action portfoliooptimizer_post_portfolio_analysis_factors_exposures {
  label: "Factor Exposures"
  description: "Compute the exposures of one or several portfolio(s) to a set of factors, using a returns-based linear regression analysis.\n\nReferences\n* [Measuring Factor Exposures: Uses and Abuses, Ronen Israel and Adrienne Ross, The Journal of Alternative Investments Summer 2017, 20 (1) 10-25](https://jai.pm-research.com/content/20/1/10.short) \n"
  provider: portfoliooptimizer
  method: POST
  path: "/portfolio/analysis/factors/exposures"
  encoding: json
  input: {
    type: "object"
    required: ["factorReturns", "portfolios"]
    properties: {
      factors: {
        type: "array"
        items: {
          type: "object"
          required: ["factorReturns"]
          properties: {
            factorReturns: {
              type: "array"
              description: "factorReturns[t] is the return of the factor at the time t; all the factorReturns arrays must have the same length, equal to the common length of the portfolioReturns arrays"
              items: {
                type: "number"
              }
            }
          }
        }
      }
      portfolios: {
        type: "array"
        items: {
          type: "object"
          required: ["portfolioReturns"]
          properties: {
            portfolioReturns: {
              type: "array"
              description: "portfolioReturns[t] is the return of the portfolio at the time t, all the portfolioReturns arrays must have the same length, equal to the common length of the factorReturns arrays"
              items: {
                type: "number"
              }
            }
          }
        }
      }
    }
  }
  output: {
    type: "object"
    required: ["portfolios"]
    properties: {
      portfolios: {
        type: "array"
        items: {
          type: "object"
          required: ["portfolioAlpha", "portfolioBetas", "portfolioRSquared"]
          properties: {
            portfolioAlpha: {
              type: "number"
              description: "The portfolio alpha, which correponds to the portion of the portfolio returns that cannot be explained by the portfolio factor exposures"
            }
            portfolioBetas: {
              type: "array"
              description: "The portfolio betas, which correspond to the portfolio factor exposures"
              items: {
                type: "number"
              }
            }
            portfolioRSquared: {
              type: "number"
              description: "The portfolio R^2, which indicates how much of the variability in the portfolio returns can be explained by the portfolio factor exposures; generally, the higher the R^2 the better the portfolio factor exposures explain the portfolio returns"
            }
          }
        }
      }
    }
  }
}