Black-Litterman Posterior Returns & Weights
curl --request POST \
--url https://api.fincept.in/quantlib/portfolio/black-litterman/posterior \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"covariance_matrix": [
[
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": [
5000000000,
3000000000,
2000000000,
1000000000
],
"risk_aversion": 2.5,
"views": [
{
"type": "absolute",
"asset": 0,
"value": 0.09,
"confidence": 0.7
},
{
"type": "relative",
"asset_long": 1,
"asset_short": 2,
"value": 0.03,
"confidence": 0.6
}
]
}
'import requests
url = "https://api.fincept.in/quantlib/portfolio/black-litterman/posterior"
payload = {
"covariance_matrix": [[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": [5000000000, 3000000000, 2000000000, 1000000000],
"risk_aversion": 2.5,
"views": [
{
"type": "absolute",
"asset": 0,
"value": 0.09,
"confidence": 0.7
},
{
"type": "relative",
"asset_long": 1,
"asset_short": 2,
"value": 0.03,
"confidence": 0.6
}
]
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({
covariance_matrix: [
[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: [5000000000, 3000000000, 2000000000, 1000000000],
risk_aversion: 2.5,
views: [
{type: 'absolute', asset: 0, value: 0.09, confidence: 0.7},
{type: 'relative', asset_long: 1, asset_short: 2, value: 0.03, confidence: 0.6}
]
})
};
fetch('https://api.fincept.in/quantlib/portfolio/black-litterman/posterior', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/portfolio/black-litterman/posterior",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'covariance_matrix' => [
[
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' => [
5000000000,
3000000000,
2000000000,
1000000000
],
'risk_aversion' => 2.5,
'views' => [
[
'type' => 'absolute',
'asset' => 0,
'value' => 0.09,
'confidence' => 0.7
],
[
'type' => 'relative',
'asset_long' => 1,
'asset_short' => 2,
'value' => 0.03,
'confidence' => 0.6
]
]
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/portfolio/black-litterman/posterior"
payload := strings.NewReader("{\n \"covariance_matrix\": [\n [\n 0.04,\n 0.006,\n 0.008,\n 0.01\n ],\n [\n 0.006,\n 0.09,\n 0.012,\n 0.015\n ],\n [\n 0.008,\n 0.012,\n 0.0625,\n 0.018\n ],\n [\n 0.01,\n 0.015,\n 0.018,\n 0.16\n ]\n ],\n \"market_caps\": [\n 5000000000,\n 3000000000,\n 2000000000,\n 1000000000\n ],\n \"risk_aversion\": 2.5,\n \"views\": [\n {\n \"type\": \"absolute\",\n \"asset\": 0,\n \"value\": 0.09,\n \"confidence\": 0.7\n },\n {\n \"type\": \"relative\",\n \"asset_long\": 1,\n \"asset_short\": 2,\n \"value\": 0.03,\n \"confidence\": 0.6\n }\n ]\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/portfolio/black-litterman/posterior")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"covariance_matrix\": [\n [\n 0.04,\n 0.006,\n 0.008,\n 0.01\n ],\n [\n 0.006,\n 0.09,\n 0.012,\n 0.015\n ],\n [\n 0.008,\n 0.012,\n 0.0625,\n 0.018\n ],\n [\n 0.01,\n 0.015,\n 0.018,\n 0.16\n ]\n ],\n \"market_caps\": [\n 5000000000,\n 3000000000,\n 2000000000,\n 1000000000\n ],\n \"risk_aversion\": 2.5,\n \"views\": [\n {\n \"type\": \"absolute\",\n \"asset\": 0,\n \"value\": 0.09,\n \"confidence\": 0.7\n },\n {\n \"type\": \"relative\",\n \"asset_long\": 1,\n \"asset_short\": 2,\n \"value\": 0.03,\n \"confidence\": 0.6\n }\n ]\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/portfolio/black-litterman/posterior")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"covariance_matrix\": [\n [\n 0.04,\n 0.006,\n 0.008,\n 0.01\n ],\n [\n 0.006,\n 0.09,\n 0.012,\n 0.015\n ],\n [\n 0.008,\n 0.012,\n 0.0625,\n 0.018\n ],\n [\n 0.01,\n 0.015,\n 0.018,\n 0.16\n ]\n ],\n \"market_caps\": [\n 5000000000,\n 3000000000,\n 2000000000,\n 1000000000\n ],\n \"risk_aversion\": 2.5,\n \"views\": [\n {\n \"type\": \"absolute\",\n \"asset\": 0,\n \"value\": 0.09,\n \"confidence\": 0.7\n },\n {\n \"type\": \"relative\",\n \"asset_long\": 1,\n \"asset_short\": 2,\n \"value\": 0.03,\n \"confidence\": 0.6\n }\n ]\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"posterior_returns": [
0.085,
0.12,
0.098,
0.142
],
"optimal_weights": [
0.32,
0.28,
0.25,
0.15
]
}
}{
"detail": "Invalid API key"
}{
"detail": "Insufficient credits. This endpoint requires 5 credits."
}{
"detail": [
{
"loc": [
"body",
"expected_returns"
],
"msg": "field required",
"type": "value_error.missing"
}
]
}quantlib-portfolio
Black-Litterman Posterior Returns & Weights
Computes posterior (updated) returns by combining market equilibrium with investor views using Bayesian inference. Returns optimal portfolio weights based on the posterior distribution.
Use Cases:
- Incorporating proprietary views into portfolio construction
- Blending quantitative signals with market equilibrium
- Creating more stable, diversified portfolios than MVO
- Tactical asset allocation with strategic baseline
Mathematical Background: Posterior returns: E[R] = [(τΣ)^-1 + P^T Ω^-1 P]^-1 [(τΣ)^-1 Π + P^T Ω^-1 Q]
Where Π is equilibrium returns, P is the picking matrix, Q is views, and Ω is view uncertainty.
Credits: 5 per request [Tier: PRO, Credits: 5]
POST
/
quantlib
/
portfolio
/
black-litterman
/
posterior
Black-Litterman Posterior Returns & Weights
curl --request POST \
--url https://api.fincept.in/quantlib/portfolio/black-litterman/posterior \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"covariance_matrix": [
[
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": [
5000000000,
3000000000,
2000000000,
1000000000
],
"risk_aversion": 2.5,
"views": [
{
"type": "absolute",
"asset": 0,
"value": 0.09,
"confidence": 0.7
},
{
"type": "relative",
"asset_long": 1,
"asset_short": 2,
"value": 0.03,
"confidence": 0.6
}
]
}
'import requests
url = "https://api.fincept.in/quantlib/portfolio/black-litterman/posterior"
payload = {
"covariance_matrix": [[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": [5000000000, 3000000000, 2000000000, 1000000000],
"risk_aversion": 2.5,
"views": [
{
"type": "absolute",
"asset": 0,
"value": 0.09,
"confidence": 0.7
},
{
"type": "relative",
"asset_long": 1,
"asset_short": 2,
"value": 0.03,
"confidence": 0.6
}
]
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({
covariance_matrix: [
[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: [5000000000, 3000000000, 2000000000, 1000000000],
risk_aversion: 2.5,
views: [
{type: 'absolute', asset: 0, value: 0.09, confidence: 0.7},
{type: 'relative', asset_long: 1, asset_short: 2, value: 0.03, confidence: 0.6}
]
})
};
fetch('https://api.fincept.in/quantlib/portfolio/black-litterman/posterior', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/portfolio/black-litterman/posterior",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'covariance_matrix' => [
[
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' => [
5000000000,
3000000000,
2000000000,
1000000000
],
'risk_aversion' => 2.5,
'views' => [
[
'type' => 'absolute',
'asset' => 0,
'value' => 0.09,
'confidence' => 0.7
],
[
'type' => 'relative',
'asset_long' => 1,
'asset_short' => 2,
'value' => 0.03,
'confidence' => 0.6
]
]
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/portfolio/black-litterman/posterior"
payload := strings.NewReader("{\n \"covariance_matrix\": [\n [\n 0.04,\n 0.006,\n 0.008,\n 0.01\n ],\n [\n 0.006,\n 0.09,\n 0.012,\n 0.015\n ],\n [\n 0.008,\n 0.012,\n 0.0625,\n 0.018\n ],\n [\n 0.01,\n 0.015,\n 0.018,\n 0.16\n ]\n ],\n \"market_caps\": [\n 5000000000,\n 3000000000,\n 2000000000,\n 1000000000\n ],\n \"risk_aversion\": 2.5,\n \"views\": [\n {\n \"type\": \"absolute\",\n \"asset\": 0,\n \"value\": 0.09,\n \"confidence\": 0.7\n },\n {\n \"type\": \"relative\",\n \"asset_long\": 1,\n \"asset_short\": 2,\n \"value\": 0.03,\n \"confidence\": 0.6\n }\n ]\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/portfolio/black-litterman/posterior")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"covariance_matrix\": [\n [\n 0.04,\n 0.006,\n 0.008,\n 0.01\n ],\n [\n 0.006,\n 0.09,\n 0.012,\n 0.015\n ],\n [\n 0.008,\n 0.012,\n 0.0625,\n 0.018\n ],\n [\n 0.01,\n 0.015,\n 0.018,\n 0.16\n ]\n ],\n \"market_caps\": [\n 5000000000,\n 3000000000,\n 2000000000,\n 1000000000\n ],\n \"risk_aversion\": 2.5,\n \"views\": [\n {\n \"type\": \"absolute\",\n \"asset\": 0,\n \"value\": 0.09,\n \"confidence\": 0.7\n },\n {\n \"type\": \"relative\",\n \"asset_long\": 1,\n \"asset_short\": 2,\n \"value\": 0.03,\n \"confidence\": 0.6\n }\n ]\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/portfolio/black-litterman/posterior")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"covariance_matrix\": [\n [\n 0.04,\n 0.006,\n 0.008,\n 0.01\n ],\n [\n 0.006,\n 0.09,\n 0.012,\n 0.015\n ],\n [\n 0.008,\n 0.012,\n 0.0625,\n 0.018\n ],\n [\n 0.01,\n 0.015,\n 0.018,\n 0.16\n ]\n ],\n \"market_caps\": [\n 5000000000,\n 3000000000,\n 2000000000,\n 1000000000\n ],\n \"risk_aversion\": 2.5,\n \"views\": [\n {\n \"type\": \"absolute\",\n \"asset\": 0,\n \"value\": 0.09,\n \"confidence\": 0.7\n },\n {\n \"type\": \"relative\",\n \"asset_long\": 1,\n \"asset_short\": 2,\n \"value\": 0.03,\n \"confidence\": 0.6\n }\n ]\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"posterior_returns": [
0.085,
0.12,
0.098,
0.142
],
"optimal_weights": [
0.32,
0.28,
0.25,
0.15
]
}
}{
"detail": "Invalid API key"
}{
"detail": "Insufficient credits. This endpoint requires 5 credits."
}{
"detail": [
{
"loc": [
"body",
"expected_returns"
],
"msg": "field required",
"type": "value_error.missing"
}
]
}Authorizations
API key for authentication. Get your key at https://api.fincept.in/auth/register
Body
application/json
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 capitalizations for each asset
Example:
[ 5000000000, 3000000000, 2000000000, 1000000000 ]
Market risk aversion parameter
Example:
2.5
List of investor views to incorporate. Can be empty for pure equilibrium.
Show child attributes
Show child attributes
Example:
[ { "type": "absolute", "asset": 0, "value": 0.09, "confidence": 0.7 }, { "type": "relative", "asset_long": 1, "asset_short": 2, "value": 0.03, "confidence": 0.6 } ]
⌘I