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Hedging a position across legs

A position is not one risk. It is several legs whose risks point in different directions, and a hedge is the act of making one leg pay for another so that no single event can end the whole thing.

What you will see

over. The book exceeds the budget, and the fix is a size change, not a new leg.

About 1 min of reading

Try It

Bound the worst case of a book

1

Write the worst case per leg

printf 'core -90\nhedge -30\nhedge -30\n' > /tmp/wc.txt; awk '{s+=$2} END {print s}' /tmp/wc.txt

Before you run it, say out loud what it will print. Then open the answer.

What it prints
-150. The sum is the position worst case, and it is the number to budget against.
2

Check the paying leg is not short

awk '$1=="hedge"{n++; s+=-$2} END {print (s>= -($0)) ? "ok" : "short"}' /tmp/wc.txt; grep -c hedge /tmp/wc.txt

Before you run it, say out loud what it will print. Then open the answer.

What it prints
2. Two paying legs against one core is the shape; one is not.
3

Compare to the budget

awk '{s+=$2} END {print (s< -120) ? "over" : "inside"}' /tmp/wc.txt

Before you run it, say out loud what it will print. Then open the answer.

What it prints
over. The book exceeds the budget, and the fix is a size change, not a new leg.

Data Flow

Legs to a bounded worst case
1 Each leg gets its worst case
↓
2 The paying leg is sized in risk units
↓
3 The position worst case is computed
↓
4 The worst case is compared to the budget
Why this works
Why the worst case is printed per leg

The worst case per leg is a table. The worst case of the position is a number, and the table is what makes the number trustworthy.

The one leg that must never be short

The leg that pays the others. If it is short, the hedge is not a hedge, it is a stop.

Examples

The event that ends it

A gap, an expiry, a bad print. A position that survives none of them is a position that is a coin flip.

Why the hedge is sized in risk

Legs have different curvature. Equal notional is not equal risk, and the sizing has to be in the unit that is equal.

The hedge that is too large

A hedge larger than the core turns the position into a different bet. The size of the hedge is a claim about the claim.

Words this lesson uses

Each one is defined here on this site. Open the entry for the full definition and the other words it points at.

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