Thirty-One Signals, Six Bets — §4 · The arithmetic that ends it

Thirty-One Signals, Six Bets · part 7 of 10

§ 4

The arithmetic that ends it

At the measured mean |IC| of 0.014, the breadth needed for a usable information ratio follows directly from IR = IC × √BR:

Figure 3 — Independent bets per year: required against available Logarithmic scale. The gap between what 31 price-derived signals supply at a monthly rebalance and what a marginally useful information ratio requires is a factor of nineteen; against IR 1.0 it is a factor of seventy-six.

Table 9 — What the measured breadth supports
Configuration	Bets/yr	IR	Years to t = 2
5.57 breadth × monthly rebalance	67	0.11	305
5.57 breadth × weekly rebalance	290	0.24	70
8.40 breadth × weekly rebalance	437	0.29	47

Weekly rebalancing was already eliminated in §2.6: at that turnover the measured spreads consume the edge. So the honest row is the first one.

Going from 3 signals to 31 bought an effective breadth of 5.57. The marginal signal is worth about 0.2 of a bet. Closing a two-orders-of-magnitude gap by continuing down that path would require thousands of additions, each less independent than the last. This is not a statement that our search was insufficiently thorough. It is a statement about the slope.

There is also a structural reason it had to come out this way. Every signal in the catalogue is computable by anyone with a CSV of daily bars and has been for thirty years.