{"id":3271,"date":"2024-05-22T17:03:31","date_gmt":"2024-05-22T17:03:31","guid":{"rendered":"http:\/\/blog.valuengine.com\/?p=3271"},"modified":"2024-05-31T18:48:08","modified_gmt":"2024-05-31T18:48:08","slug":"quantitative-investment-modeling-120-years-since-bachelier-part-1-before-computers","status":"publish","type":"post","link":"http:\/\/blog.valuengine.com\/index.php\/quantitative-investment-modeling-120-years-since-bachelier-part-1-before-computers\/","title":{"rendered":"Quantitative Investment Modeling \u2013 120 Years Since Bachelier: Part 1 (Before Computers)"},"content":{"rendered":"\t\t
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The history of quantitative analysis goes back far before computers, and this work leads directly into how the field progresses once computers can be applied. In this first post we explore the history and development of quantitative analysis as it applied to finance in the pre-computer world of the early through mid 20th century.<\/p>

Actively managed ETFs are dominating new launches.\u00a0 However, the vast preponderance of assets remain in ETFs managed through quantitative investment modeling and dominated by index funds in particular.\u00a0 What many people don\u2019t know is that the roots of such investing approaches came many years before the 1940 Investment Act governing mutual funds and well before the dawn of computers.<\/p>

All 5,000 stocks, 16 sector groups, 140 industries, and 500 ETFs have been updated: Two-week free trial:<\/b> www.ValuEngine.com<\/b><\/a>\u00a0<\/b><\/h5>

Let\u2019s start with a couple of working definitions:<\/p>

Quantitative investment models<\/b>\u00a0offer a systematic and data-driven\u00a0approach<\/b>\u00a0to investment strategies in financial markets.\u00a0 Quantitative investment management <\/b>may loosely be described as the application of rigorous mathematical models and statistical principles, informed by economic theory, to the study of financial markets with the primary goal of selecting stocks and constructing investment portfolios.<\/p>

This diagram depicts an overview of components common to most quantitative investment models:<\/p>

\"A<\/p>

  1. The data series used in modeling must generally have two dimensions: a)<\/b> They must be values recorded at regular intervals across time, referred to as time series and b)<\/b> they must constitute a typical or representative sample of a larger group referred to as a cross-sectional sample.<\/li>
  2. Whether this data is being collected from historical records, culled from surveys, scraped from the web or some other alternative source, they must be cleaned and processed before modeling.<\/li>
  3. The modeling itself requires a methodology.\u00a0 The modeling technique used should be carefully selected to be appropriate for its purpose.<\/li>
  4. Along with the model\u2019s results, it is important to provide analytics that explain what the results mean and the size of potential estimation errors.<\/li><\/ol>
    Current ValuEngine reports on all covered stocks and ETFS can be viewed<\/b> HERE<\/b><\/a><\/h6>

    With the basic construct of quantitative investment modeling now broadly defined, the beginning of most models used in the 20th Century and beyond started with a master\u2019s thesis by Louis Bachelier in 1900.\u00a0 The original title in French was \u201cTh\u00e9orie de la Sp\u00e9culation\u201d <\/i>(Theory of Speculation) 1900.<\/p>

    <\/p>

    In mathematical terms, Bachelier’s achievement was to introduce the physics concept of Brownian motion, small random fluctuations, to stock price movements.\u00a0 His immediate purpose was to give a theory for the valuation of financial options.\u00a0 This was more than 70 years ahead of the Black-Scholes model for options valuation.\u00a0 Nevertheless, this landmark thesis was resurrected by Harry Markowitz in 1953 and William Sharpe in 1964 to provide the underpinnings of Modern Portfolio Theory.<\/p>

    The major achievement in the annals of the progress of quantitative investment research was also born in a master\u2019s thesis.\u00a0 Somewhat paradoxically, this came during The Great Depression and the global build-up to World War II.\u00a0 Even though the US stayed clear of the war for three more years, almost everyone in the country was talking about it.<\/p>

    The research in question was John Burr Williams and the year was 1938.\u00a0 Dr. Williams was a security analyst who sought a better understanding of what caused the stock market crash of 1929 and the subsequent Great Depression. He enrolled as a PhD student at Harvard and his thesis, which was to explore the intrinsic value of common stock, was published as The Theory of Investment Value.\u00a0 Williams proposed that the value of an asset should be calculated using \u201cevaluation by the rule of present worth\u201d. Thus, for a\u00a0common stock, the intrinsic, long-term worth is the\u00a0present value\u00a0of its future net cash flows\u2014in the form of\u00a0dividend\u00a0distributions and selling price.\u00a0 Eventually, The Theory of Investment Value was published as a book and is still being sold today.<\/p>

    \"John<\/p>

    1938 also saw the beginnings of an economic research study that would later become one of the most important linchpins of quantitative investing today.\u00a0 Alfred Cowles established the Cowles Commission for Research in Economics six years earlier.\u00a0 The Commission\u2019s motto \u201cScience is Measurement\u201d turned out to be quite prophetic indeed.\u00a0 In need of a measurement stick, Cowles created a market index.\u00a0 For the index, he aggregated the sum of the products of the closing price times the shares outstanding of every stock traded on the New York Stock Exchange.\u00a0 This was very laborious manual work done with only the aid of an adding machine.\u00a0 The idea was to capture the daily fund flows in the US Stock Market for econometric purposes.\u00a0 He considered this to be more representative of the average investors\u2019 experience than any of the Dow Jones Averages.\u00a0 The comparison proved apt because it was the continuing Cowles Commission research and index, sold to Standard & Poor\u2019s in 1957, that later grew to be the S&P 500 Index.<\/p>

    Let\u2019s skip another 14 years from 1938 to a PhD dissertation by Harry Markowitz.\u00a0 It was named simply \u2013 \u201cPortfolio Selection\u201d (1952).\u00a0 12 years later, no less an authority than William Sharpe, Ph.D. would characterize it as the seminal document laying out the underpinnings of Modern Portfolio Theory.\u00a0 The paper introduced the concept of optimizing portfolio diversification in an effort to lower portfolio risk (variance) without sacrificing return.<\/p>

    Current ValuEngine reports on these stocks or ETFS can be viewed<\/b> HERE<\/b><\/a><\/h6>

    The Markowitz model of portfolio <\/b>suggests that the risks can be minimized through diversification. Simultaneously, the model assures maximization of overall portfolio returns. Investors are presented with two types of stocks\u2014low-risk, low-return, and high-risk, high-return stocks.\u00a0 It introduced the concept of paired covariances rather than correlation coefficients for each pair of stocks in the portfolio.<\/p>

    The Markowitz\u00a0<\/b>formula is as follows:<\/p>

    R<\/b>P<\/b>\u00a0= I<\/b>RF<\/b>\u00a0+ (R<\/b>M<\/b>\u00a0\u2013 I<\/b>RF<\/b>) * \u03c3<\/b>P<\/b>\/\u03c3<\/b>M<\/b><\/p>

    Here, RP\u00a0= Expected Portfolio Return; RM\u00a0= Market Portfolio Return;<\/p>

    IRF\u00a0= Risk-free Rate of Interest; \u03c3M\u00a0= Market\u2019s Standard Deviation;<\/p>

    \u03c3P\u00a0\u00a0=\u00a0Standard Deviation of Portfolio<\/p>

    Many people consider the recently deceased Dr. Markowitz as the father of modern quantitative investing.\u00a0 Again, this concept was more theoretical than anything that was implementable by practitioners.\u00a0 The computing ability that was available in the 1950\u2019s simply could not handle all the required calculations for a portfolio of 30 stocks or more.<\/p>

    \"iCAPITAL<\/p>

    In the early 1960\u2019s, a number of interesting papers were written by soon-to-be very important people in quant finance including work on the Efficient Market Hypothesis and theories that stock prices move in a random walk, building on Bachelier\u2019s application of Brownian motion to stock prices. Dr. Jack Treynor and Dr. Paul Samuelson are just two of the authors writing during this period.<\/p>

    That said, I consider William Sharpe\u2019s \u201cPortfolio Selection\u201d in 1964 to be the next major event in the advancement of quantitative investing.\u00a0 It was his exposition of the underpinnings of Modern Portfolio Theory that really put the concept on the map.\u00a0 The article forever changed the curricula for students in finance throughout academia, starting with the University of Chicago and soon including Harvard, Yale, Cal-Berkeley and Stanford.\u00a0 After that it was mainstream teaching in almost all business schools in the United States.<\/p>

    \"A<\/p>

    \u201cPortfolio Selection\u201d introduces the Capital Asset Pricing Model.\u00a0 The CAPM is a cornerstone in portfolio management and seeks to find the expected return by looking at the risk-free rate, beta, and market risk premium.<\/p>

    CAPM Formula<\/b><\/p>

    Calculate the expected return of an\u00a0asset, given its\u00a0risk, is:<\/p>

    \ud835\udc38\ud835\udc45\ud835\udc56<\/b>=<\/b>\ud835\udc45\ud835\udc53<\/b>+<\/b>\ud835\udefd\ud835\udc56 * <\/b>(<\/b>\ud835\udc38\ud835\udc45\ud835\udc5a<\/b>\u2212<\/b>\ud835\udc45\ud835\udc53<\/b>) <\/b>where:<\/p>

    \ud835\udc38\ud835\udc45\ud835\udc56=expected\u00a0return\u00a0of\u00a0investment; \ud835\udc38\ud835\udc45\ud835\udc56=expected\u00a0return\u00a0of\u00a0market;<\/p>

    \ud835\udc45\ud835\udc53=risk-free\u00a0rate; \ud835\udefd\ud835\udc56=beta\u00a0of\u00a0the\u00a0investment; (\ud835\udc38\ud835\udc45\ud835\udc5a\u2212\ud835\udc45\ud835\udc53) = market\u00a0risk\u00a0premium<\/p>

    From this formula the formula for the Capital Market Line (CML) is derived.<\/p>

    \"CML<\/span><\/span><\/span><\/p>

    Dr. Sharpe\u2019s next major contribution, still used today, was the creation of the Sharpe Ratio.\u00a0 The Sharpe ratio helps investors evaluate which investments provide better returns per risk level.<\/p>

    Sharpe\u00a0Ratio<\/i><\/b>=<\/b> (<\/b>Rp<\/i><\/b>\u2212<\/b>Rf) <\/i><\/b>\/ <\/b>\u03c3p<\/i><\/b>\u00a0<\/b><\/p>

    where:<\/b><\/p>

    Rp<\/i><\/b> = return\u00a0of\u00a0portfolio <\/b>Rf<\/i><\/b>=risk-free\u00a0rate<\/b><\/p>

    \u03c3p<\/i><\/b> = standard\u00a0deviation\u00a0of\u00a0the\u00a0portfolio\u2019s\u00a0excess\u00a0return<\/b><\/p>

    Many of Sharpe\u2019s new constructs became the new focus of academia.\u00a0 This includes two 1965 efforts to advance the Efficient Market Hypothesis.<\/p>

    In 1965, Paul Samuelson, PhD (1965) (right pic) expanded on Bachelier\u2019s earlier work.\u00a0 He published a proof showing that if the market is efficient, prices will exhibit random-walk behavior\u2026However, from a practical application perspective, \u201ca nonempirical base of axioms does not yield empirical results.\u201d<\/p>

    \"Paul\"Eugene<\/p>

    Samuelson Fama<\/p>

    Eugene Fama\u2019s dissertation (1965): An \u2018efficient\u2019 market is defined as a market where there are large numbers of rational profit-maximizers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants.\u201d<\/p>

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    Random Walk Asset Pricing Defined<\/strong><\/p>

    Mu is a drift constant; Sigma is the standard deviation of the returns;<\/p>

    Delta{t} is the change in time; Y-sub-I is an independent and identically distributed random variable between 0 and 1.<\/p>

    <\/p>

    All of these were theoretical contributions to the underpinnings of quantitative investment research.\u00a0 By the mid-1960\u2019s, it was being taught in academia but not implemented as of yet for a variety of reasons including, but not limited to, lack of sufficient computing power.\u00a0 All that would change soon.<\/p>

    This journey through the past to the present will continue in next week\u2019s blog chapter with the progression of quantitative analysis through the computer age.<\/p>

    _______________________________________________________________<\/p>

    By Herbert Blank<\/b><\/h5>
    Senior Quantitative Analyst, ValuEngine Inc<\/b><\/h5>
    www.ValuEngine.com<\/b><\/a><\/h5>
    support@ValuEngine.com<\/b><\/h5>
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    Subscribers log in<\/b> HERE<\/b><\/a><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

    The history of quantitative analysis goes back far before computers, and this work leads directly into how the field progresses once computers can be applied. In this first post we explore the history and development of quantitative analysis as it applied to finance in the pre-computer world of the early through mid 20th century. Actively … Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[130,1,39],"tags":[2334,1731,2335,2011,1911,1938,28,1659],"_links":{"self":[{"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/posts\/3271"}],"collection":[{"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/comments?post=3271"}],"version-history":[{"count":55,"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/posts\/3271\/revisions"}],"predecessor-version":[{"id":3338,"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/posts\/3271\/revisions\/3338"}],"wp:attachment":[{"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/media?parent=3271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/categories?post=3271"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.valuengine.com\/index.php\/wp-json\/wp\/v2\/tags?post=3271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}