": 0.9406,
              "bucket_median": 925579.7890822752,
              "matched_success": 0.9481,
              "matched_median": 913839.1474359167,
              "paired_median": 19478.40901845321,
              "share_higher": 0.6576
            },
            "this_study": {
              "bucket_success": 0.9406,
              "bucket_median": 925579.7890822752,
              "matched_success": 0.9481,
              "matched_median": 913839.1474359167,
              "paired_median": 19478.40901845321,
              "share_higher": 0.6576
            }
          },
          {
            "spend": 35000,
            "bucket_years": 5,
            "bucket_study": {
              "bucket_success": 0.9379,
              "bucket_median": 812088.5926173524,
              "matched_success": 0.9527,
              "matched_median": 830549.1691891538,
              "paired_median": 3571.157033205731,
              "share_higher": 0.5235
            },
            "this_study": {
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              "matched_success": 0.9527,
              "matched_median": 830549.1691891538,
              "paired_median": 3571.157033205731,
              "share_higher": 0.5235
            }
          },
          {
            "spend": 40000,
            "bucket_years": 3,
            "bucket_study": {
              "bucket_success": 0.852,
              "bucket_median": 629937.569484335,
              "matched_success": 0.8697,
              "matched_median": 634170.4866232636,
              "paired_median": 10704.805717655923,
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            },
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          },
          {
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            "bucket_study": {
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              "matched_success": 0.8684,
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              "paired_median": 0,
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          },
          {
            "spend": 45000,
            "bucket_years": 3,
            "bucket_study": {
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              "bucket_median": 204208.19678626224,
              "matched_success": 0.7118,
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        ],
        "max_gap": 0
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      "periods_key_honoured": true
    }
  },
  "first_decade_cagr": {
    "all": {
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      "p10": -0.0024712788795695495,
      "p25": 0.015862054626514244,
      "p50": 0.03745037032026022,
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      "p95": 0.09203711677654969,
      "mean": 0.03790463705250873
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    "deciles": [
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        "decile": 1,
        "mean_cagr": -0.01669235947742122,
        "min_cagr": -0.07274648481819024,
        "max_cagr": -0.0024712788795695495
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      "spend": 35000,
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      "success_annual": 0.9413,
      "paired_annual_minus_monthly": {
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      "kind": "fixed",
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      "success_rate": 0.9417,
      "success_ci95": [
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