Quant log | 3 min read

Singular Value Decomposition: From Astrophysics to Quantitative Trading 

Summary: We discuss an unexpected link between astrophysics and quantitative trading in our latest Quant Log. We explore the realm of Singular Value Decomposition (SVD), a robust matrix factorization tool, how SVD aids astrophysicists in unraveling cosmic enigmas, and SVDs role in extracting actionable insights from complex market data in quantitative trading. 

Each night when you gaze into the starry night sky, you probably would not think that the method astrophysicists use to study the origin and early history of the universe has a stellar connection with how we endeavor to steadily grow our investors’ wealth at Graham.  

In this Quant Log, we introduce Singular Value Decomposition (SVD), arguably the most widely used matrix factorization technique across all science and engineering fields. As a quantitative researcher with a background in gravitational-wave astrophysics, I have witnessed the prevalence and growing popularity of SVD in applications such as recommender systems, latent semantic analysis, political spectrum analysis, gene expression, and many more. Here, let’s turn the spotlight on two seemingly unrelated fields to appreciate the use of SVD: in astrophysics and in quantitative trading.  


Suppose you have a network of gravitational wave interferometers, and suppose you want to detect the relic gravitational wave background coming from a 10^(-32) second after the Big Bang. However, the detector network, operated as a phased array, encodes the superposition of these sinusoidal plane waves from all directions in the sky into stochastic gravitational-wave time series. How do you then map the distribution of relic radiation from the Big Bang with such noisy time series? Via SVD! Along with the antenna patterns of these detectors, you can decode information from the Big Bang and discard unwanted noise from other sources using SVD. So, has LIGO detected the cosmological gravitational wave background after the first ever direct observation of gravitational waves in 2015? Spoiler alert: the LIGO Lab has yet to reach the sensitivity for a detection of any gravitational wave backgrounds.

[Data source: Caltech/MIT/LIGO Lab] 

Quantitative Trading 

Like how astrophysicists decode the mystery of the universe using SVD, in quantitative trading, we often use Principal Component Analysis (PCA), which is just a special case of SVD applied to the data covariance matrix, to extract low-dimensional and efficient information from market data. PCA orthogonally projects noisy market data into a new coordinate system to identify a small number of principal components that explain most of the variation in the data. As a way of dimensionality reduction, we can then keep the first few dimensions and safely throw away the rest with minimal information loss. What’s neat here is that to implement PCA numerically, it is standard practice to compute the SVD of the data.  


This presentation includes statements that may constitute forward-looking statements. These statements may be identified by words such as “expects,” “looks forward to,” “anticipates,” “intends,” “plans,” “believes,” “seeks,” “estimates,” “will,” “project” or words of similar meaning. In addition, our representatives may from time to time make oral forward-looking statements. Such statements are based on the current expectations and certain assumptions of Graham Capital Management’s (“GCM”) management, and are, therefore, subject to certain risks and uncertainties. A variety of factors, many of which are beyond GCM’s control, affect the operations, performance, business strategy and results of the accounts that it manages and could cause the actual results, performance or achievements of such accounts to be materially different from any future results, performance or achievements that may be expressed or implied by such forward-looking statements or anticipated on the basis of historical trends.

This document is not a private offering memorandum and does not constitute an offer to sell, nor is it a solicitation of an offer to buy, any security. The views expressed herein are exclusively those of the authors and do not necessarily represent the views of Graham Capital Management. The information contained herein is not intended to provide accounting, legal, or tax advice and should not be relied on for investment decision making.

Tables, charts and commentary contained in this document have been prepared on a best efforts basis by Graham using sources it believes to be reliable although it does not guarantee the accuracy of the information on account of possible errors or omissions in the constituent data or calculations. No part of this document may be divulged to any other person, distributed, resold and/or reproduced without the prior written permission of GCM.

Subscribe to our Resource Center

By clicking the Button you confirming that you’re agree with our following Terms and Conditions

Subscribe to our Resource Center

Welcome to Graham Capital Management

By entering this website you are agreeing to its Terms of Use.

The risk of loss in trading commodities can be substantial. You should therefore carefully consider whether such trading is suitable for you in light of your financial condition. The high degree of leverage that is often obtainable in commodity trading can work against you as well as for you. The use of leverage can lead to large losses as well as gains.

In some cases, managed commodity accounts are subject to substantial charges for management and advisory fees. It may be necessary for those accounts that are subject to these charges to make substantial trading profits to avoid depletion or exhaustion of their assets. The disclosure document contains a complete description of the principal risk factors and each fee to be charged to your account by the commodity trading advisor (“CTA”). The regulations of the commodity futures trading commission (“CFTC”) require that prospective clients of a CTA receive a disclosure document when they are solicited to enter into an agreement whereby the CTA will direct or guide the client’s commodity interest trading and that certain risk factors be highlighted. This brief statement cannot disclose all of the risks and other significant aspects of the commodity markets. Therefore, eligible investors should carefully study the disclosure document to determine whether such trading is appropriate for you in light of your financial condition. Eligible investors are encouraged to access the disclosure document by contacting Graham, which will be provided  at no additional cost. The CFTC has not passed upon the merits of participating in this trading program nor on the adequacy or accuracy of the disclosure document. Other disclosure statements are required to be provided to you before a commodity account may be opened for you.  By accepting the terms of this statement and entering the site you are confirming your understanding of this statement.

Any “benefit plan investor” (e.g. An IRA or other ERISA investor) investor is hereby deemed to represent to Graham Capital Management (“Graham”) that an independent fiduciary (as defined in the ERISA fiduciary rule) is exercising its independent judgment with regard to such investor’s investment in any Graham managed fund and is aware of and acknowledges and agrees that Graham and its affiliates are relying on the exception set forth in clause (c)(1) of the ERISA fiduciary rule (i.e., the “transactions with independent fiduciaries with financial expertise” exception) with respect to any communications made to the investor or the investor’s fiduciary that are considered recommendations concerning any transaction and such benefit plan investor.

Although the site may include investment-related information, nothing on the site is a recommendation that you purchase, sell or hold any security or other investment, or that you pursue any investment style or strategy.

We do not give any advice or make any representations through the site as to whether any investment is suitable to you or will be profitable.

Nothing on the site is intended to be, and you should not consider anything on the site to be, investment, accounting, tax or legal advice. If you would like investment, accounting, tax or legal advice, you should consult with your own financial advisors, accountants or attorneys regarding your individual circumstances and needs.

The past performance of any investment, investment strategy or investment style is not indicative of future performance.

If you have been provided with a password to access the site you are solely responsible for maintaining the confidentiality and security of your password. You may not disclose your password to any third party. You accept full responsibility for any use of your password. You must notify Graham immediately of any actual or suspected loss, theft or unauthorized use of your password.

We are not obligated to inquire as to the authority or propriety of any use of or action taken under your password. We will not be responsible for any loss to you that arises from such use or action or from your failure to comply with these provisions.

The site, including all content, is provided as is and as available.

We disclaim all representations and warranties, express or implied, of any kind with respect to the site and the content including warranties of merchantability, fitness for a particular purpose and non-infringement of intellectual property and proprietary rights.

Without limiting our general disclaimer, we do not warrant the availability, accuracy, completeness, timeliness, functionality, reliability, sequencing or speed of delivery of the site or the content.