Factor Exposures

v1.0.0

Compute the exposures of one or several portfolio(s) to a set of factors, using a returns-based linear regression analysis.

References

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"
          }
        }
      }
    }
  }
}