{"openapi":"3.0.1","servers":[{"url":"https://api.portfoliooptimizer.io/v1"},{"url":"https://eu-west-1.api.portfoliooptimizer.io/v1"}],"info":{"contact":{"email":"contact@portfoliooptimizer.io","name":"Support","url":"https://portfoliooptimizer.io/"},"description":"Portfolio Optimizer is a [Web API](https://en.wikipedia.org/wiki/Web_API) to analyze and optimize investment portfolios (collection of financial assets such as stocks, bonds, ETFs, crypto-currencies) using modern portfolio theory algorithms (mean-variance, VaR, etc.).\n\n# API General Information\n\n Portfolio Optimizer is based on [REST](https://en.wikipedia.org/wiki/Representational_state_transfer) for easy integration, uses [JSON](https://en.wikipedia.org/wiki/JSON) for the exchange of data and uses a standard [HTTP verb](https://en.wikipedia.org/wiki/Hypertext_Transfer_Protocol#Request_methods) (`POST`) to represent the action(s).\n\nPortfolio Optimizer is also as secured as a Web API could be: \n* [256-bit HTTPS Encryption](https://en.wikipedia.org/wiki/HTTPS)\n* No usage of cookies\n* No usage of personal data \n\n## API Headers \nThe following HTTP header(s) are required when calling Portfolio Optimizer endpoints:\n* `Content-type: application/json` \n This header specifies that the data provided in input to the endpoint is in JSON format\n\nThe following HTTP header(s) are optional when calling Portfolio Optimizer endpoints:\n* `Content-Encoding: gzip` \n This header indicates that the data provided in input to the endpoint is compressed with gzip.\n* `X-API-Key: ` \n This header enables [authenticated users](#auth) to provide their private [API key](#overview--api-key) in order to [benefit from higher API limits](#overview--api-limits)\n\n## API Key\nPortfolio Optimizer is free to use, but not free to run.\n\nIn order to obtain an API key and benefit from [higher API limits](#overview--api-limits), a *small* participation to Portfolio Optimizer running costs is required.\n\nThis participation takes the form of coffee(s), with one coffee = one month of usage.\n\n

Buy a Coffee at buymeacoffee.com

\n\n\n> **Notes:** \n> * Please make sure not to expose your API key publicly!\n\n## API Limits \n\nPortfolio Optimizer comes with *fairly reasonable* API limits.\n\nFor anonymous users: \n* The API requests are restricted to a subset of all the available endpoints and/or endpoints features \n* The API requests are limited to 1 request per second for all the anonymous users combined, with concurrent requests rejected \n* The API requests are limited to 1 second of execution time\n* The API requests are limited to 20 assets, 250 portfolios, 500 series data points and 5 factors\n\nFor authenticated users with an [API key](#overview--api-key): \n* The API requests have access to all the available endpoints and endpoints features\n* The API requests are limited to 10000 requests per 24 hour per API key, with concurrent requests queued\n* The API requests are limited to 2.5 seconds of execution time\n* The API requests are limited to 100 assets, 1250 portfolios, 2500 series data points and 25 factors\n\n> **Notes:** \n> * It is possible to further relax the API limits, or to disable the API limits alltogether; please [contact the support](https://portfoliooptimizer.io/contact/) for more details.\n> * Information on the API rate limits are provided in response messages HTTP headers `x-ratelimit-*`: \n> * `x-ratelimit-limit-second`, the limit on the number of API requests per second\n> * `x-ratelimit-remaining-second`, the number of remaining API requests in the current second \n> * `x-ratelimit-limit-minute`, the limit on the number of API requests per minute\n> * ...\n\n## API Regions\nPortfolio Optimizer servers are located in Western Europe.\n\n> **Notes:** \n> * It is possible to deploy Portfolio Optimizer in other geographical regions, for example to improve the API latency; please [contact the support](https://portfoliooptimizer.io/contact/) for more details. \n\n## API Response Codes \n\nStandard [HTTP response codes](https://en.wikipedia.org/wiki/List_of_HTTP_status_codes) are used by Portfolio Optimizer to provide details on the status of API requests.\n\n| HTTP Code | Description | Notes |\n| --------- | ----------- | ----- |\n| 200 | Request successfully processed | - |\n| 400 | Request failed to be processed because of incorrect content | The response message body contains information on the incorrect content |\n| 401 | Request failed to be processed because of invalid API key | - |\n| 404 | Request failed to be processed because of non existing endpoint | The requested endpoint might exist, but needs to be accessed with another HTTP method (e.g., `POST` instead of `GET`) |\n| 429 | Request failed to be processed because of API limits violated | The response message HTTP headers `x-ratelimit-*` contain information on the [API limits](#overview--api-limits) |\n| 500 | Request failed to be processed because of an internal error | Something went wrong on Portfolio Optimizer side, do not hesitate to [report the issue](#overview--support) |\n| 502 | Request failed to be processed because of a temporary connectivity error | Something went wrong on Portfolio Optimizer side, please check the [API status](#overview--api-status) and do not hesitate to [report the issue](#overview--support) |\n\n## API Status \n\nPortfolio Optimizer is monitored 24/7 by [UptimeRobot](https://stats.uptimerobot.com/wgW71SL1AW).\n\n# Support\n\nFor any issue or question about Portfolio Optimizer, please do not hesitate to [contact the support](https://portfoliooptimizer.io/contact/).\n","license":{"name":"Apache 2.0","url":"http://www.apache.org/licenses/LICENSE-2.0.html"},"termsOfService":"https://portfoliooptimizer.io/terms-of-service","title":"Portfolio Optimizer","version":"1.0.9","x-apisguru-categories":["financial"],"x-logo":{"url":"https://portfoliooptimizer.io/assets/images/88x88.png"},"x-origin":[{"format":"openapi","url":"https://docs.portfoliooptimizer.io/openapi/portfoliooptimizer.yaml","version":"3.0"}],"x-providerName":"portfoliooptimizer.io"},"externalDocs":{"description":"External documentation","url":"https://docs.portfoliooptimizer.io/"},"security":[{"ApiKeyAuth":[]}],"paths":{"/assets/analysis/absorption-ratio":{"post":{"description":"Compute the absorption ratio associated to a universe of assets.\n\nReferences\n* [Mark Kritzman, Yuanzhen Li, Sebastien Page and Roberto Rigobon, Principal Components as a Measure of Systemic Risk, The Journal of Portfolio Management Summer 2011, 37 (4) 112-126](https://jpm.pm-research.com/content/37/4/112)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the absorption ratio of 2 assets","value":{"assets":2,"assetsCovarianceMatrix":[[9,1],[1,1]]}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":1,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsCovarianceMatrixEigenvectors":{"properties":{"eigenvectorsRetained":{"description":"The number of eigenvectors to retain in the numerator of the absorption ratio, which must be lower than the number of assets; 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Kritzman, Y. Li, Skulls, Financial Turbulence, and Risk Management,Financial Analysts Journal, Volume 66, Number 5, Pages 30-41, Year 2010](https://www.tandfonline.com/doi/abs/10.2469/faj.v66.n5.3)\n* [Kinlaw, W., Turkington, D. Correlation surprise. J Asset Manag 14, 385–399 (2013)](https://link.springer.com/article/10.1057/jam.2013.27)\n","requestBody":{"content":{"application/json":{"examples":{"Example (1 asset)":{"description":"Compute the turbulence index of 1 asset","value":{"assets":1,"assetsAverageReturns":[0.5],"assetsCovarianceMatrix":[[1]],"assetsReturns":[1]}},"Example (2 assets)":{"description":"Compute the turbulence index of 2 assets","value":{"assets":2,"assetsAverageReturns":[1,1],"assetsCovarianceMatrix":[[9,1],[1,1]],"assetsReturns":[1,0]}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":1,"type":"integer"},"assetsAverageReturns":{"description":"assetsAverageReturns[i] is the average return of asset i over an historical reference period","items":{"type":"number"},"minItems":1,"type":"array"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j over an historical reference period","items":{"items":{"type":"number"},"minItems":1,"type":"array"},"minItems":1,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the return of asset i over a period different from the historical reference period","items":{"type":"number"},"minItems":1,"type":"array"}},"required":["assets","assetsCovarianceMatrix","assetsAverageReturns","assetsReturns"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed turbulence index","value":{"assetsTurbulenceIndex":0.5624999999999999}}},"schema":{"properties":{"assetsTurbulenceIndex":{"description":"the turbulence index of the universe of assets","type":"number"}},"required":["assetsTurbulenceIndex"],"type":"object"}}},"description":"OK"}},"summary":"Turbulence Index","tags":["Assets / Analysis"],"x-codegen-request-body-name":"body"}},"/assets/correlation/matrix":{"post":{"description":"Compute the Pearson asset correlation matrix from either: \n* The asset returns\n* The asset covariance matrix\n\nReferences\n* [Wikipedia, Correlation and Dependence](https://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_matrices)\n","requestBody":{"content":{"application/json":{"examples":{"From covariance matrix":{"description":"Computes the correlation matrix of 2 assets based on their covariance matrix","value":{"assets":2,"assetsCovarianceMatrix":[[0.01,-0.0025],[-0.0025,0.0025]]}},"From returns":{"description":"Computes the correlation matrix of 2 assets based on 4 returns per asset","value":{"assets":[{"assetReturns":[0.01,0,0.02,-0.03]},{"assetReturns":[0.01,0,0.02,-0.03]}]}}},"schema":{"oneOf":[{"properties":{"assets":{"items":{"properties":{"assetReturns":{"description":"assetReturns[t] is the return of the asset at the time t; 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Rev. Lett. 83, 1467](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.83.1467)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Denoise an asset correlation matrix of 3 assets","value":{"assets":3,"assetsCorrelationMatrix":[[1,0.5,0.9],[0.5,1,0.7],[0.9,0.7,1]],"assetsCorrelationMatrixAspectRatio":0.5}}},"schema":{"properties":{"assets":{"minimum":2,"type":"integer"},"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsCorrelationMatrixAspectRatio":{"description":"The aspect ratio of the asset correlation matrix, defined as the number of assets divided by the number of asset returns per asset used to compute the asset correlation matrix","exclusiveMinimum":true,"minimum":0,"type":"number"},"denoisingMethod":{"default":"eigenvaluesClipping","description":"The method used to denoise the asset correlation matrix","enum":["eigenvaluesClipping"],"type":"string"}},"required":["assets","assetsCorrelationMatrix","assetsCorrelationMatrixAspectRatio"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Denoised correlation matrix","value":{"assetsCorrelationMatrix":[[1,0.6838346015086407,0.7246659534718176],[0.6838346015086407,1,0.6978824315038066],[0.7246659534718176,0.6978824315038066,1]]}},"Example of failing denoising method":{"description":"No denoised correlation matrix","value":{"assetsCorrelationMatrix":null}}},"schema":{"properties":{"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j; assetsCorrelationMatrix is possibly null in case the denoising method did not manage to denoise the provided asset correlation matrix","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"}},"required":["assetsCorrelationMatrix"],"type":"object"}}},"description":"OK"}},"summary":"Denoised Correlation Matrix","tags":["Assets / Correlation Matrix"],"x-codegen-request-body-name":"body"}},"/assets/correlation/matrix/distance":{"post":{"description":"Compute the distance between an asset correlation matrix and a reference correlation matrix, using one of the following distance metrics:\n* Euclidean distance (default), which is the distance induced by [the Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm)\n* Correlation matrix distance, defined in the first reference, which corresponds to [the cosine distance](https://en.wikipedia.org/wiki/Cosine_similarity) between the two vectorized asset correlation matrices\n* Bures distance, defined in the second reference\n\n References\n * [M. Herdin, N. Czink, H. Ozcelik and E. Bonek, Correlation matrix distance, a meaningful measure for evaluation of non-stationary MIMO channels, 2005 IEEE 61st Vehicular Technology Conference, 2005, pp. 136-140 Vol. 1](https://ieeexplore.ieee.org/document/1543265)\n * [Rajendra Bhatia, Tanvi Jain, Yongdo Lim, On the Bures–Wasserstein distance between positive definite matrices, Expositiones Mathematicae, Volume 37, Issue 2, 2019](https://www.sciencedirect.com/science/article/pii/S0723086918300021)\n","requestBody":{"content":{"application/json":{"examples":{"Example (correlation matrix distance)":{"description":"Compute the correlation matrix distance between an asset correlation matrix and an equicorrelation matrix","value":{"assets":3,"assetsCorrelationMatrix":[[1,0.5,0.9],[0.5,1,0.7],[0.9,0.7,1]],"distanceMetric":"correlationMatrix","referenceCorrelationMatrix":[[1,1,1],[1,1,1],[1,1,1]]}},"Example (euclidean distance)":{"description":"Compute the euclidean distance between an asset correlation matrix and an equicorrelation matrix","value":{"assets":3,"assetsCorrelationMatrix":[[1,0.5,0.9],[0.5,1,0.7],[0.9,0.7,1]],"referenceCorrelationMatrix":[[1,1,1],[1,1,1],[1,1,1]]}}},"schema":{"properties":{"assets":{"minimum":2,"type":"integer"},"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"distanceMetric":{"default":"euclidean","description":"The distance metric to use to compute the distance between the asset correlation matrix and the reference correlation matrix","enum":["euclidean","correlationMatrix","bures"],"type":"string"},"referenceCorrelationMatrix":{"description":"referenceCorrelationMatrix[i][j] is the reference correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"}},"required":["assets","assetsCorrelationMatrix","referenceCorrelationMatrix"]}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed distance","value":{"assetsCorrelationMatrixDistance":0.8366600265340757}}},"schema":{"properties":{"assetsCorrelationMatrixDistance":{"description":"The computed distance between the two correlation matrices","minimum":0,"type":"number"}},"required":["assetsCorrelationMatrixDistance"],"type":"object"}}},"description":"OK"}},"summary":"Correlation Matrix Distance","tags":["Assets / Correlation Matrix"],"x-codegen-request-body-name":"body"}},"/assets/correlation/matrix/effective-rank":{"post":{"description":"Compute the effective rank of an asset correlation matrix.\n\nReferences\n* [Olivier Roy and Martin Vetterli, The effective rank: A measure of effective dimensionality, 15th European Signal Processing Conference, 2007](https://ieeexplore.ieee.org/document/7098875)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the effective rank of a correlation matrix of 2 assets","value":{"assets":2,"assetsCorrelationMatrix":[[1,0],[0,1]]}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"}},"required":["assets","assetsCorrelationMatrix"]}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed effective rank","value":{"assetsCorrelationMatrixEffectiveRank":2}}},"schema":{"properties":{"assetsCorrelationMatrixEffectiveRank":{"description":"The effective rank of the asset correlation matrix","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"}},"required":["assetsCorrelationMatrixEffectiveRank"],"type":"object"}}},"description":"OK"}},"summary":"Correlation Matrix Effective Rank","tags":["Assets / Correlation Matrix"],"x-codegen-request-body-name":"body"}},"/assets/correlation/matrix/informativeness":{"post":{"description":"Compute the informativeness of an asset correlation matrix, using one of the following distance metrics:\n* Euclidean distance (default), which is the distance induced by [the Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm)\n* Correlation matrix distance, defined in the second reference, which corresponds to [the cosine distance](https://en.wikipedia.org/wiki/Cosine_similarity) between the two vectorized asset correlation matrices\n* Bures distance, defined in the third reference\n\n References\n * [Austin J. Brockmeier and Tingting Mu and Sophia Ananiadou and John Y. Goulermas, Quantifying the Informativeness of Similarity Measurements, Journal of Machine Learning Research, 2017](http://jmlr.org/papers/v18/16-296.html)\n * [M. Herdin, N. Czink, H. Ozcelik and E. Bonek, Correlation matrix distance, a meaningful measure for evaluation of non-stationary MIMO channels, 2005 IEEE 61st Vehicular Technology Conference, 2005, pp. 136-140 Vol. 1](https://ieeexplore.ieee.org/document/1543265)\n * [Rajendra Bhatia, Tanvi Jain, Yongdo Lim, On the Bures–Wasserstein distance between positive definite matrices, Expositiones Mathematicae, Volume 37, Issue 2, 2019](https://www.sciencedirect.com/science/article/pii/S0723086918300021)\n","requestBody":{"content":{"application/json":{"examples":{"Example (Bures distance)":{"description":"Compute the informativeness of an asset correlation matrix usingn the Bures distance","value":{"assets":3,"assetsCorrelationMatrix":[[1,0.5,0.9],[0.5,1,0.7],[0.9,0.7,1]],"distanceMetric":"bures"}},"Example (euclidean distance)":{"description":"Compute the informativeness of an asset correlation matrix usingn the euclidean distance","value":{"assets":3,"assetsCorrelationMatrix":[[1,0.5,0.9],[0.5,1,0.7],[0.9,0.7,1]]}}},"schema":{"properties":{"assets":{"minimum":2,"type":"integer"},"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"distanceMetric":{"default":"euclidean","description":"The distance metric to use to compute the informativeness of the asset correlation matrix","enum":["euclidean","correlationMatrix","bures"],"type":"string"}},"required":["assets","assetsCorrelationMatrix"]}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed informativeness","value":{"assetsCorrelationMatrixInformativeness":0.020539611658192996}}},"schema":{"properties":{"assetsCorrelationMatrixInformativeness":{"description":"The informativeness of the asset correlation matrix","minimum":0,"type":"number"}},"required":["assetsCorrelationMatrixInformativeness"],"type":"object"}}},"description":"OK"}},"summary":"Correlation Matrix Informativeness","tags":["Assets / Correlation Matrix"],"x-codegen-request-body-name":"body"}},"/assets/correlation/matrix/nearest":{"post":{"description":"Compute the _closest_ - in terms of [the Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm) - asset correlation matrix to an approximate asset correlation matrix, optionally keeping a selected number of correlations fixed.\n\nReferences\n* [Nicholas J. Higham, Computing the Nearest Correlation Matrix—A Problem from Finance, IMA J. Numer. Anal. 22, 329–343, 2002.](http://www.maths.manchester.ac.uk/~higham/narep/narep369.pdf)\n","requestBody":{"content":{"application/json":{"examples":{"Nearest correlation matrix":{"description":"Compute the nearest correlation matrix to an approximate correlation matrix","value":{"assets":3,"assetsApproximateCorrelationMatrix":[[1,1,0],[1,1,1],[0,1,1]]}},"Nearest correlation matrix with fixed a correlation":{"description":"Compute the nearest correlation matrix to an approximate correlation matrix, keeping one correlation coefficient fixed","value":{"assets":3,"assetsApproximateCorrelationMatrix":[[1,0.5,0.9],[0.5,1,-0.2],[0.9,-0.2,1]],"assetsFixedCorrelations":[[2,3]]}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsApproximateCorrelationMatrix":{"description":"assetsApproximateCorrelationMatrix[i][i] is the approximate correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsFixedCorrelations":{"description":"assetsFixedCorrelations[k] is the couple of indices (i,j) of the assets i and j for which to keep the approximate correlation assetsApproximateCorrelationMatrix[i][j] fixed","items":{"items":{"type":"integer"},"maxItems":2,"minItems":2,"type":"array"},"type":"array"}},"required":["assets","assetsApproximateCorrelationMatrix"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Nearest correlation matrix":{"description":"Computed nearest correlation matrix","value":{"assetsCorrelationMatrix":[[1,0.7606306078350177,0.15733356650676536],[0.7606306078350177,1,0.7606306078350177],[0.15733356650676536,0.7606306078350177,1]]}},"Nearest correlation matrix with fixed a correlation":{"description":"Computed nearest correlation matrix keeping one correlation coefficient fixed","value":{"assetsCorrelationMatrix":[[1,0.4314569968899409,0.7974943959465133],[0.4314569968899409,1,-0.2],[0.7974943959465133,-0.2,1]]}}},"schema":{"properties":{"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"}},"required":["assetsCorrelationMatrix"],"type":"object"}}},"description":"OK"}},"summary":"Nearest Correlation Matrix","tags":["Assets / Correlation Matrix"],"x-codegen-request-body-name":"body"}},"/assets/correlation/matrix/random":{"post":{"description":"Generate an asset correlation matrix uniformly at random over the space of positive definite correlation matrices.\n\nReferences\n* [Joe, H., Generating random correlation matrices based on partial correlations. Journal of Multivariate Analysis, 2006, 97, 2177-2189](https://www.sciencedirect.com/science/article/pii/S0047259X05000886)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Generate a 2x2 correlation matrix","value":{"assets":2}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"}},"required":["assets"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed random correlation matrix","value":{"assetsCorrelationMatrix":[[1,0.7606306078350177,0.15733356650676536],[0.7606306078350177,1,0.7606306078350177],[0.15733356650676536,0.7606306078350177,1]]}}},"schema":{"properties":{"assetsCorrelationMatrix":{"description":"assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset 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RiskMetrics technical document, Technical Report fourth edition](https://www.msci.com/documents/10199/5915b101-4206-4ba0-aee2-3449d5c7e95a)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Computes an exponentially weighted covariance matrix of 2 assets based on 4 returns per asset and a decay factor of 0.5","value":{"assets":[{"assetReturns":[0.01,0.01,0.02,0.01]},{"assetReturns":[-0.02,-0.02,-0.04,-0.02]}],"decayFactor":0.5}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetReturns":{"description":"assetReturns[t] is the return of the asset at the time t; all the assetReturns arrays must have the same length","items":{"type":"number"},"minItems":2,"type":"array"}},"required":["assetReturns"],"type":"object"},"minItems":2,"type":"array"},"decayFactor":{"default":0.94,"description":"The exponential decay 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(1979), Bootstrap methods: Another look at the jackknife, The Annals of Statistics 7, 1-26](https://projecteuclid.org/journals/annals-of-statistics/volume-7/issue-1/Bootstrap-Methods-Another-Look-at-the-Jackknife/10.1214/aos/1176344552.full)\n* [Politis, D. N. and Romano, J. P., A circular block resampling procedure for stationary data, in R. Lepage and L. Billard, eds, Exploring the Limits of Bootstrap, Wiley, New York, pp. 263-270](https://statistics.stanford.edu/technical-reports/circular-block-resampling-procedure-stationary-data)\n* [Politis, D. N. and Romano, J. 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Monville, and Kai-Hong Tee. Making Cornish–Fisher Fit for Risk Measurement, Journal of Risk, Volume 21, Number 5, p. 53-81](http://doi.org/10.21314/JOR.2019.408)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Perform 5 simulations over 4 time periods using a Cornish-Fisher distribution with mean parameter 5%, standard deviation parameter 20%, skewness parameter 0.5 and (excess) kurtosis parameter 1.","value":{"assetAverageReturnParameter":0.05,"assetKurtosisParameter":1,"assetSkewnessParameter":0.5,"assetVolatilityParameter":0.2,"simulations":5,"simulationsLength":4}}},"schema":{"properties":{"assetAverageReturnParameter":{"description":"The mean parameter of the Cornish-Fisher distribution, corresponding to the arithmetic average return of the asset","type":"number"},"assetKurtosisParameter":{"description":"The (excess) kurtosis parameter of the Cornish-Fisher distribution, corresponding approximately to the (excess) kurtosis of the asset returns","type":"number"},"assetSkewnessParameter":{"description":"The skewness parameter of the Cornish-Fisher distribution, corresponding approximately to the skewness of the asset returns","type":"number"},"assetVolatilityParameter":{"description":"The volatility parameter of the Cornish-Fisher distribution, corresponding approximately to the volatility of the asset returns","exclusiveMinimum":true,"minimum":0,"type":"number"},"simulations":{"default":1,"description":"The number of simulations to perform","minimum":1,"type":"integer"},"simulationsLength":{"default":1,"description":"The number of time period(s) to simulate per simulation","minimum":1,"type":"integer"}},"required":["assetAverageReturnParameter","assetVolatilityParameter","assetSkewnessParameter","assetKurtosisParameter"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Results of 1 simulation of returns for 2 time periods","value":{"simulations":[{"assets":[{"assetReturns":[0.01,0.02]}]}]}}},"schema":{"properties":{"simulations":{"items":{"properties":{"assets":{"description":"assets[i] is the data for the i-th asset","items":{"properties":{"assetReturns":{"description":"assetReturns[t] is the simulated return of the i-th asset for the t-th time period","items":{"type":"number"},"minItems":1,"type":"array"}},"required":["assetReturns"],"type":"object"},"maxItems":1,"minItems":1,"type":"array"}},"required":["assets"],"type":"object"},"type":"array"}},"required":["simulations"],"type":"object"}}},"description":"OK"}},"summary":"Cornish-Fisher Distribution","tags":["Assets / Monte Carlo Returns Simulation"],"x-codegen-request-body-name":"body"}},"/assets/returns/simulation/monte-carlo/cornish-fisher/corrected":{"post":{"description":"Simulate the return(s) of one asset for one or several time period(s) using a corrected Cornish-Fisher distribution.\n\nReferences\n* [Maillard, Didier, A User’s Guide to the Cornish Fisher Expansion](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1997178)\n* [Lamb, John D., Maura E. Monville, and Kai-Hong Tee. Making Cornish–fisher Fit for Risk Measurement, Journal of Risk, Volume 21, Number 5, p. 53-81](http://doi.org/10.21314/JOR.2019.408)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Perform 5 simulations over 4 time periods using a corrected Cornish-Fisher distribution with mean 5%, standard deviation 20%, skewness 0.5 and (excess) kurtosis 1.","value":{"assetAverageReturn":0.05,"assetKurtosis":1,"assetSkewness":0.5,"assetVolatility":0.2,"simulations":5,"simulationsLength":4}}},"schema":{"properties":{"assetAverageReturn":{"description":"The arithmetic average return of the asset, corresponding to the mean of the corrected Cornish-Fisher distribution","type":"number"},"assetKurtosis":{"description":"The kurtosis of the asset returns, corresponding to the kurtosis of the Cornish-Fisher distribution","type":"number"},"assetSkewness":{"description":"The skewness of the asset returns, corresponding to the skewness of the Cornish-Fisher 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(1999). Optimal Portfolios in Good Times and Bad. Financial Analysts Journal, 55(3), 65–73.](https://www.jstor.org/stable/4480169)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Partition the asset returns of 2 assets, using two turbulence thresholds of 80% and 95%","value":{"assets":[{"assetReturns":[0,0.1,0.05,-0.01,0.025]},{"assetReturns":[0.005,0.05,0.1,-0.02,0]}],"turbulenceThresholds":[0.8,0.95]}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetReturns":{"description":"assetReturns[t] is the return of the asset at the time t; all the assetReturns arrays must have the same length","items":{"type":"number"},"minItems":2,"type":"array"}},"required":["assetReturns"],"type":"object"},"minItems":1,"type":"array"},"turbulenceThresholds":{"description":"The turbulence threshold(s), in percentage; in case several turbulence thresholds are provided, they must be provided in increasing 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Garcia, Román Salmeron, Claudia Garcia & Jose Garcia (2019): Residualization: justification, properties and application, Journal of Applied Statistics](https://doi.org/10.1080/02664763.2019.1701638)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Residualize the returns of the first factor among a set of 2 factors, observed during 3 time periods","value":{"factors":[{"factorReturns":[0.01,0.02,-0.01]},{"factorReturns":[0.025,0.005,-0.02]}],"residualizedFactor":1}}},"schema":{"properties":{"factors":{"items":{"properties":{"factorReturns":{"description":"factorReturns[t] is the return of the factor at the time t; all the factorReturns arrays must have the same length","items":{"type":"number"},"minItems":2,"type":"array"}},"required":["factorReturns"],"type":"object"},"minItems":2,"type":"array"},"residualizedFactor":{"description":"The index of the factor to residualize","minimum":1,"type":"integer"}},"required":["factors","residualizedFactor"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed returns of a residualized factor, observed during 3 time periods","value":{"residualizedFactorReturns":[-0.001885245901639342,0.017622950819672134,-0.0004918032786885261]}}},"schema":{"properties":{"residualizedFactorReturns":{"description":"residualizedFactorReturns[t] is the return of the residualized factor at the time t","items":{"type":"number"},"type":"array"}},"required":["residualizedFactorReturns"],"type":"object"}}},"description":"OK"}},"summary":"Residualization","tags":["Factors"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/alpha":{"post":{"description":"Compute the Jensen’s alpha of one or several portfolio(s) in the Capital Asset Pricing Model (CAPM).\n\nReferences\n* Carl R. 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J Asset Manag 8, 308–336 (2007)](https://link.springer.com/article/10.1057/palgrave.jam.2250084)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the bias-adjusted Sharpe ratio of a portfolio","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed bias-adjusted Sharpe ratio of a portfolio","value":{"portfolios":[{"portfolioBiasAdjustedSharpeRatio":-0.8314248234836994}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioBiasAdjustedSharpeRatio":{"description":"The bias-adjusted Sharpe ratio of the portfolio","type":"number"}},"required":["portfolioBiasAdjustedSharpeRatio"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Bias-Adjusted Sharpe Ratio","tags":["Portfolio Analysis / Sharpe ratio"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/sharpe-ratio/confidence-interval":{"post":{"description":"Build a confidence interval for the Sharpe ratio of one or several portfolio(s).\n\nReferences\n* [Opdyke, J.D., Comparing Sharpe ratios: So where are the p-values?. J Asset Manag 8, 308–336 (2007)](https://link.springer.com/article/10.1057/palgrave.jam.2250084)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Build a two-sided confidence interval at a confidence level 99%","value":{"confidenceIntervalType":"twoSided","confidenceLevel":0.99,"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}}},"schema":{"properties":{"confidenceIntervalType":{"default":"twoSided","description":"The type of confidence interval to build","enum":["twoSided","lowerOneSided","upperOneSided"],"type":"string"},"confidenceLevel":{"default":0.95,"description":"The confidence level of the confidence interval to build, in percentage","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example of a one-sided confidence interval":{"description":"A one-sided lower confidence interval of a portfolio","value":{"portfolios":[{"portfolioSharpeRatioConfidenceInterval":[null,0.3309901925834179]}]}},"Example of a two-sided confidence interval":{"description":"A two-sided confidence interval of a portfolio","value":{"portfolios":[{"portfolioSharpeRatioConfidenceInterval":[-2.2283045143292535,0.46123772931706875]}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioSharpeRatioConfidenceInterval":{"description":"portfolioSharpeRatioConfidenceInterval[0] (resp. portfolioSharpeRatioConfidenceInterval[1]) is the lower (resp. upper) bound of the built confidence interval, possibly equal to null in case of a negative infinite (resp. positive infinite) bound","items":{"type":"number"},"maxItems":2,"minItems":2,"type":"array"}},"required":["portfolioSharpeRatioConfidenceInterval"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Sharpe Ratio Confidence Interval","tags":["Portfolio Analysis / Sharpe ratio"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/sharpe-ratio/probabilistic":{"post":{"description":"Compute the probabilistic Sharpe ratio of one or several portfolio(s).\n\nReferences\n* [Opdyke, J.D., Comparing Sharpe ratios: So where are the p-values?. J Asset Manag 8, 308–336 (2007)](https://link.springer.com/article/10.1057/palgrave.jam.2250084)\n* [Bailey, David H. and Lopez de Prado, Marcos, The Sharpe Ratio Efficient Frontier (April 1, 2012). Journal of Risk, Vol. 15, No. 2, Winter 2012/13](https://ssrn.com/abstract=1821643)\n","requestBody":{"content":{"application/json":{"examples":{"Probabilistic Sharpe ratio of a portfolio v.s. a benchmark":{"description":"Compute the probabilistic Sharpe ratio for a portfolio v.s. a benchmark","value":{"benchmarkValues":[100,101,98,102,95,90],"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}},"Probabilistic Sharpe ratio of a portfolio v.s. a benchmark Sharpe ratio":{"description":"Compute the probabilistic Sharpe ratio for a portfolio v.s. a benchmark Sharpe ratio","value":{"benchmarkSharpeRatio":0,"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}}},"schema":{"oneOf":[{"properties":{"benchmarkSharpeRatio":{"description":"The Sharpe ratio of the benchmark, in the same sampling frequency as the sampling frequency of the portfolio values","type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate","benchmarkSharpeRatio"],"type":"object"},{"properties":{"benchmarkValues":{"description":"benchmarkValues[t] is the value of the benchmark at the time t; the benchmarkValues array must have the same length as all the portfolioValues arrays","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t; all the portfolioValues arrays must have the same length as the benchmarkValues array","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate","benchmarkValues"],"type":"object"}]}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"The probabilistic Sharpe ratio of a portfolio","value":{"portfolios":[{"portfolioProbabilisticSharpeRatio":0.0452890775705429}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioProbabilisticSharpeRatio":{"description":"The probabilistic Sharpe ratio of the portfolio, in percentage","type":"number"}},"required":["portfolioProbabilisticSharpeRatio"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Probabilistic Sharpe Ratio","tags":["Portfolio Analysis / Sharpe ratio"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/sharpe-ratio/probabilistic/minimum-track-record-length":{"post":{"description":"Compute the minimum track record length of one or several portfolio(s).\n\nReferences\n* [Bailey, David H. and Lopez de Prado, Marcos, The Sharpe Ratio Efficient Frontier (April 1, 2012). Journal of Risk, Vol. 15, No. 2, Winter 2012/13](https://ssrn.com/abstract=1821643)\n","requestBody":{"content":{"application/json":{"examples":{"Minimum Track Record Length of a portfolio v.s. a benchmark":{"description":"Compute the minimum track record length of a portfolio v.s. a benchmark at a confidence level of 95%","value":{"benchmarkValues":[100,101,98,85,75,65],"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}},"Minimum Track Record Length of a portfolio v.s. a benchmark Sharpe ratio":{"description":"Compute the minimum track record length of a portfolio v.s. a benchmark Sharpe ratio of 0 at a confidence level of 95%","value":{"benchmarkSharpeRatio":0,"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}}},"schema":{"oneOf":[{"properties":{"benchmarkSharpeRatio":{"description":"The Sharpe ratio of the benchmark, in the same sampling frequency as the sampling frequency of the portfolio values","type":"number"},"confidenceLevel":{"default":0.95,"description":"The confidence level of the minimum track record length, in percentage","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate","benchmarkSharpeRatio"],"type":"object"},{"properties":{"benchmarkValues":{"description":"benchmarkValues[t] is the value of the benchmark at the time t; the benchmarkValues array must have the same length as all the portfolioValues arrays","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"},"confidenceLevel":{"default":0.95,"description":"The confidence level of the minimum track record length, in percentage","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":4,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate","benchmarkSharpeRatio"],"type":"object"}]}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example of non-existing minimum track record length":{"description":"Non-existing minimum track record length of a portfolio","value":{"portfolios":[{"portfolioSharpeRatioMinimumTrackRecordLength":null}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioSharpeRatioMinimumTrackRecordLength":{"description":"The minimum track record length of the portfolio, in number of required arithmetic returns, possibly equal to null in case the minimum track record length does not exist","type":"number"}},"required":["portfolioSharpeRatioMinimumTrackRecordLength"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Minimum Track Record Length","tags":["Portfolio Analysis / Sharpe ratio"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/tracking-error":{"post":{"description":"Compute the tracking error between a benchmark and one or several portfolio(s).\n\nReferences\n* [Wikipedia, Tracking error](https://en.wikipedia.org/wiki/Tracking_error) \n* Carl R. Bacon, Practical Portfolio Performance Measurement and Attribution \n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Computes the tracking error using the example in Bacon's book","value":{"benchmarkReturns":[0.002,0.025,0.018,-0.011,0.014,0.018,0.014,0.065,-0.015,0.042,-0.006,0.083,0.039,-0.038,-0.062,0.015,-0.048,0.021,0.06,0.056,-0.067,0.019,-0.003,0],"portfolios":[{"portfolioReturns":[0.003,0.026,0.011,-0.01,0.015,0.025,0.016,0.067,-0.014,0.04,-0.005,0.081,0.04,-0.037,-0.061,0.017,-0.049,-0.022,0.07,0.058,-0.065,0.024,-0.005,-0.009]}]}}},"schema":{"properties":{"benchmarkReturns":{"description":"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","items":{"type":"number"},"minItems":2,"type":"array"},"portfolios":{"items":{"properties":{"portfolioReturns":{"description":"portfolioReturns[t] is the return of the portfolio at the time t, the portfolioReturns must have the same length as the benchmarkReturns array","items":{"type":"number"},"minItems":2,"type":"array"}},"required":["portfolioReturns"],"type":"object"},"minItems":1,"type":"array"}},"required":["benchmarkReturns","portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"The computed tracking error using the example in Bacon's book","value":{"portfolios":[{"portfolioTrackingError":0.00950648535942116}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioTrackingError":{"description":"The tracking error of the portfolio","minimum":0,"type":"number"}},"required":["portfolioTrackingError"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Tracking Error","tags":["Portfolio Analysis"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/ulcer-index":{"post":{"description":"Compute the Ulcer Index of one or several portfolio(s).\n\nReferences\n* Carl R. Bacon, Practical Portfolio Performance Measurement and Attribution\n* [Peter G. Martin, Ulcer Index, An Alternative Approach to the Measurement of Investment Risk & Risk-Adjusted Performance](http://www.tangotools.com/ui/ui.htm)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the Ulcer Index of a portfolio based on portfolio values","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed Ulcer Index of a portfolio","value":{"portfolios":[{"portfolioUlcerIndex":0.14433756729740643}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioUlcerIndex":{"description":"The Ulcer Index of the portfolio","type":"number"}},"required":["portfolioUlcerIndex"],"type":"object"},"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Ulcer Index","tags":["Portfolio Analysis"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/ulcer-performance-index":{"post":{"description":"Compute the Ulcer Performance Index of one or several portfolio(s).\n\nReferences\n* Carl R. Bacon, Practical Portfolio Performance Measurement and Attribution\n* [Peter G. Martin, Ulcer Index, An Alternative Approach to the Measurement of Investment Risk & Risk-Adjusted Performance](http://www.tangotools.com/ui/ui.htm)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the Ulcer Performance Index of a portfolio based on portfolio values","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}],"riskFreeRate":0}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["portfolios","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed Ulcer Performance Index of a portfolio","value":{"portfolios":[{"portfolioUlcerPerformanceIndex":-0.45642249763676057}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioUlcerPerformanceIndex":{"description":"The Ulcer Performance Index of the portfolio","type":"number"}},"required":["portfolioUlcerPerformanceIndex"],"type":"object"},"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Ulcer Performance Index","tags":["Portfolio Analysis"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/conditional/cornish-fisher":{"post":{"description":"Compute the Cornish-Fisher conditional value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Boudt, Kris and Peterson, Brian G. and Croux, Christophe, Estimation and Decomposition of Downside Risk for Portfolios with Non-Normal Returns (October 31, 2007). Journal of Risk, Vol. 11, No. 2, pp. 79-103, 2008](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1024151).\n* [Maillard, Didier, A User’s Guide to the Cornish Fisher Expansion](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1997178)\n* [Lamb, John D., Maura E. Monville, and Kai-Hong Tee. Making Cornish–fisher Fit for Risk Measurement, Journal of Risk, Volume 21, Number 5, p. 53-81](http://doi.org/10.21314/JOR.2019.408)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the Cornish-Fisher conditional value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":5,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed conditional value at risk of a portfolio","value":{"portfolios":[{"portfolioConditionalValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioConditionalValueAtRisk":{"description":"The conditional value at risk of the portfolio","type":"number"}},"required":["portfolioConditionalValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Cornish-Fisher Conditional Value At Risk","tags":["Portfolio Analysis / Conditional Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/conditional/cornish-fisher/corrected":{"post":{"description":"Compute the corrected Cornish-Fisher conditional value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Maillard, Didier, A User’s Guide to the Cornish Fisher Expansion](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1997178)\n* [Lamb, John D., Maura E. Monville, and Kai-Hong Tee. Making Cornish–fisher Fit for Risk Measurement, Journal of Risk, Volume 21, Number 5, p. 53-81](http://doi.org/10.21314/JOR.2019.408)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the corrected Cornish-Fisher conditional value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":5,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed conditional value at risk of a portfolio","value":{"portfolios":[{"portfolioConditionalValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioConditionalValueAtRisk":{"description":"The conditional value at risk of the portfolio","type":"number"}},"required":["portfolioConditionalValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Corrected Cornish-Fisher Conditional Value At Risk","tags":["Portfolio Analysis / Conditional Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/conditional/gaussian":{"post":{"description":"Compute the Gaussian conditional value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Boudt, Kris and Peterson, Brian G. and Croux, Christophe, Estimation and Decomposition of Downside Risk for Portfolios with Non-Normal Returns (October 31, 2007). Journal of Risk, Vol. 11, No. 2, pp. 79-103, 2008](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1024151).\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the Gaussian conditional value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":3,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed conditional value at risk of a portfolio","value":{"portfolios":[{"portfolioConditionalValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioConditionalValueAtRisk":{"description":"The conditional value at risk of the portfolio","type":"number"}},"required":["portfolioConditionalValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Gaussian Conditional Value At Risk","tags":["Portfolio Analysis / Conditional Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/conditional/historical":{"post":{"description":"Compute the historical conditional value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Wikipedia, Value at risk](https://en.wikipedia.org/wiki/Value_at_risk)\n* [Acerbi, C. and Tasche, D. (2002), Expected Shortfall: A Natural Coherent Alternative to Value at Risk. Economic Notes, 31: 379-388](https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0300.00091)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the historical conditional value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed conditional value at risk of a portfolio","value":{"portfolios":[{"portfolioConditionalValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioConditionalValueAtRisk":{"description":"The conditional value at risk of the portfolio","type":"number"}},"required":["portfolioConditionalValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Historical Conditional Value At Risk","tags":["Portfolio Analysis / Conditional Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/cornish-fisher":{"post":{"description":"Compute the Cornish-Fisher value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Laurent Favre and José-Antonio Galeano, Mean-Modified Value-at-Risk Optimization with Hedge Funds, The Journal of Alternative Investments Fall 2002, 5 (2) 21-25](https://jai.pm-research.com/content/5/2/21)\n* [Lamb, John D., Maura E. Monville, and Kai-Hong Tee. Making Cornish–fisher Fit for Risk Measurement, Journal of Risk, Volume 21, Number 5, p. 53-81](http://doi.org/10.21314/JOR.2019.408)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the Cornish-Fisher value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":5,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed value at risk of a portfolio","value":{"portfolios":[{"portfolioValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValueAtRisk":{"description":"The value at risk of the portfolio","type":"number"}},"required":["portfolioValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Cornish-Fisher Value At Risk","tags":["Portfolio Analysis / Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/cornish-fisher/corrected":{"post":{"description":"Compute the corrected Cornish-Fisher value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Lamb, John D., Maura E. Monville, and Kai-Hong Tee. Making Cornish–fisher Fit for Risk Measurement, Journal of Risk, Volume 21, Number 5, p. 53-81](http://doi.org/10.21314/JOR.2019.408)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the corrected Cornish-Fisher value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":5,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed value at risk of a portfolio","value":{"portfolios":[{"portfolioValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValueAtRisk":{"description":"The value at risk of the portfolio","type":"number"}},"required":["portfolioValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Corrected Cornish-Fisher Value At Risk","tags":["Portfolio Analysis / Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/gaussian":{"post":{"description":"Compute the Gaussian value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Ballotta, Laura and Fusai, Gianluca, A Gentle Introduction to Value at Risk](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2942138)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the Gaussian value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":3,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed value at risk of a portfolio","value":{"portfolios":[{"portfolioValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValueAtRisk":{"description":"The value at risk of the portfolio","type":"number"}},"required":["portfolioValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Gaussian Value At Risk","tags":["Portfolio Analysis / Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/value-at-risk/historical":{"post":{"description":"Compute the historical value at risk of one or several portfolio(s) from portfolio values.\n\nReferences\n* [Wikipedia, Value at risk](https://en.wikipedia.org/wiki/Value_at_risk)\n* [Acerbi, C. and Tasche, D. (2002), Expected Shortfall: A Natural Coherent Alternative to Value at Risk. Economic Notes, 31: 379-388](https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0300.00091)\n","requestBody":{"content":{"application/json":{"examples":{"From portfolio values":{"description":"Compute the historical value at risk of a portfolio based on portfolio values, at the default 95% confidence level","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"properties":{"confidenceLevel":{"default":0.95,"description":"The confidence level","exclusiveMaximum":true,"exclusiveMinimum":true,"maximum":1,"minimum":0,"type":"number"},"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed value at risk of a portfolio","value":{"portfolios":[{"portfolioValueAtRisk":0.17647058823529413}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValueAtRisk":{"description":"The value at risk of the portfolio","type":"number"}},"required":["portfolioValueAtRisk"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Historical Value At Risk","tags":["Portfolio Analysis / Value At Risk"],"x-codegen-request-body-name":"body"}},"/portfolio/analysis/volatility":{"post":{"description":"Compute the volatility (i.e., standard deviation) of one or several portfolio(s) from either: \n* Portfolio assets covariance matrix\n* Portfolio values\n\nReferences\n* [Wikipedia, Standard Deviation](https://en.wikipedia.org/wiki/Standard_deviation#Finance)\n* Carl R. Bacon, Practical Portfolio Performance Measurement and Attribution\n* Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"From asset covariance matrix":{"description":"Compute the volatility of 2 portfolios based on the assets covariance matrix","value":{"assets":2,"assetsCovarianceMatrix":[[0.0025,0.0005],[0.0005,0.01]],"portfolios":[{"assetsWeights":[1,0]},{"assetsWeights":[0,1]}]}},"From portfolio values":{"description":"Compute the volatility of a portfolio based on portfolio values","value":{"portfolios":[{"portfolioValues":[100,95,100,90,85,70]}]}}},"schema":{"oneOf":[{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"portfolios":{"items":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios","assets","assetsCovarianceMatrix"],"type":"object"},{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["portfolioValues"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed volatility of 2 portfolios","value":{"portfolios":[{"portfolioVolatility":0.05},{"portfolioVolatility":0.1}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioVolatility":{"description":"The volatility of the portfolio","minimum":0,"type":"number"}},"required":["portfolioVolatility"],"type":"object"},"minItems":1,"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Volatility","tags":["Portfolio Analysis"],"x-codegen-request-body-name":"body"}},"/portfolio/construction/investable":{"post":{"description":"Compute an investable portfolio as close as possible, in terms of assets weights, to a desired portfolio, taking into account:\n* The desired assets weights\n* The desired assets groups weights\n* The desired maximum assets groups weights\n* The prices of the assets\n* The portfolio value\n* The requirement to purchase some assets by round lots or by odd lots\n* The possibility to purchase some assets by a fractional quantity of shares\n* The requirement to purchase a minimum number of shares, or a minimum monetary value, for some assets\n\nReferences\n* [Steiner, Andreas, Accuracy and Rounding in Portfolio Construction](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2261131)\n","requestBody":{"content":{"application/json":{"examples":{"Example (groups weights)":{"description":"Construct an investable portfolio of 10,000$ made of 4 assets with assets groups weights","value":{"assets":4,"assetsGroups":[[1,2],[3,4]],"assetsGroupsWeights":[0.4,0.4],"assetsPrices":[10,25,100,500],"assetsWeights":[0.2,null,null,null],"portfolioValue":10000}},"Example (no groups weights)":{"description":"Construct an investable portfolio of 10,000$ made of 3 assets","value":{"assets":3,"assetsPrices":[10,25,500],"assetsWeights":[0.05,0.6,0.35],"portfolioValue":10000}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; 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Portfolios: Theory, Algorithms, Applications & Puzzles](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3331184)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets, with maximum assets weights constraints","value":{"assets":2,"assetsCovarianceMatrix":[[0.0025,0.0005],[0.0005,0.01]],"constraints":{"maximumAssetsWeights":[0.4,1]}}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"constraints":{"properties":{"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in 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volatility-weighted portfolio.\n\nReferences\n * [Tristan Froidure, Khalid Jalalzai and Yves Choueifaty, Portfolio Rho-Representativity, International Journal of Theoretical and Applied FinanceVol. 22, No. 07, 1950034 (2019)](https://www.worldscientific.com/doi/10.1142/S0219024919500341)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets with volatilities equal to 0.05 and 0.1","value":{"assets":2,"assetsVolatilities":[0.05,0.1]}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsVolatilities":{"description":"assetsVolatilities[i] is the volatility of the asset i","items":{"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assets","assetsVolatilities"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed equal volatility-weighted portfolio of 2 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assets","value":{"assets":2}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"}},"required":["assets"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed equal-weighted portfolio of 2 assets","value":{"assetsWeights":[0.5,0.5]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Equal Weighted Portfolio","tags":["Portfolio Optimization"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/hierarchical-risk-parity":{"post":{"description":"Compute the asset weights of the hierarchical risk parity portfolio, optionally subject to: \n* Minimum and maximum weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * [Lopez de Prado, M. (2016). Building diversified portfolios that outperform out-of-sample. Journal of Portfolio Management, 42(4), 59–69](https://jpm.pm-research.com/content/42/4/59)\n * [Johann Pfitzinger & Nico Katzke, 2019. A constrained hierarchical risk parity algorithm with cluster-based capital allocation. Working Papers 14/2019, Stellenbosch University, Department of Economics](https://ideas.repec.org/p/sza/wpaper/wpapers328.html)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets, with maximum assets weights and portfolio exposure constraints","value":{"assets":2,"assetsCovarianceMatrix":[[0.0025,0.0005],[0.0005,0.01]],"constraints":{"maximumAssetsWeights":[0.4,1],"maximumPortfolioExposure":0.5,"minimumPortfolioExposure":0.5}}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"clusteringMethod":{"default":"singleLinkage","description":"The hierarchical clustering method to use","enum":["singleLinkage","averageLinkage","completeLinkage","wardLinkage"],"type":"string"},"clusteringOrdering":{"default":"r-hclust","description":"The order to impose on the hierarchical clustering tree leaves","enum":["r-hclust","optimal"],"type":"string"},"constraints":{"properties":{"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"}},"required":["assets","assetsCovarianceMatrix"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed portfolio of 2 assets","value":{"assetsWeights":[0.4,0.09999999999998999]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Hierarchical Risk Parity Portfolio","tags":["Portfolio Optimization"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/hierarchical-risk-parity/clustering-based":{"post":{"description":"Compute the asset weights of the hierarchical clustering-based risk parity portfolio, optionally subject to: \n* Minimum and maximum weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * [Machine Learning for Asset Management: New Developments and Financial Applications, Emmanuel Jurczenko, Chapter 9, Harald Lohre,Carsten Rother,Kilian Axel Schäfer, Hierarchical Risk Parity: Accounting for Tail Dependencies in Multi-asset Multi-factor Allocations](https://onlinelibrary.wiley.com/doi/10.1002/9781119751182.ch9)\n * [Thomas Raffinot, Hierarchical Clustering-Based Asset Allocation, The Journal of Portfolio Management Multi-Asset Special Issue 2018, 44 (2) 89-99](https://jpm.pm-research.com/content/44/2/89.abstract)\n * [Raffinot, Thomas, The Hierarchical Equal Risk Contribution Portfolio](https://ssrn.com/abstract=3237540)\n * [Johann Pfitzinger & Nico Katzke, 2019. A constrained hierarchical risk parity algorithm with cluster-based capital allocation. Working Papers 14/2019, Stellenbosch University, Department of Economics](https://ideas.repec.org/p/sza/wpaper/wpapers328.html)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets, with maximum assets weights and portfolio exposure constraints","value":{"assets":2,"assetsCovarianceMatrix":[[0.0025,0.0005],[0.0005,0.01]],"constraints":{"maximumAssetsWeights":[0.4,1],"maximumPortfolioExposure":0.5,"minimumPortfolioExposure":0.5}}}},"schema":{"properties":{"acrossClusterAllocationMethod":{"default":"equalWeighting","description":"The allocation method to use across clusters","enum":["equalWeighting","inverseVolatility","inverseVariance"],"type":"string"},"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset 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Gillen](https://www.bengillen.com/uploads/1/2/3/8/123891022/subsets.pdf)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 3 assets, with complete enumeration of subsets","value":{"assets":3,"assetsReturns":[0.01,0.02,0.03],"subsetPortfoliosEnumerationMethod":"complete"}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix","items":{"minimum":1,"type":"integer"},"minItems":2,"type":"array","uniqueItems":true},"minItems":1,"type":"array"},"assetsGroupsMatrix":{"description":"assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":1,"type":"array"},"maximumAssetsGroupsWeights":{"description":"maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided","items":{"type":"number"},"type":"array"},"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"},"subsetPortfolios":{"default":128,"description":"The number of subset portfolios to compute; only applicable if the enumeration method for the subset portfolios is random sampling","minimum":1,"type":"integer"},"subsetPortfoliosAggregationMethod":{"default":"average","description":"The method to aggregate the subset portfolios","enum":["average","median"],"type":"string"},"subsetPortfoliosEnumerationMethod":{"default":"randomSampling","description":"The method to enumerate the subset portfolios","enum":["complete","randomSampling"],"type":"string"},"subsetSize":{"description":"The number of assets to include in each subset portfolio; defaults to a value of order the square root of the total number of assets","minimum":2,"type":"integer"}},"required":["assets","assetsReturns"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed portfolio of 3 assets","value":{"assetsWeights":[0,0.3333333333333333,0.6666666666666666]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Subset Resampling-Based Maximum Return Portfolio","tags":["Portfolio Optimization / Mean-Variance"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/maximum-sharpe-ratio":{"post":{"description":"Compute the asset weights of the maximum Sharpe ratio portfolio, optionally subject to: \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * Harry M. 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Well Diversified Efficient Portfolios, Working Papers Central Bank of Chile 336, Central Bank of Chile](https://ideas.repec.org/p/chb/bcchwp/336.html)\n * [Bouchaud, Jean-Philippe and Potters, Marc and Aguilar, Jean-Pierre, Missing Information and Asset Allocation, arXiv, 1997](https://arxiv.org/abs/cond-mat/9707042)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets with a risk free rate of 0%","value":{"assets":2,"assetsCovarianceMatrix":[[0.05,0.02],[0.02,0.07]],"assetsReturns":[0.05,0.1],"riskFreeRate":0}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix","items":{"minimum":1,"type":"integer"},"minItems":2,"type":"array","uniqueItems":true},"minItems":1,"type":"array"},"assetsGroupsMatrix":{"description":"assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":1,"type":"array"},"deltaReturn":{"default":0.1,"description":"The relative tolerance over the maximum Sharpe ratio portfolio return","minimum":0,"type":"number"},"deltaVolatility":{"default":0.1,"description":"The relative tolerance over the maximum Sharpe ratio portfolio volatility","minimum":0,"type":"number"},"maximumAssetsGroupsWeights":{"description":"maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided","items":{"type":"number"},"type":"array"},"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["assets","assetsReturns","assetsCovarianceMatrix","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed portfolio weights for 2 assets","value":{"assetsWeights":[0.44545623478220464,0.5545437652177954]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Diversified Maximum Sharpe Ratio Portfolio","tags":["Portfolio Optimization / Mean-Variance"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/maximum-sharpe-ratio/subset-resampling-based":{"post":{"description":"Compute the asset weights of the susbet resampling-based maximum Sharpe ratio portfolio, following the methodology described in the first and the second references, optionally subject to: \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * [CSSA, Random Subspace Optimization (RSO)](https://cssanalytics.wordpress.com/2013/10/06/random-subspace-optimization-rso/)\n * [Subset Optimization for Asset Allocation,Benjamin J. Gillen](https://www.bengillen.com/uploads/1/2/3/8/123891022/subsets.pdf)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets with a risk free rate of 0%","value":{"assets":3,"assetsCovarianceMatrix":[[0.05,0.02,0],[0.02,0.07,0.5],[0,0.5,0.1]],"assetsReturns":[0.05,0.1,0.025],"riskFreeRate":0}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix","items":{"minimum":1,"type":"integer"},"minItems":2,"type":"array","uniqueItems":true},"minItems":1,"type":"array"},"assetsGroupsMatrix":{"description":"assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":1,"type":"array"},"maximumAssetsGroupsWeights":{"description":"maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided","items":{"type":"number"},"type":"array"},"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"},"riskFreeRate":{"description":"The risk free rate","type":"number"},"subsetPortfolios":{"default":128,"description":"The number of subset portfolios to compute; only applicable if the enumeration method for the subset portfolios is random sampling","minimum":1,"type":"integer"},"subsetPortfoliosAggregationMethod":{"default":"average","description":"The method to aggregate the subset portfolios","enum":["average","median"],"type":"string"},"subsetPortfoliosEnumerationMethod":{"default":"randomSampling","description":"The method to enumerate the subset portfolios","enum":["complete","randomSampling"],"type":"string"},"subsetSize":{"description":"The number of assets to include in each subset portfolio; defaults to a value of order the square root of the total number of assets","minimum":2,"type":"integer"}},"required":["assets","assetsReturns","assetsCovarianceMatrix","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed portfolio weights for 3 assets","value":{"assetsWeights":[0.35454545454545444,0.5845170454545454,0.06093750000000007]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Subset Resampling-Based Maximum Sharpe Ratio Portfolio","tags":["Portfolio Optimization / Mean-Variance"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/maximum-ulcer-performance-index":{"post":{"description":"Compute the asset weights of the maximum Ulcer Performance Index portfolio, optionally subject to: \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nNotes: \n* This endpoint will return an error if the maximum Ulcer Performance Index portfolio has a negative Ulcer Performance Index\n\nReferences\n * [Peter G. Martin, Ulcer Index, An Alternative Approach to the Measurement of Investment Risk & Risk-Adjusted Performance](http://www.tangotools.com/ui/ui.htm)\n * [A. Chekhlov, S. Uryasev, M. Zabarankin, Portfolio Optimization with Drawdown Constraints, Supply Chain and Finance, p 209-228](https://doi.org/10.1142/9789812562586_0013)\n * [A. Chekhlov, S. Uryasev, M. Zabarankin, Drawdown Measure in Portfolio Optimization, International Journal of Theoretical and Applied FinanceVol. 08, No. 01, pp. 13-58 (2005)](https://www.worldscientific.com/doi/10.1142/S0219024905002767)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets with a risk free rate of 0%","value":{"assets":[{"assetPrices":[100,95,110]},{"assetPrices":[100,105,100]}],"riskFreeRate":0}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetPrices":{"description":"assetPrices[t] is the price of the asset at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetPrices"],"type":"object"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix","items":{"minimum":1,"type":"integer"},"minItems":2,"type":"array","uniqueItems":true},"minItems":1,"type":"array"},"assetsGroupsMatrix":{"description":"assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":1,"type":"array"},"maximumAssetsGroupsWeights":{"description":"maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided","items":{"type":"number"},"type":"array"},"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"},"riskFreeRate":{"description":"The risk free rate","type":"number"}},"required":["assets","riskFreeRate"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed portfolio weights for 2 assets","value":{"assetsWeights":[0.3101913068855954,0.6898086931144047]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Maximum Ulcer Performance Index Portfolio","tags":["Portfolio Optimization"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/mean-variance-efficient":{"post":{"description":"Compute the asset weights of a mean-variance efficient portfolio, optionally subject to: \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\n> A mean-variance efficient portfolio is a portfolio belonging to [the mean-variance efficient frontier](#post-/portfolio/analysis/mean-variance/efficient-frontier).\n\nReferences\n * Harry M. 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Well Diversified Efficient Portfolios, Working Papers Central Bank of Chile 336, Central Bank of Chile](https://ideas.repec.org/p/chb/bcchwp/336.html)\n * [Bouchaud, Jean-Philippe and Potters, Marc and Aguilar, Jean-Pierre, Missing Information and Asset Allocation, arXiv, 1997](https://arxiv.org/abs/cond-mat/9707042)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets with a portfolio return constraint of 15%","value":{"assets":2,"assetsCovarianceMatrix":[[1,0.3],[0.3,1]],"assetsReturns":[0.1,0.2],"constraints":{"deltaReturn":0.05,"deltaVolatility":0.05,"portfolioReturn":0.175}}},"Example with group constraints":{"description":"Compute the portfolio weights for 3 assets with a maximum group weights constraint and a portfolio return constraint of 15%","value":{"assets":3,"assetsCovarianceMatrix":[[1,0.3,-0.2],[0.3,1,0.2],[-0.2,0.2,1]],"assetsReturns":[0.1,0.2,0.15],"constraints":{"assetsGroups":[[1,2]],"maximumAssetsGroupsWeights":[0.5],"portfolioReturn":0.15}}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; 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Gillen](https://www.bengillen.com/uploads/1/2/3/8/123891022/subsets.pdf)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 3 assets with a risk tolerance constraint of 2","value":{"assets":3,"assetsCovarianceMatrix":[[1,0,0],[0,1,0],[0,0,1]],"assetsReturns":[0.1,0.2,0.3],"constraints":{"riskTolerance":2}}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; 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Martin, Ulcer Index, An Alternative Approach to the Measurement of Investment Risk & Risk-Adjusted Performance](http://www.tangotools.com/ui/ui.htm)\n * [A. Chekhlov, S. Uryasev, M. Zabarankin, Portfolio Optimization with Drawdown Constraints, Supply Chain and Finance, p 209-228](https://doi.org/10.1142/9789812562586_0013)\n * [A. Chekhlov, S. Uryasev, M. Zabarankin, Drawdown Measure in Portfolio Optimization, International Journal of Theoretical and Applied FinanceVol. 08, No. 01, pp. 13-58 (2005)](https://www.worldscientific.com/doi/10.1142/S0219024905002767)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets","value":{"assets":[{"assetPrices":[100,95,110]},{"assetPrices":[100,105,100]}]}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetPrices":{"description":"assetPrices[t] is the price of the asset at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetPrices"],"type":"object"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix","items":{"minimum":1,"type":"integer"},"minItems":2,"type":"array","uniqueItems":true},"minItems":1,"type":"array"},"assetsGroupsMatrix":{"description":"assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":1,"type":"array"},"maximumAssetsGroupsWeights":{"description":"maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided","items":{"type":"number"},"type":"array"},"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"}},"required":["assets"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed portfolio weights for 2 assets","value":{"assetsWeights":[0.24615095383708674,0.7538490461629133]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Minimum Ulcer Index Portfolio","tags":["Portfolio Optimization"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/minimum-variance":{"post":{"description":"Compute the asset weights of the minimum variance portfolio, optionally subject to: \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * Harry M. 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Well Diversified Efficient Portfolios, Working Papers Central Bank of Chile 336, Central Bank of Chile](https://ideas.repec.org/p/chb/bcchwp/336.html)\n * [Bouchaud, Jean-Philippe and Potters, Marc and Aguilar, Jean-Pierre, Missing Information and Asset Allocation, arXiv, 1997](https://arxiv.org/abs/cond-mat/9707042)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets, with maximum assets weights and portfolio exposure constraints","value":{"assets":2,"assetsCovarianceMatrix":[[0.0025,0.0005],[0.0005,0.01]],"constraints":{"maximumAssetsWeights":[0.4,1],"maximumPortfolioExposure":0.5,"minimumPortfolioExposure":0.5}}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix","items":{"minimum":1,"type":"integer"},"minItems":2,"type":"array","uniqueItems":true},"minItems":1,"type":"array"},"assetsGroupsMatrix":{"description":"assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":1,"type":"array"},"deltaReturn":{"default":0.1,"description":"The relative tolerance over the minimum variance portfolio return, if applicable","minimum":0,"type":"number"},"deltaVolatility":{"default":0.1,"description":"The relative tolerance over the minimum variance portfolio volatility","minimum":0,"type":"number"},"maximumAssetsGroupsWeights":{"description":"maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided","items":{"type":"number"},"type":"array"},"maximumAssetsWeights":{"description":"maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"maximumPortfolioExposure":{"default":1,"description":"The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure","maximum":1,"minimum":0,"type":"number"},"minimumAssetsWeights":{"description":"minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"type":"array"},"minimumPortfolioExposure":{"default":1,"description":"The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure","maximum":1,"minimum":0,"type":"number"}},"type":"object"}},"required":["assets","assetsCovarianceMatrix"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Computed diversified minimum variance portfolio of 2 assets","value":{"assetsWeights":[0.31288809725799416,0.18711190967754268]}}},"schema":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetsWeights"],"type":"object"}}},"description":"OK"}},"summary":"Diversified Minimum Variance Portfolio","tags":["Portfolio Optimization / Mean-Variance"],"x-codegen-request-body-name":"body"}},"/portfolio/optimization/minimum-variance/subset-resampling-based":{"post":{"description":"Compute the asset weights of the subset resampling-based minimum variance portfolio, following the methodology described in the first and the second references, optionally subject to: \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * [CSSA, Random Subspace Optimization (RSO)](https://cssanalytics.wordpress.com/2013/10/06/random-subspace-optimization-rso/)\n * [Subset Optimization for Asset Allocation,Benjamin J. Gillen](https://www.bengillen.com/uploads/1/2/3/8/123891022/subsets.pdf)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Compute the portfolio weights for 2 assets, with maximum assets weights and portfolio exposure constraints; because of only 2 assets, the computed portfolio will be identical to the equivalent minimum variance portfolio","value":{"assets":2,"assetsCovarianceMatrix":[[0.0025,0.0005],[0.0005,0.01]],"constraints":{"maximumAssetsWeights":[0.4,1],"maximumPortfolioExposure":0.5,"minimumPortfolioExposure":0.5},"subsetPortfolios":1}}},"schema":{"properties":{"assets":{"description":"The number of assets","minimum":2,"type":"integer"},"assetsCovarianceMatrix":{"description":"assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j","items":{"items":{"type":"number"},"minItems":2,"type":"array"},"minItems":2,"type":"array"},"assetsReturns":{"description":"assetsReturns[i] is the arithmetic return of asset i","items":{"type":"number"},"minItems":1,"type":"array"},"constraints":{"properties":{"assetsGroups":{"items":{"description":"assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; 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INSEAD Working Paper No. 2016/15/FIN](https://ssrn.com/abstract=2746471)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Simulate 3 buy and hold portfolios, each made of 3 assets with only one asset invested","value":{"assets":[{"assetPrices":[100,105,110]},{"assetPrices":[15,12.5,11.25]},{"assetPrices":[0.5,0.51,0.49]}],"portfolios":[{"assetsWeights":[1,0,0]},{"assetsWeights":[0,1,0]},{"assetsWeights":[0,0,1]}]}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetPrices":{"description":"assetPrices[t] is the price of the asset at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetPrices"],"type":"object"},"minItems":1,"type":"array"},"portfolios":{"items":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":1,"type":"array"}},"required":["assetsWeights"],"type":"object"},"minItems":1,"type":"array"}},"required":["assets","portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Simulated portfolios over 2 time periods","value":{"portfolios":[{"portfolioValues":[100,105,110]},{"portfolioValues":[100,83.33333333333334,75]},{"portfolioValues":[100,102,98]}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"minimum":0,"type":"number"},"type":"array"}},"required":["portfolioValues"],"type":"object"},"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Drift-weight Portfolio Rebalancing","tags":["Portfolio Simulation"],"x-codegen-request-body-name":"body"}},"/portfolio/simulation/rebalancing/fixed-weight":{"post":{"description":"Simulate the evolution of one or several portfolio(s) over one or several time period(s), the portfolio(s) being rebalanced toward fixed weights at the beginning of each time period.\n\nReferences\n* [Hillion, Pierre, The Ex-Ante Rebalancing Premium (March 11, 2016). INSEAD Working Paper No. 2016/15/FIN](https://ssrn.com/abstract=2746471) \n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Simulate 3 portfolios, each rebalanced toward the provided assets weights at the beginning of each of the 2 time periods","value":{"assets":[{"assetPrices":[100,105,110]},{"assetPrices":[15,12.5,11.25]},{"assetPrices":[0.5,0.51,0.49]}],"portfolios":[{"assetsWeights":[0.5,0.5,0]},{"assetsWeights":[0,0.5,0.5]},{"assetsWeights":[0.5,0,0.5]}]}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetPrices":{"description":"assetPrices[t] is the price of the asset at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetPrices"],"type":"object"},"minItems":1,"type":"array"},"portfolios":{"items":{"properties":{"assetsWeights":{"description":"assetsWeights[i] is the weight of the asset i in the portfolio, in percentage","items":{"maximum":1,"minimum":0,"type":"number"},"minItems":1,"type":"array"}},"required":["assetsWeights"],"type":"object"},"minItems":1,"type":"array"}},"required":["assets","portfolios"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Simulated portfolios over 2 time periods","value":{"portfolios":[{"portfolioValues":[100,94.16666666666667,91.70039682539684]},{"portfolioValues":[100,92.66666666666667,86.21633986928106]},{"portfolioValues":[100,103.5,103.93487394957984]}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"minimum":0,"type":"number"},"type":"array"}},"required":["portfolioValues"],"type":"object"},"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Fixed-weight Portfolio Rebalancing","tags":["Portfolio Simulation"],"x-codegen-request-body-name":"body"}},"/portfolio/simulation/rebalancing/random-weight":{"post":{"description":"Simulate the evolution of one or several portfolio(s) over one or several time period(s), the portfolio(s) being rebalanced toward random weights at the beginning of each time period.\n\nReferences\n* [R Stein, Not fooled by randomness: Using random portfolios to analyse investment funds, Investment Analysts Journal, 43:79, 1-15, DOI: 10.1080/10293523.2014.11082564](https://www.tandfonline.com/doi/abs/10.1080/10293523.2014.11082564)\n","requestBody":{"content":{"application/json":{"examples":{"Example":{"description":"Simulate 2 portfolios each rebalanced toward random assets weights at the beginning of each of the 2 time periods","value":{"assets":[{"assetPrices":[100,105,110]},{"assetPrices":[15,12.5,11.25]},{"assetPrices":[0.5,0.51,0.49]}],"portfolios":2}}},"schema":{"properties":{"assets":{"items":{"properties":{"assetPrices":{"description":"assetPrices[t] is the price of the asset at the time t","items":{"exclusiveMinimum":true,"minimum":0,"type":"number"},"minItems":2,"type":"array"}},"required":["assetPrices"],"type":"object"},"minItems":1,"type":"array"},"portfolios":{"default":25,"description":"The number of portfolios to simulate","minimum":1,"type":"integer"}},"required":["assets"],"type":"object"}}},"required":true},"responses":{"200":{"content":{"application/json":{"examples":{"Example":{"description":"Simulated portfolios over 2 time periods","value":{"portfolios":[{"portfolioValues":[100,90.8178403620342,84.65407625993741]},{"portfolioValues":[100,102.43258698946813,101.32419718013273]}]}}},"schema":{"properties":{"portfolios":{"items":{"properties":{"portfolioValues":{"description":"portfolioValues[t] is the value of the portfolio at the time t","items":{"minimum":0,"type":"number"},"type":"array"}},"required":["portfolioValues"],"type":"object"},"type":"array"}},"required":["portfolios"],"type":"object"}}},"description":"OK"}},"summary":"Random-weight Portfolio Rebalancing","tags":["Portfolio Simulation"],"x-codegen-request-body-name":"body"}}},"components":{"securitySchemes":{"ApiKeyAuth":{"description":"An [API key](#overview--api-key) is required to benefit from [higher API limits](#overview--api-limits).\n","in":"header","name":"X-API-Key","type":"apiKey"}}}}