# Independent Bets Worksheet

*Signal Pilot Education — companion to Lesson 71: How Many Bets You Are Carrying.*

Two rules on one instrument look like two positions. They are not two bets. This worksheet turns your own book into the number of independent bets it is actually carrying, which is the number every risk figure downstream depends on.

> **Educational only.** Trading involves substantial risk of loss. Not financial
> advice. Past performance does not guarantee future results. Every number in
> this worksheet is one you measure on your own record; the figures in the
> right-hand column are what the lesson measured on its own bars, and they are
> there to be disagreed with rather than copied.

---

## 1. Line the rules up on the same bars

Pick **two rules you actually run** and step them over the same series, marking
what each holds at the close of every bar: long, flat or short.

| Bar | Rule A position | Rule B position | Agree? |
| --- | --- | --- | --- |
| 1 | | | |
| … | | | |
| n | | | |

| | Your number | Lesson 71's grid |
| --- | --- | --- |
| Bars where both hold the same side | | |
| Bars in the sample | | |
| **Agreement share** | | |
| **Correlation of the two return streams** | | 0.9472 median |

Across all 31,878 pairs the lesson forms, the **median** correlation between
two rules is **0.9472** and the least alike pair still reads 0.4845. Your own
pair will land somewhere on that spread, and where it lands is what the rest of
this sheet is for.

## 2. Turn the correlation into a count

For n rules at an average pairwise correlation ρ, the independent bets are
n ÷ (1 + (n − 1)ρ).

| | Your number | Lesson 71's grid |
| --- | --- | --- |
| Number of rules, n | | 2 |
| Average pairwise correlation, ρ | | 0.9472 (median) |
| **Independent bets** | | 1.03 |

Now add rules on paper and recompute. The count does not keep rising.

| Rules added | Independent bets |
| --- | --- |
| 2 | |
| 4 | |
| 8 | |
| **All of them** | |

However many rules you add, the bets you carry top out at one divided by the
correlation, which on the lesson's grid is **1.06**. Adding members does not
move the ceiling; only a genuinely less correlated object does.

## 3. Price what you thought you had

| | Your number |
| --- | --- |
| Rules you run | |
| Risk per rule, in R | |
| Total risk if the rules were independent | |
| **Total risk at your measured correlation** | |
| **Ratio of the two** | |

The last row is the factor by which a book of correlated rules overstates its
own diversification. Read it before you size the next one.

---

## What you are holding when this is filled in

One correlation and one count. The correlation is measured rather than assumed;
the count is how many bets your book carries no matter how many lines are in it;
and the ratio is what your risk figure was wrong by.

*Signal Pilot Labs, Inc. — /education/curriculum/professional/71-positions-are-one-position.html*