Peer-Multiple Regression

Install and import#

bash

npm install fintech-algorithms

import { peerMultipleRegression } from "fintech-algorithms/fundamental-analysis-and-valuation/relative-valuation/peer-multiple-regression";

Signature#

peerMultipleRegression(rawInputs)

Fits an ordinary least squares regression of each peer's log multiple on an intercept, expected growth, return on equity and net debt to EBITDA, then exponentiates the target's fitted value into an implied multiple and applies it to the target's valuation metric.

Parameters#

Name	Type	Notes
`rawInputs`	`unknown`	Declared `unknown` and narrowed at runtime. It must be a plain object with a `target` object and a `peers` array. Every regression row reads `expected_growth_percent` and `return_on_equity_percent` (percentage points, divided by 100 before fitting) and `net_debt_to_ebitda`, each a finite number of any sign. `peers` holds at least six objects, each also carrying a nonempty and unique string `id` and a positive `multiple`. `target` also carries a positive `valuation_metric` and an optional `current_value`.

Returns#

Record<string, unknown>

model, peer_count, feature_order, coefficients keyed intercept, expected_growth_decimal, return_on_equity_decimal and net_debt_to_ebitda, r_squared_log_space measured against the log multiples rather than the levels, fitted_peers (per peer: id, observed_multiple, fitted_multiple, log_residual), target_predicted_log_multiple, implied_multiple, target_valuation_metric, implied_value (implied multiple times the metric), premium_discount_to_current measured against target.current_value and null when that is absent, smearing_correction fixed at not-applied, and state, always valuation-complete.

Errors#

When rawInputs, target or a peer row is not a plain object, or a feature or metric is not a finite number — throws TypeError
When peers is not an array of at least six rows, or a peer id is missing, blank or duplicated — throws RangeError
When a peer multiple, target.valuation_metric or target.current_value is not greater than zero — throws RangeError
When the normal-equation matrix is rank deficient, meaning Gaussian elimination finds a pivot of magnitude at or below 1e-12 — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

rawInputs

{
  "target": {
    "expected_growth_percent": 11,
    "return_on_equity_percent": 15,
    "net_debt_to_ebitda": 1,
    "valuation_metric": 5,
    "current_value": 35
  },
  "peers": [
    {
      "id": "R1",
      "multiple": 3.6692966676192453,
      "expected_growth_percent": 4,
      "return_on_equity_percent": 8,
      "net_debt_to_ebitda": 3
    },
    {
      "id": "R2",
      "multiple": 4.6043430528623635,
      "expected_growth_percent": 6,
      "return_on_equity_percent": 11,
      "net_debt_to_ebitda": 2.4
    },
    {
      "id": "R3",
      "multiple": 5.124331102904436,
      "expected_growth_percent": 8,
      "return_on_equity_percent": 14,
      "net_debt_to_ebitda": 1.8
    }
  ]
}

Call#

peerMultipleRegression(rawInputs)

Returns#

object with 13 fields: model, peer_count, feature_order, coefficients, r_squared_log_space, fitted_peers, target_predicted_log_multiple, implied_multiple, …

{
  "model": "ols-log-multiple-on-growth-roe-and-leverage",
  "peer_count": 8,
  "feature_order": [
    "intercept",
    "expected_growth_decimal",
    "return_on_equity_decimal",
    "net_debt_to_ebitda"
  ],
  "coefficients": {
    "intercept": 1.5364545140362829,
    "expected_growth_decimal": 1.6438862781409074,
    "return_on_equity_decimal": 1.6061067701607943,
    "net_debt_to_ebitda": -0.13216626876457388
  },
  "r_squared_log_space": 0.9870676723439116,
  "fitted_peers": [
    {
      "id": "R1",
      "observed_multiple": 3.6692966676192453,
      "fitted_multiple": 3.7969560280762247,
      "log_residual": -0.0341997004810608
    },
    {
      "id": "R2",
      "observed_multiple": 4.6043430528623635,
      "fitted_multiple": 4.457376616557734,
      "log_residual": 0.032439609592552765
    },
    {
      "id": "R3",
      "observed_multiple": 5.124331102904436,
      "fitted_multiple": 5.232666945553791,
      "log_residual": -0.020921080333833775
    }
  ],
  "target_predicted_log_multiple": 1.8260317513913278,
  "implied_multiple": 6.209198064103231,
  "target_valuation_metric": 5,
  "implied_value": 31.045990320516154,
  "premium_discount_to_current": -0.11297170512810994,
  "smearing_correction": "not-applied",
  "state": "valuation-complete"
}

Other exports#

This module also exports calculate, pEComparableValuation, evEbitdaComparableValuation, priceToBookValuation, pegRatio. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.