Lesson 1

The score model is useful, but it hides the hardest question: where did the scores come from? A different financial goal is to avoid predicting winners and instead imitate a given plan as closely as possible.

This is the basic idea behind an index fund. The plan may be a public benchmark, such as an index of large companies, or some fixed target allocation chosen in advance. If the benchmark says that stock \(i\) should have weight \(w_{i}\), then the fund tries to keep approximately the same weight in its own portfolio.

Of course, the fund cannot buy fractional shares to match the plan exactly. Prices move, cash comes in and out, and shares are bought in integer amounts. The difference between the plan and the actual portfolio is called tracking error. Our mathematical problem is to make this error small.