Correlation Matrix Distance

v1.0.0

Compute the distance between an asset correlation matrix and a reference correlation matrix, using one of the following distance metrics:

Euclidean distance (default), which is the distance induced by
Correlation matrix distance, defined in the first reference, which corresponds to between the two vectorized asset correlation matrices
Bures distance, defined in the second reference

References

Input

{
  "required": [
    "assets",
    "assetsCorrelationMatrix",
    "referenceCorrelationMatrix"
  ],
  "properties": {
    "assets": {
      "type": "integer"
    },
    "assetsCorrelationMatrix": {
      "type": "array",
      "description": "assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      }
    },
    "distanceMetric": {
      "type": "string",
      "description": "The distance metric to use to compute the distance between the asset correlation matrix and the reference correlation matrix",
      "enum": [
        "euclidean",
        "correlationMatrix",
        "bures"
      ]
    },
    "referenceCorrelationMatrix": {
      "type": "array",
      "description": "referenceCorrelationMatrix[i][j] is the reference correlation between the asset i and the asset j",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      }
    }
  }
}

Output

{
  "type": "object",
  "required": [
    "assetsCorrelationMatrixDistance"
  ],
  "properties": {
    "assetsCorrelationMatrixDistance": {
      "type": "number",
      "description": "The computed distance between the two correlation matrices"
    }
  }
}