> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Black-Litterman Equilibrium Returns

> Computes market equilibrium (implied) returns using reverse optimization from market capitalizations. These returns represent the market's consensus expectations implied by current market weights.

**Use Cases:**
- Deriving implied returns from market capitalization weights
- Starting point for Black-Litterman optimization
- Calibrating expected returns to market consensus
- Understanding market-implied risk premia

**Mathematical Background:**
Π = δ × Σ × w_mkt

Where Π is equilibrium returns, δ is risk aversion, Σ is covariance, and w_mkt are market cap weights.

**Credits:** 5 per request [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/portfolio.json post /quantlib/portfolio/black-litterman/equilibrium
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Portfolio
  description: >-
    Portfolio optimization and risk management module for institutional-grade
    portfolio construction, analysis, and monitoring. Includes mean-variance
    optimization, Black-Litterman, risk parity, and comprehensive risk metrics.


    **Tier:** Pro (5 credits per request)


    **Key Features:**

    - Mean-variance optimization (minimum variance, maximum Sharpe, target
    return)

    - Efficient frontier construction with tangency portfolio identification

    - Black-Litterman model for Bayesian view incorporation

    - Risk parity strategies (ERC, HRP, inverse volatility)

    - Comprehensive risk metrics (VaR, CVaR, tracking error, information ratio)

    - Advanced portfolio analytics (risk contribution, drawdown,
    diversification)
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-portfolio
    description: Portfolio optimization and risk management endpoints
    x-displayName: Portfolio
paths:
  /quantlib/portfolio/black-litterman/equilibrium:
    post:
      tags:
        - quantlib-portfolio
      summary: Black-Litterman Equilibrium Returns
      description: >-
        Computes market equilibrium (implied) returns using reverse optimization
        from market capitalizations. These returns represent the market's
        consensus expectations implied by current market weights.


        **Use Cases:**

        - Deriving implied returns from market capitalization weights

        - Starting point for Black-Litterman optimization

        - Calibrating expected returns to market consensus

        - Understanding market-implied risk premia


        **Mathematical Background:**

        Π = δ × Σ × w_mkt


        Where Π is equilibrium returns, δ is risk aversion, Σ is covariance, and
        w_mkt are market cap weights.


        **Credits:** 5 per request [Tier: PRO, Credits: 5]
      operationId: bl_equilibrium
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - covariance_matrix
                - market_caps
              properties:
                covariance_matrix:
                  type: array
                  items:
                    type: array
                    items:
                      type: number
                  description: Asset covariance matrix (annualized)
                  example:
                    - - 0.04
                      - 0.006
                      - 0.008
                      - 0.01
                    - - 0.006
                      - 0.09
                      - 0.012
                      - 0.015
                    - - 0.008
                      - 0.012
                      - 0.0625
                      - 0.018
                    - - 0.01
                      - 0.015
                      - 0.018
                      - 0.16
                market_caps:
                  type: array
                  items:
                    type: number
                  description: >-
                    Market capitalizations for each asset (in any consistent
                    currency unit). Will be normalized to weights.
                  example:
                    - 5000000000
                    - 3000000000
                    - 2000000000
                    - 1000000000
                risk_aversion:
                  type: number
                  description: >-
                    Market risk aversion parameter (δ). Typical values range
                    from 2.0 to 4.0. Higher values imply more conservative risk
                    preferences.
                  default: 2.5
                  example: 2.5
                  minimum: 0.1
                  maximum: 10
      responses:
        '200':
          description: Equilibrium returns successfully computed
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      equilibrium_returns:
                        type: array
                        items:
                          type: number
                        description: Market-implied equilibrium returns (annualized)
                        example:
                          - 0.075
                          - 0.115
                          - 0.095
                          - 0.145
                      risk_aversion:
                        type: number
                        description: Risk aversion parameter used
                        example: 2.5
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient API credits
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Insufficient credits. This endpoint requires 5 credits.
    ValidationError:
      description: Request validation error
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: array
                items:
                  type: object
                  properties:
                    loc:
                      type: array
                      items:
                        type: string
                    msg:
                      type: string
                    type:
                      type: string
          example:
            detail:
              - loc:
                  - body
                  - expected_returns
                msg: field required
                type: value_error.missing
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````