---
title: "Beta"
method: POST
path: "/portfolios/analysis/beta"
tags: ["Portfolio Analysis / Risk Measures"]
---

# Beta

`POST /portfolios/analysis/beta`

Compute the beta of a portfolio in the Capital Asset Pricing Model (CAPM).

References
* [Sharpe, William F., Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk., The Journal of Finance, vol. 19, no. 3, 1964, pp. 425–42](https://www.jstor.org/stable/2977928)
* [Jensen, Michael C., The Performance of Mutual Funds in the Period 1945-1964 (May 1, 1967). Journal of Finance, Vol. 23, No. 2, pp. 389-416, 1967](https://onlinelibrary.wiley.com/doi/full/10.1111/j.1540-6261.1968.tb00815.x)
* Carl R. Bacon, Practical Portfolio Performance Measurement and Attribution

## Request body

- object
  - `benchmarkReturns` number[], required — benchmarkReturns[t] is the return of the benchmark at the time t; the benchmarkReturns array must have the same length as all the portfolioReturns arrays
  - `riskFreeReturn` number — The constant risk-free arithmetic return over the considered time period, in percentage; exclusive with riskFreeReturns
  - `riskFreeReturns` number[] — riskFreeReturns[t] is the risk-free arithmetic return at the time t; the riskFreeReturns array must have the same length as all the portfolioReturns arrays or the same length minus 1 as all the portfolioValues arrays; exclusive with riskFreeReturn
  - `portfolios` object[], required
    - `portfolioReturns` number[] — portfolioReturns[t] is the arithmetic return of the portfolio at the time t; exclusive with portfolioValues
    - `portfolioValues` number[] — portfolioValues[t] is the value of the portfolio at the time t; exclusive with portfolioReturns
  - `portfoliosBetaEstimationMethod` 'ordinaryLeastSquares' | 'robustLeastSquares' — The method to use to estimate the Jensen’s alpha

## Response `200`

OK

- object
  - `portfolios` object[], required
    - `portfolioBeta` number, required — The portfolio beta, which correponds to the portfolio systematic risk in the Capital Asset Pricing Model (CAPM)

---

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