Chapter 05 – A Gentle Introduction to Computerized Investing

Computerized Investing, Index Funds, Quantitative Investing, and Active Management

“Life would be so much easier if we only had the source code.” — Hacker proverb

The beginning of index investing in the 1970s was the result of a convergence of events, one of those ripe apple moments. Institutional investors began to use firms like A.G. Becker to actually compare the total performance of their hired managers with index benchmarks, and found that many of them fell short, especially after the substantial fees the investors were paying.

Yale professor Burton Malkiel popularized the academic efficient market arguments in A Random Walk Down Wall Street, writing in 1973, “[We need] a new investment instrument: a no – load, minimum – management – fee mutual fund that simply buys the hundreds of stocks making up the market averages and does no trading [of securities]. . . . Fund spokesmen are quick to point out, ‘you can’t buy the averages.’ It’s about time the public could.”

Computers had gotten to the point where one could be put in an office setting without having to tear out walls and bring in industrial – strength air – conditioning, raised floors for the cables, and special power systems. It was slightly easier to install a computer in an office building than a particle accelerator, but not by much. I recall visiting an insurance company in Hartford one winter where they were using their IBM System 360 to heat several floors of a large building. Minicomputers, like the Digital Equipment Corporation (DEC) systems described in the Introduction, the Data General Nova, and the Prime, all from companies in the first Silicon Valley, Boston’s Route 128 (the same crowd that came to the TX – 2 going – away party), were manageable enough to fit in a normal office setting. You needed to crank the AC and have a high tolerance for noise, but they didn’t break the bank, or the floor.

The idea, the desire, and the means to achieve it all came together in the early 1970s for index funds. But this is a chapter about alpha strategies, the anti-index funds — so why are we talking about them at all? Because they are a starting point for all active quantitative computerized equity strategies.

Indexing 101 and Tracking Error

Calculating an index is fairly simple. Multiply the prices of the stocks in the index by their weights (usually their share of the total capitalization of the index constituents), add them up, and there’s your index. Charles Dow, a journalist, started doing it with a pencil and paper in 1896. You need to make adjustments for mergers, splits, and the like, and can get fancy, including dividends for total return.

Running an index fund is less simple. You have to figure out how many of hundreds or thousands of different stocks to buy (or sell) each time cash moves in or out of the portfolio in the form of investments, withdrawals, and dividends. For the most common S & P 500 there are 500 stocks to deal with. For a total market index like the Russell 3000, there are 3,000. For the Wilshire 5000, there are about 6,700.

The measure of how well you are doing in an index fund is clearly not alpha; that should be zero. It is tracking error, a measure of the difference between the calculated index and the actual portfolio. An ideal index fund has a tracking error of zero. Real-world index funds have tracking errors around 0.1 percent. If it gets much larger than that, someone is confused.

Index Funds: The Godfather of Quantitative Investing

Index funds have an interesting history. Prior to the 1960s, most institutional equity portfolios were managed by bank trust departments, and performance reporting was not the refined art that it has become today. Bill Fouse, one of the founders of the world’s first indexing group at Wells Fargo in the 1970s, tells stories of when performance reporting by a bank trust department consisted of a table listing all stocks held, the acquisition price of each, the current price, and the size of the position. This introduced some unusual biases into the perception of these reports. Looking at stocks just by price and ignoring dividends tends to favor stocks that don’t pay dividends. Simply listing acquisition price and current price ignores the aspect of time, and not comparing it to any well-defined benchmark (like the S & P 500 index) leaves the meaning of even a well-studied report unclear.

A.G. Becker was the first firm to compare the total return of a stock portfolio to an index. Since an S & P 500 index fund is just a passive investment consisting of a capitalization-weighted portfolio of the 500 stocks in the index, it will do no better than the index — and if managed effectively, no worse.

An index fund can’t just be started up and left alone to run itself forever. The stocks in the index change; dividends need to be reinvested, and most significantly, there are cash flows in and out of the portfolio from new funding or payment requirements. All of these events result in a need to trade, and it costs money to trade, not just in the explicit commissions, but in the market impact incurred when large volumes of stock are bought or sold. Managing an index fund effectively means keeping control of trading costs. These costs can drag the index portfolio’s performance down from the theoretically calculated index we see reported all the time. The reported index levels don’t include any real or simulated trading costs. They incur no commission costs and no market impact. For smaller index portfolios, under $ 20 million or so, the trading costs can become a significant problem. The lower-weighted stocks in the index will be held in very small quantities, and the cost associated with trading 100 shares is much more than one-tenth of the cost of trading 1,000, or one-hundredth the cost of trading 10,000.

For large index portfolios, the sheer size of trades can impose another trading cost in the form of market impact. Even so, there are economies of scale to be had in managing large index funds. This is reflected by the current business situation in which there are a small number of large index fund providers around the world, such as State Street and Barclays Global Investments. Estimates of total assets managed using this sort of passive approach, in a variety of markets, now exceed $4 trillion.

Setting aside considerations of trading costs for now, the idea of an index fund is a very simple one. Nevertheless, it is a quantitative concept, and running an index fund requires the use of a computer. The most straightforward way to manage an index fund is simply to hold all of the stocks in the index: every single one of them, each in its index weight. This is illustrated in Figure 5.1, which represents all of the stocks in the S & P 500 put into a portfolio. This is simple and will, in fact, ignoring trading costs, replicate the index exactly. This type of index fund is called a full replication fund.

Even with full replication funds, the trading costs and fixed 100-share increments for holdings will cause the portfolio to have a performance somewhat different from that of the index.

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All notes for this chapter about computerized investing, index funds, quantitative investing, and active management:

1. Tim Loughran and Jay R. Ritter, “The New Issues Puzzle,” Journal of Finance 50, no. 1 (March 1995): 23–51.

2. Vanessa O’Connell, “Some Stock Funds Beat Rivals by Following Insiders’ Trades,” Wall Street Journal, January 29, 1997.

3. This is true when the long and short portfolios have equal betas, or sensitivity to broad market moves. For long-short portfolios where this is not the case, a portion of the overall return may be due to exposure to the overall market.

4. Jia Ye, “Excess Returns, Stock Splits, and Analyst Earnings Forecasts,” Journal of Portfolio Management 25, no. 2 (1999): 70–76.

5. See for a world of information on this subject.

6. David Leinweber, “Uses and Views of Equity Style,” in Handbook of Equity Style Management, ed. T. Daniel Coggin and Frank J. Fabozzi (New Hope, PA: Fabozzi Associates, 1997).

7. The all-time classic paper on trading costs is “Implementation Shortfall” by Andre Perold, published in the Journal of Portfolio Management (Spring 1988). It is a hot topic in algo trading, so a search may be overwhelming. Perold was the first to demonstrate the significance of trading costs in such a persuasive manner. The transaction cost measurement industry, which followed, was really originated by one firm, Plexus Group, founded by Wayne Wagner and now part of Investment Technology Group, Inc. (ITG). Wayne’s personal perspective is found in “The Incredible Story of Transaction Cost Management: A Personal Recollection,” Journal of Trading 3, no. 3 (Summer 2008).

8. See “Founders of Modern Finance” (c) 1991, Research Foundation of the Institute of Chartered Financial Analysts, ) for the goods from the founders themselves, or Capital Ideas by Peter Bernstein for the salient points, intellectual history, and best stories.

9. Visit for the word from the Crackpot himself. He has an extensive web site on quantitative finance.

10. The difference between index enhancement and active management is a matter of degree. Enhanced index and fully active portfolios each have two components: one piece to provide the benchmark index return and another to provide additional return on top of the benchmark. The difference between enhanced index strategies and active management is really just a matter of the relative sizes of the two pieces. Use just a little bit of active management, and you are enhancing the index. Use some more and you have an active strategy. Make really large active, often leveraged, bets and you have a hedge fund.

It is like the progression from 3.2-proof beer to 151-proof rum. The active ingredient is the same; the difference is a matter of degree. The distinction can be quantified by specifying a target tracking error for the portfolio, analogous to the proof content of your favorite bar beverages. The tracking error is just the standard deviation of the pre-tax difference between the portfolio return and the benchmark index return. A perfect index fund would have a tracking error of zero before any taxes and transactions costs are taken into consideration. Often, for example, enhanced index funds can have a tracking error under a few percent, but you want to make sure that it stays that way over time. Thus, using investment tracking software is definitely a wise move considering the nature of common investment monitoring situations like this.

11. Value and growth are called “equity styles.” When all stocks are ranked by book-to-price ratio, value stocks are in the top half and growth stocks are in the bottom half. Net performance depends upon appreciation, costs, and taxes. Taxes for individuals may vary depending upon the long-term capital gains of the various equity styles. For businesses things tend to be more complex and corporate tax software can help with the estimation of pro-forma taxes on tax realization events for various equity strategies.

Regarding the underlying assets, value stocks tend to have lots of real assets, like land and plants. Extreme examples are utilities. Growth stocks are generally the more exciting, newer firms, with ideas and products that get on the covers of magazines. Historically, value stocks have outperformed growth stocks, though this changed for a while in the late 1990s when the tech stocks, all growth stocks, did so well. Now we have returned to the old pattern.

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