{
  "slug": "leva-raddoppia-rendimento-mercato",
  "period": {
    "start": "1976-01-05",
    "end": "2025-12-30",
    "n_days": 12603
  },
  "params": {
    "leverages": [
      1,
      2,
      3
    ],
    "rolling_step_months": 3,
    "windows_months": {
      "5y": 60,
      "10y": 120,
      "20y": 240
    },
    "rebalancing": "daily"
  },
  "calibration": {
    "method": "Empirical drag from ProShares SSO (real 2x ETF) vs synthetic 2x, decomposed into TER + funding cost. Funding then applied to UCITS TERs.",
    "ter_sso_proshares": 0.0089,
    "ter_ucits": {
      "1": 0.0005,
      "2": 0.006,
      "3": 0.0075
    },
    "sso_calibration_result": {
      "years": 17.522245037645447,
      "cagr_real_2x": 0.1317354772755024,
      "cagr_synth_2x": 0.16321210365853367,
      "drag_total_2x": 0.027432958070858212,
      "ter_sso": 0.0089,
      "funding_cost": 0.01853295807085821,
      "drag_ucits_per_lev": {
        "1": 0.0005,
        "2": 0.02453295807085821,
        "3": 0.04456591614171642
      },
      "calibration_period": {
        "start": "2006-06-21",
        "end": "2023-12-29"
      }
    },
    "applied_drag_annual_ucits": {
      "1": 0.0005,
      "2": 0.02453295807085821,
      "3": 0.04456591614171642
    }
  },
  "underlying_volatility_annual": 0.17406149573525315,
  "scenarios": {
    "gross": {
      "description": "No TER, no funding cost \u2014 leva matematicamente pura.",
      "full_sample": {
        "1": {
          "cagr": 0.11840317548932178,
          "mdd": -0.5525983172081748,
          "vol": 0.17406149573525315,
          "theoretical_drag_annual": 0.0,
          "applied_drag_annual": 0.0
        },
        "2": {
          "cagr": 0.21258742344101167,
          "mdd": -0.8374195642789228,
          "vol": 0.3481229914705063,
          "theoretical_drag_annual": 0.03029740429759355,
          "applied_drag_annual": 0.0
        },
        "3": {
          "cagr": 0.2724368481376893,
          "mdd": -0.9626669684697273,
          "vol": 0.5221844872057594,
          "theoretical_drag_annual": 0.09089221289278065,
          "applied_drag_annual": 0.0
        }
      },
      "rolling_percentiles": {
        "5y": {
          "1": {
            "cagr": {
              "p5": -0.018095554378061873,
              "p25": 0.07985316691085087,
              "p50": 0.13837078903011713,
              "p75": 0.1623331041106868,
              "p95": 0.23597441722904988
            },
            "mdd": {
              "p5": -0.5525983172081748,
              "p25": -0.3379638805741829,
              "p50": -0.24534563255804287,
              "p75": -0.18706396135444725,
              "p95": -0.10715353341924372
            },
            "n_windows": 181,
            "share_negative_cagr": 0.09944751381215469,
            "share_dd_worse_50pct": 0.09944751381215469,
            "share_dd_worse_75pct": 0.0
          },
          "2": {
            "cagr": {
              "p5": -0.08087917460462224,
              "p25": 0.13560424818444594,
              "p50": 0.252459913897384,
              "p75": 0.3147243648821705,
              "p95": 0.4913958868287376
            },
            "mdd": {
              "p5": -0.8374195642789225,
              "p25": -0.5963438058459253,
              "p50": -0.45599523121606655,
              "p75": -0.35422987642007464,
              "p95": -0.2081729728974412
            },
            "n_windows": 181,
            "share_negative_cagr": 0.1712707182320442,
            "share_dd_worse_50pct": 0.46408839779005523,
            "share_dd_worse_75pct": 0.16574585635359115
          },
          "3": {
            "cagr": {
              "p5": -0.18602485089432574,
              "p25": 0.1396894482096096,
              "p50": 0.3306117513484379,
              "p75": 0.4506114908935095,
              "p95": 0.780310554245649
            },
            "mdd": {
              "p5": -0.9524094990266784,
              "p25": -0.7948962616010488,
              "p50": -0.6257366047682398,
              "p75": -0.4895333223500278,
              "p95": -0.3031092920713838
            },
            "n_windows": 181,
            "share_negative_cagr": 0.19337016574585636,
            "share_dd_worse_50pct": 0.6961325966850829,
            "share_dd_worse_75pct": 0.4419889502762431
          }
        },
        "10y": {
          "1": {
            "cagr": {
              "p5": 0.01685917815848814,
              "p25": 0.08031795175009937,
              "p50": 0.1289511840301374,
              "p75": 0.14979633990218888,
              "p95": 0.18042744329478833
            },
            "mdd": {
              "p5": -0.5525983172081752,
              "p25": -0.47415335962415994,
              "p50": -0.3379638805741827,
              "p75": -0.32958070309432896,
              "p95": -0.1920353947941954
            },
            "n_windows": 161,
            "share_negative_cagr": 0.049689440993788817,
            "share_dd_worse_50pct": 0.2360248447204969,
            "share_dd_worse_75pct": 0.0
          },
          "2": {
            "cagr": {
              "p5": -0.014296391262485608,
              "p25": 0.11873839124755659,
              "p50": 0.23867450407522872,
              "p75": 0.2860953699796338,
              "p95": 0.3624978626873958
            },
            "mdd": {
              "p5": -0.8374195642789226,
              "p25": -0.7577554098720481,
              "p50": -0.5963438058459253,
              "p75": -0.5906369972603748,
              "p95": -0.3569377185789885
            },
            "n_windows": 161,
            "share_negative_cagr": 0.055900621118012424,
            "share_dd_worse_50pct": 0.8260869565217391,
            "share_dd_worse_75pct": 0.391304347826087
          },
          "3": {
            "cagr": {
              "p5": -0.08982057186302539,
              "p25": 0.11093964063139694,
              "p50": 0.31769584066473544,
              "p75": 0.39886441288013885,
              "p95": 0.5431669465995264
            },
            "mdd": {
              "p5": -0.9524094990266785,
              "p25": -0.9025186116371565,
              "p50": -0.7948962616010489,
              "p75": -0.7659283807265098,
              "p95": -0.5024999478254333
            },
            "n_windows": 161,
            "share_negative_cagr": 0.10559006211180125,
            "share_dd_worse_50pct": 0.9751552795031055,
            "share_dd_worse_75pct": 0.8260869565217391
          }
        },
        "20y": {
          "1": {
            "cagr": {
              "p5": 0.06288441487756247,
              "p25": 0.08241857254755014,
              "p50": 0.09947303292113951,
              "p75": 0.13044255318325737,
              "p95": 0.17310279427419561
            },
            "mdd": {
              "p5": -0.5525983172081755,
              "p25": -0.552598317208175,
              "p50": -0.5525983172081745,
              "p75": -0.4741533596241585,
              "p95": -0.32958070309432896
            },
            "n_windows": 121,
            "share_negative_cagr": 0.0,
            "share_dd_worse_50pct": 0.5702479338842975,
            "share_dd_worse_75pct": 0.0
          },
          "2": {
            "cagr": {
              "p5": 0.0873694532568976,
              "p25": 0.12902494823098332,
              "p50": 0.16644372683524367,
              "p75": 0.24002453768003273,
              "p95": 0.3436201007726931
            },
            "mdd": {
              "p5": -0.8374195642789228,
              "p25": -0.8374195642789225,
              "p50": -0.8374195642789224,
              "p75": -0.7577554098720478,
              "p95": -0.5963438058459252
            },
            "n_windows": 121,
            "share_negative_cagr": 0.0,
            "share_dd_worse_50pct": 1.0,
            "share_dd_worse_75pct": 0.768595041322314
          },
          "3": {
            "cagr": {
              "p5": 0.07106052987672773,
              "p25": 0.134926339167744,
              "p50": 0.19062297226252434,
              "p75": 0.31573702413380667,
              "p95": 0.4979107749214622
            },
            "mdd": {
              "p5": -0.9626669684697273,
              "p25": -0.9626669684697272,
              "p50": -0.9524094990266784,
              "p75": -0.9025186116371562,
              "p95": -0.7948962616010488
            },
            "n_windows": 121,
            "share_negative_cagr": 0.0,
            "share_dd_worse_50pct": 1.0,
            "share_dd_worse_75pct": 1.0
          }
        }
      }
    },
    "realistic": {
      "description": "Drag annualizzato calibrato da ETF UCITS reali (WisdomTree 1x/3x, Xtrackers 2x) sui calendar year 2024-2025.",
      "full_sample": {
        "1": {
          "cagr": 0.11784437160176076,
          "mdd": -0.5529141455659166,
          "vol": 0.17406149573525315,
          "theoretical_drag_annual": 0.0,
          "applied_drag_annual": 0.0005
        },
        "2": {
          "cagr": 0.18321685500552598,
          "mdd": -0.8607473335092763,
          "vol": 0.3481229914705063,
          "theoretical_drag_annual": 0.03029740429759355,
          "applied_drag_annual": 0.02453295807085821
        },
        "3": {
          "cagr": 0.21699396104033752,
          "mdd": -0.9749468768226699,
          "vol": 0.5221844872057594,
          "theoretical_drag_annual": 0.09089221289278065,
          "applied_drag_annual": 0.04456591614171642
        }
      },
      "rolling_percentiles": {
        "5y": {
          "1": {
            "cagr": {
              "p5": -0.018586074635053573,
              "p25": 0.079313949165563,
              "p50": 0.13780243814310644,
              "p75": 0.16175286471478922,
              "p95": 0.2353575542377926
            },
            "mdd": {
              "p5": -0.5529141455659163,
              "p25": -0.33799467676639294,
              "p50": -0.24563801115269424,
              "p75": -0.18723850373571382,
              "p95": -0.10717854089290157
            },
            "n_windows": 181,
            "share_negative_cagr": 0.10497237569060773,
            "share_dd_worse_50pct": 0.09944751381215469,
            "share_dd_worse_75pct": 0.0
          },
          "2": {
            "cagr": {
              "p5": -0.10315163300582997,
              "p25": 0.10810681016555224,
              "p50": 0.22214529433893282,
              "p75": 0.2829178284896827,
              "p95": 0.4553315728577967
            },
            "mdd": {
              "p5": -0.8429768815175769,
              "p25": -0.5991694833214611,
              "p50": -0.4662620419084613,
              "p75": -0.3581448127950966,
              "p95": -0.2092705552298899
            },
            "n_windows": 181,
            "share_negative_cagr": 0.17679558011049723,
            "share_dd_worse_50pct": 0.4696132596685083,
            "share_dd_worse_75pct": 0.1712707182320442
          },
          "3": {
            "cagr": {
              "p5": -0.2215372388269099,
              "p25": 0.0900288455729712,
              "p50": 0.2726791622718061,
              "p75": 0.38749306936338845,
              "p95": 0.7029178093309647
            },
            "mdd": {
              "p5": -0.9554231928717892,
              "p25": -0.7975420096597725,
              "p50": -0.6385006678715119,
              "p75": -0.49516480690208164,
              "p95": -0.30488138464447134
            },
            "n_windows": 181,
            "share_negative_cagr": 0.19889502762430938,
            "share_dd_worse_50pct": 0.7458563535911602,
            "share_dd_worse_75pct": 0.4530386740331492
          }
        },
        "10y": {
          "1": {
            "cagr": {
              "p5": 0.01635106283903376,
              "p25": 0.0797782621493277,
              "p50": 0.12838731631783884,
              "p75": 0.14922209927090768,
              "p95": 0.17983797560836656
            },
            "mdd": {
              "p5": -0.5529141455659166,
              "p25": -0.4747015614075374,
              "p50": -0.33799467676639294,
              "p75": -0.329631824085854,
              "p95": -0.1921351316861255
            },
            "n_windows": 161,
            "share_negative_cagr": 0.049689440993788817,
            "share_dd_worse_50pct": 0.2360248447204969,
            "share_dd_worse_75pct": 0.0
          },
          "2": {
            "cagr": {
              "p5": -0.038186508693004106,
              "p25": 0.09163857451915014,
              "p50": 0.20868324090421786,
              "p75": 0.25496198537804293,
              "p95": 0.32952461214889284
            },
            "mdd": {
              "p5": -0.8429768815175772,
              "p25": -0.7723596623483564,
              "p50": -0.5991694833214611,
              "p75": -0.5915938087620247,
              "p95": -0.36058912073486893
            },
            "n_windows": 161,
            "share_negative_cagr": 0.08695652173913043,
            "share_dd_worse_50pct": 0.8322981366459627,
            "share_dd_worse_75pct": 0.39751552795031053
          },
          "3": {
            "cagr": {
              "p5": -0.1295292168114559,
              "p25": 0.06252319519868155,
              "p50": 0.260306009632582,
              "p75": 0.33794983687495583,
              "p95": 0.4760140285781813
            },
            "mdd": {
              "p5": -0.9595933498252047,
              "p25": -0.9129502523881408,
              "p50": -0.7975420096597725,
              "p75": -0.7669531808832191,
              "p95": -0.5076476169018248
            },
            "n_windows": 161,
            "share_negative_cagr": 0.11180124223602485,
            "share_dd_worse_50pct": 0.9751552795031055,
            "share_dd_worse_75pct": 0.8260869565217391
          }
        },
        "20y": {
          "1": {
            "cagr": {
              "p5": 0.06235330122015226,
              "p25": 0.08187773569988233,
              "p50": 0.09892370897529146,
              "p75": 0.1298778263727307,
              "p95": 0.17251684917100318
            },
            "mdd": {
              "p5": -0.552914145565917,
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              "p50": -0.5529141455659159,
              "p75": -0.4747015614075363,
              "p95": -0.329631824085854
            },
            "n_windows": 121,
            "share_negative_cagr": 0.0,
            "share_dd_worse_50pct": 0.5702479338842975,
            "share_dd_worse_75pct": 0.0
          },
          "2": {
            "cagr": {
              "p5": 0.06102189897666843,
              "p25": 0.10167271231855524,
              "p50": 0.13818856955781667,
              "p75": 0.20999570146007507,
              "p95": 0.31109437270687224
            },
            "mdd": {
              "p5": -0.8607473335092763,
              "p25": -0.8607473335092759,
              "p50": -0.8429768815175769,
              "p75": -0.7723596623483556,
              "p95": -0.5991694833214609
            },
            "n_windows": 121,
            "share_negative_cagr": 0.0,
            "share_dd_worse_50pct": 1.0,
            "share_dd_worse_75pct": 0.7768595041322314
          },
          "3": {
            "cagr": {
              "p5": 0.024363550406281353,
              "p25": 0.0854527906489404,
              "p50": 0.13873298934819744,
              "p75": 0.25842058988101013,
              "p95": 0.43269842567340255
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            "mdd": {
              "p5": -0.97494687682267,
              "p25": -0.9749468768226699,
              "p50": -0.9554231928717892,
              "p75": -0.9129502523881404,
              "p95": -0.7975420096597725
            },
            "n_windows": 121,
            "share_negative_cagr": 0.008264462809917356,
            "share_dd_worse_50pct": 1.0,
            "share_dd_worse_75pct": 1.0
          }
        }
      }
    }
  }
}