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Portfolio level risk

A book is not a list of positions, it is one risk made of several. Portfolio risk is the number that decides whether anything can be added, and it is the number that most books get wrong by ignoring how the parts move together.

What you will see

One line. A correlation without a window is a number that stops being about the market.

About 1 min of reading

Try It

Compute combined risk for two positions

Write the two risks

printf 'pos1 60\npos2 60\n' > /tmp/r.txt; awk '{s+=$2} END {print s}' /tmp/r.txt

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

What it prints

120. That is the wrong answer, and it is the answer independence gives.

Apply the correlation

awk 'BEGIN {a=60;b=60;c=0.8; printf "%.1f\n", sqrt(a*a+b*b+2*a*b*c)}'

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

What it prints

107.7. Correlated risk is less than the sum, and the square root is why it is not additive.

Stamp the window used

printf 'corr=0.8 window=20d date=2026-10-10\n' > /tmp/c.txt; cat /tmp/c.txt

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

What it prints

One line. A correlation without a window is a number that stops being about the market.

Data Flow

A book to one ceiling decision

1 Each position gets its risk vector

↓

2 The correlation matrix is estimated and stamped

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3 The combined risk is computed

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4 The next position is compared to the ceiling

Why this works

Why the risk is reported per underlying

Per underlying is the grouping that matters, because that is the grouping that moves together. A report per instrument hides the fact that two instruments are one bet.

The one action the number unlocks

It unlocks a refusal. Portfolio risk is the input to the question can anything else be added, and the answer is the whole point of the number.

Examples

Correlation is the whole error

Two positions on the same underlying are one position with a label. Adding their risk as if they were independent is the error.

The budget is a ceiling, not a target

A book at the ceiling cannot take a new position. The ceiling is what makes the next decision a refusal instead of a surprise.

The matrix is estimated on one window

Correlations change with the market. The window used for the matrix is stamped, because the answer is not a constant.

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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