Nerds on Wall Street: Math, Machines, and Wired Markets

5.1. Indexing 101

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.

5.1.1. 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, ...