The calculation
value to neutralise = position value × beta × share hedged
hedge size = value to neutralise ÷ (hedge price × multiplier)
A $50,000 portfolio with a beta of 1.15 against the S&P behaves like $57,500 of index exposure. One ES contract at 5,200 points and a $50 multiplier is worth $260,000, so a full hedge is 0.22 contracts — which does not exist.
Rounding is the whole problem at retail size
You can trade 0 contracts or 1. Zero leaves the position entirely unhedged; one is a $260,000 short against $57,500 of exposure — a net short position four times the size of what you were protecting.
That is why the residual row is here. It is the part that turns a hedge into a new trade, and it is invisible unless someone prints it.
The practical answers:
- Micros. MES at a $5 multiplier is $26,000 per contract, so the same hedge is 2.2 contracts and rounds to 2 with a small residual. This is the main reason micros exist for hedging.
- Options, where the contract sizes are smaller and the cost is bounded.
- Partial hedging — deliberately covering 50% or 70% and knowing that is what you did.
Beta is doing real work here
A hedge sized on face value alone is wrong whenever the two instruments do not move one-for-one.
A portfolio of high-beta technology names with a beta of 1.4 needs 40% more hedge than its dollar value suggests. A defensive portfolio at 0.7 needs 30% less, and hedging it at face value creates a net short.
Two cautions about the number itself. Beta is backward-looking, estimated over some historical window, and it changes. And it is an average — it describes the typical relationship, not the one that holds during a sharp move, which is precisely when the hedge is being relied on.
What a hedge costs
Removing direction does not remove expense. The hedge carries spread and commission on entry and exit, financing or roll costs if held, and it caps the upside as completely as it caps the downside.
That last point deserves stating plainly: a fully hedged portfolio makes nothing. It is a position taken to survive a specific period — an earnings event, a vote, a holiday with thin liquidity — not a state to occupy.
Which is why the honest first question is whether the exposure genuinely must be held. If it does not, selling part of the position is simpler, cheaper and does not require a beta estimate to be right.