action portfoliooptimizer_post_portfolio_analysis_mean_variance_efficient_frontier {
  label: "Mean-Variance Efficient Frontier"
  description: "Compute the discretized mean-variance efficient frontier associated to a list of assets, optionally subject to:\n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraint\n\nReferences\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n"
  provider: portfoliooptimizer
  method: POST
  path: "/portfolio/analysis/mean-variance/efficient-frontier"
  encoding: json
  input: {
    type: "object"
    required: ["assets", "assetsCovarianceMatrix", "assetsReturns"]
    properties: {
      assets: {
        type: "integer"
        description: "The number of assets"
      }
      assetsCovarianceMatrix: {
        type: "array"
        description: "assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j"
        items: {
          type: "array"
          items: {
            type: "number"
          }
        }
      }
      assetsReturns: {
        type: "array"
        description: "assetsReturns[i] is the arithmetic return of asset i"
        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"
          }
        }
      }
      portfolios: {
        type: "integer"
        description: "The number of portfolios to compute on the mean-variance efficient frontier"
      }
    }
  }
  output: {
    type: "object"
    required: ["portfolios"]
    properties: {
      portfolios: {
        type: "array"
        items: {
          type: "object"
          required: ["assetsWeights", "portfolioReturn", "portfolioVolatility"]
          properties: {
            assetsWeights: {
              type: "array"
              description: "assetsWeights[i] is the weight of the asset i in the portfolio, in percentage"
              items: {
                type: "number"
              }
            }
            portfolioReturn: {
              type: "number"
              description: "The arithmetic return of the portfolio"
            }
            portfolioVolatility: {
              type: "number"
              description: "The volatility of the portfolio"
            }
          }
        }
      }
    }
  }
}