Mimicking Portfolio

v1.0.0

Construct a portfolio as close as possible, in terms of returns, to a benchmark, optionally subject to:

Minimum and maximum weights constraints
Maximum group weights constraints
Minimum and maximum portfolio exposure constraints

References

Konstantinos Benidis, Yiyong Feng, Daniel P. Palomar, Optimization Methods for Financial Index Tracking: From Theory to Practice, now publishers Inc (7 juin 2018)

Input

{
  "type": "object",
  "required": [
    "assets",
    "benchmarkReturns"
  ],
  "properties": {
    "assets": {
      "type": "array",
      "items": {
        "type": "object",
        "required": [
          "assetReturns"
        ],
        "properties": {
          "assetReturns": {
            "type": "array",
            "description": "assetReturns[t] is the return of the asset at the time t; all the assetReturns arrays must have the same length",
            "items": {
              "type": "number"
            }
          }
        }
      }
    },
    "benchmarkReturns": {
      "type": "array",
      "description": "benchmarkReturns[t] is the return of the benchmark at the time t; the benchmarkReturns array must have the same length as all the assetReturns arrays",
      "items": {
        "type": "number"
      }
    },
    "constraints": {
      "type": "object",
      "properties": {
        "assetsGroups": {
          "type": "array",
          "items": {
            "type": "array",
            "description": "assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix",
            "items": {
              "type": "integer"
            }
          }
        },
        "assetsGroupsMatrix": {
          "type": "array",
          "description": "assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups",
          "items": {
            "type": "array",
            "items": {
              "type": "number"
            }
          }
        },
        "maximumAssetsGroupsWeights": {
          "type": "array",
          "description": "maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided",
          "items": {
            "type": "number"
          }
        },
        "maximumAssetsWeights": {
          "type": "array",
          "description": "maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage",
          "items": {
            "type": "number"
          }
        },
        "maximumPortfolioExposure": {
          "type": "number",
          "description": "The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure"
        },
        "minimumAssetsWeights": {
          "type": "array",
          "description": "minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage",
          "items": {
            "type": "number"
          }
        },
        "minimumPortfolioExposure": {
          "type": "number",
          "description": "The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure"
        }
      }
    }
  }
}

Output

{
  "type": "object",
  "required": [
    "assetsWeights"
  ],
  "properties": {
    "assetsWeights": {
      "type": "array",
      "description": "assetsWeights[i] is the weight of the asset i in the portfolio, in percentage",
      "items": {
        "type": "number"
      }
    }
  }
}