Size it: a risk budget, a stop, and the smaller of the two
Conviction picks the idea; arithmetic picks the size. Volatility, correlation with the book and the distance to the point where you are wrong set the position, and the tighter rule wins.
- Size a position to a risk-contribution budget
- Size the same position to a stop-loss rule, and take the smaller
- Back out the correlation a risk system is assuming
- Say what would let the PM give the idea more room
The intuition
A pod runs on a loss limit. Lose a few percent of the capital and the book is cut; lose more and it is closed. So the PM cannot size ideas by how sure the analyst sounds; every position has to be sized by how much it can cost. Two numbers do that. How much risk does it add to the book: its volatility, scaled by how much it moves with everything else the pod owns. And how much is lost if it hits the stop: the distance to the point where the pitch is wrong.
Each rule gives a size. The risk budget divided by volatility times correlation is one; the maximum loss divided by the distance to the stop is the other. The position is the smaller of the two, and the rule that gave it is the one binding. That is why the downside case from chapter 3 matters so much: it is where the stop goes, and a pitch that cannot say where it is wrong cannot have a large position.
Weight for the risk budget = budget ÷ (volatility × correlation). Weight for the loss cap = maximum loss ÷ distance to stop. Position = the smaller. Quiet, diversifying, close-to-stop names get big; volatile, correlated, far-from-stop names get small, whatever the analyst thinks of them.
Why it works
- The conventions here: a position's contribution to the book's risk is approximated as weight × its annual volatility × its correlation with the rest of the book, in percent of NAV. The stop rule is independent: weight × distance to stop ≤ the maximum loss. Both weights are shares of NAV; the position is the smaller.
- Correlation is why pairs get more room. A hedged pair moves less with the book than a naked long, so the same budget buys a bigger position. That is the sizing reward for the work in chapter 4.
- The stop is the downside case. Where the pitch is wrong is where the position is cut, and the loss there is weight × distance. A tight stop lets the idea be bigger; a vague one does not.
- Which rule binds tells you what to fix. If the risk rule binds, the constraint is volatility and correlation: hedge it better or ask for budget. If the stop rule binds, the constraint is where you are wrong: sharpen the thesis.
- Volatility is not fixed. It jumps into earnings, and the risk rule then says sell; good desks size for the volatility they expect at the catalyst, not the volatility of a quiet tape.
- Conviction still matters, for which ideas get a slot and which get the full budget rather than half. It does not override the arithmetic.
| Risk rule: 0.5% ÷ (40% × 0.5) | 2.5% of NAV |
| Stop rule: 0.75% ÷ 15% | 5.0% of NAV |
| Position: the smaller | 2.5%, so $25M; the risk rule binds |
| Loss if the stop is hit: 2.5% × 15% | 0.375% of NAV, inside the cap |
| Same stock as a hedged pair at correlation 0.25: 0.5% ÷ (40% × 0.25) | 5.0% of NAV; now both rules agree |
Halving the correlation doubled the position. Nothing about the idea changed; only how much of the book's risk it repeats.
The formulas
How much risk the position adds to the book, in percent of NAV.
The risk rule's size.
The stop rule's size.
Whichever rule is tighter binds.
Run it backwards to see what the risk system assumes.
Worked example
The risk rule on its own: the budget divided by volatility times correlation gives the weight, and the weight times NAV gives the dollars. The follow-up says why correlation shrinks it.
See it move
Same fund and the same stock. Change the volatility, the correlation with the book, the risk budget, the distance to the stop and the loss the PM will accept at it.
- Raise the volatility. The risk-rule bar falls and the stop-rule bar does not move; the position never rises.
- Lower the correlation, as a good hedge does. The risk-rule bar rises; the position rises until the stop rule takes over, then stops.
- Widen the stop. The stop-rule bar falls and the risk-rule bar does not move: a pitch that is only wrong far away gets a smaller position.
- Raise the loss the PM will accept at the stop. The stop-rule bar rises.
- Raise the risk budget. The risk-rule bar rises.
Run it backwards
The risk report says how much your position adds to the book. Run the rule backwards to see what correlation the system is assuming, and whether you agree with it.
Contribution = weight × volatility × correlation, so correlation = contribution ÷ (weight × volatility). Weight × volatility is the position's own risk; the ratio says how much of it counts against the book.
A high implied correlation means the risk system thinks your idea repeats a bet the book already has. Either it is right, and the position is a smaller idea than it looks, or the hedge is not doing what you think.
Traps
Say it in the interview
“How big would you make it?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Risk rule: budget ÷ (volatility × correlation). Stop rule: maximum loss ÷ distance to stop.
- Position = the smaller. The binding rule tells you what to fix.
- The stop is the downside case. No stop, no size.
- A good hedge lowers correlation, which is why pairs get more room.