function jensenalpha
jensenalpha(
x: array,
y: array,
frisk?: number,
dim?: 0 | 1,
): number

Jensen alpha.

Ex-post alpha calculated with regression line. Free-risk is the average free-risk for the timeframe selected. Jensen alpha measures the excess return of a portfolio over the theoretical expected return based on the portfolio's beta and CAPM model.

Examples

Single asset vs benchmark

import { assertEquals } from "jsr:@std/assert";

var x = [0.003,0.026,0.015,-0.009,0.014,0.024,0.015,0.066,-0.014,0.039];
var y = [-0.005,0.081,0.04,-0.037,-0.061,0.058,-0.049,-0.021,0.062,0.058];
assertEquals(jensenalpha(x,y), 0.01760907323602524);

Multiple assets vs benchmark

import { assertEquals } from "jsr:@std/assert";

var x = [0.003,0.026,0.015,-0.009,0.014,0.024,0.015,0.066,-0.014,0.039];
var y = [-0.005,0.081,0.04,-0.037,-0.061,0.058,-0.049,-0.021,0.062,0.058];

var z = [0.04,-0.022,0.043,0.028,-0.078,-0.011,0.033,-0.049,0.09,0.087];
assertEquals(jensenalpha(x,z), 0.02077158416670001);
assertEquals(jensenalpha(y,z), 0.006256147026618015);

Parameters

x: array

asset/portfolio values

y: array

benchmark values

optional
frisk: number

free-risk (def: 0)

optional
dim: 0 | 1

dimension 0: row, 1: column (def: 0)

Return Type

number

Jensen alpha value

jensenalpha(
x: matrix,
y: array,
frisk?: number,
dim?: 0 | 1,
): array | matrix

Jensen alpha.

Ex-post alpha calculated with regression line. Free-risk is the average free-risk for the timeframe selected. Jensen alpha measures the excess return of a portfolio over the theoretical expected return based on the portfolio's beta and CAPM model.

Examples

Single asset vs benchmark

import { assertEquals } from "jsr:@std/assert";

var x = [0.003,0.026,0.015,-0.009,0.014,0.024,0.015,0.066,-0.014,0.039];
var y = [-0.005,0.081,0.04,-0.037,-0.061,0.058,-0.049,-0.021,0.062,0.058];
assertEquals(jensenalpha(x,y), 0.01760907323602524);

Multiple assets vs benchmark

import { assertEquals } from "jsr:@std/assert";

var x = [0.003,0.026,0.015,-0.009,0.014,0.024,0.015,0.066,-0.014,0.039];
var y = [-0.005,0.081,0.04,-0.037,-0.061,0.058,-0.049,-0.021,0.062,0.058];

var z = [0.04,-0.022,0.043,0.028,-0.078,-0.011,0.033,-0.049,0.09,0.087];
assertEquals(jensenalpha(x,z), 0.02077158416670001);
assertEquals(jensenalpha(y,z), 0.006256147026618015);

Parameters

asset/portfolio values

y: array

benchmark values

optional
frisk: number

free-risk (def: 0)

optional
dim: 0 | 1

dimension 0: row, 1: column (def: 0)

Return Type

Jensen alpha value

Usage

import jensenalpha from "quants/jensenalpha.ts";