The experiment: hypothesis and random selection

The brief is a test — say what it tests

Lesson 3.7 handed you the project: 12 stocks you expect to rise, 12 drawn at random, and the S&P/TSX Composite and S&P 500 beside them, tracked weekly for the term. Most groups start typing tickers. Start instead by writing the hypothesis, because the instructor's first question in the final tutorial is what did you expect, and did it happen?

If the market is semi-strong efficient (Lesson 13.5), every public reason you have for expecting a stock to rise — its results, its news, its analyst coverage — is already in its price. Then:

> H₀ (efficiency): the chosen 12 will not systematically beat the random 12, and neither basket will beat the index by more than luck allows. > > H₁ (pickable): the chosen 12 beat the random 12 by more than luck allows.

Write this on the first sheet of the workbook, dated before the first weekly close. A hypothesis written after the results is not a hypothesis; it is a caption.

Making the random 12 random

The random basket is the control. A control picked "at random" by eye — twelve names the group happens to know — is a second chosen basket, and the experiment can no longer separate skill from luck. The documented method:

1. Paste the index constituents into a column named Tickers (the S&P/TSX Composite is the natural pool).
2. In twelve cells, draw =INDEX(Tickers,RANDBETWEEN(1,COUNTA(Tickers))).
3. Copy the twelve cells and paste them as values at once — RANDBETWEEN recalculates on every edit to the workbook, so an un-frozen draw silently changes each time a weekly close is typed.
4. Record the date of the draw; re-draw any duplicate and note that too.
5. Keep the draw sheet. It is evidence — the instructor will ask "why these 12?", and the answer for the control is "the sheet drew them".

COUNTA counts the non-empty cells, so the draw covers the whole list even after the pool is edited; INDEX turns the drawn row number into the ticker.

How big is luck?

Before a single real price arrives, you can see the size of the noise the experiment has to beat. Give 24 imaginary stocks the same distribution — a weekly return drawn from a normal with mean 0.1 % and standard deviation 3 % — split them into a "chosen" 12 and a "random" 12, and run twelve weeks. Neither basket has any edge; they differ only by the dice. The code block below does exactly this for five terms, seeded so the result is reproducible: in three of five terms the "random" basket wins, in two the "chosen", and the gap runs from 4 to 9 percentage points either way. That is the yardstick. A chosen basket that beats the random one by four points over a term has done what pure noise does routinely.

Freezing the picks

The chosen 12 must be frozen too — the same day, the same sheet. Swapping a loser for a winner in week six, or "correcting" a pick after a bad earnings print, is selection bias: the basket you present is no longer the basket you expected to rise, and whatever it returns says nothing about the hypothesis. Freeze both baskets, freeze the benchmarks, and let the term run.

Cold

Hypothesis in EMH terms, dated before the first close; the random 12 drawn by a documented rule and pasted as values; both baskets frozen; the size of luck estimated before the result is known.