Lesson 24 of 25 · 7 min
Basis risk: when the hedge and the holding diverge
An index hedge answers only the shared half of a move, and single names travel mostly in the unshared half.
Lessons 2 and 4 split a single holding's variance into a market part and a residual part, and found the residual larger. A hedge written on a broad index addresses the market part only, and the gap between the two is basis risk.
The sizing convention is beta-weighting. A $1,240,000 holding with a beta of 1.18 is matched with $1,240,000 × 1.18 = $1,463,200 of index notional, so that a 1 percent index move produces roughly the same dollar change on both sides.
Then a company event arrives. The index falls 12 percent and the holding falls 31 percent. The hedge produces roughly $1,463,200 × 0.12 = $175,584, ignoring premium and curvature. The holding loses $1,240,000 × 0.31 = $384,400. The net loss is $208,816, which is exactly the residual: 31 − (1.18 × 12) = 16.84 percent, and $1,240,000 × 0.1684 = $208,816. The hedge did what it was sized to do and the residual passed straight through.
Divergence runs both ways. If the index falls 12 percent while the holding rises 4 percent, the hedge gains $175,584 and the holding gains $49,600, for $225,184 of gain — which is the same mechanism producing the opposite sign. Basis risk is not a tendency to lose; it is the absence of any relationship between the hedge and the residual.
A beta-weighted index hedge is precise about the part of the move that is shared and silent about the part that is not, which on a single holding is usually the larger part.
Key terms
- Basis risk
- The risk that a hedge and the holding it addresses do not move together, leaving an uncovered remainder.
- Beta-weighted notional
- The amount of index exposure chosen so that a 1 percent index move affects both sides by about the same number of dollars.
- Curvature
- The way an option hedge's sensitivity changes as prices move, so a hedge sized for today's price is differently sized tomorrow.
Worked example
The residual passes through the hedge
A $1,240,000 single-name holding with a beta of 1.18, hedged with $1,463,200 of broad index notional. The index falls 12% and the holding falls 31%. Illustrative figures, ignoring premium and curvature.
- Index notional
- $1,463,200
- Hedge result
- +$175,584
- Holding result
- −$384,400
- Net
- −$208,816
- Residual move
- 16.84%
- Residual in dollars
- $208,816
$1,240,000 × 1.18.
$1,463,200 × 0.12.
$1,240,000 × 0.31.
31 − (1.18 × 12).
$1,240,000 × 0.1684. The net loss is the residual, exactly.
The hedge neutralised the market component to the dollar and left the company component untouched, which is what it was built to do.
Check yourself
A $780,000 holding with a beta of 0.86 is hedged with beta-weighted index notional. The index falls 18 percent and the holding falls 27 percent. What is the net result?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.