Against the index used for the hedge, not against the market in general.
Zero is a full hedge. Above the current beta gives a negative count, which is a long position.
In index points, typed. Nothing here reads a quote.
Dollars per index point. It is not one number across contracts.
Rounding is what leaves a residual: a whole contract cannot be split, so the beta after the hedge lands -0.1000 from the target. A negative residual means the position is over-hedged.
Hypothetical illustration, computed only from the figures entered. The multiplier is a contract specification and differs across contracts, so it is typed rather than assumed.
Beta is estimated from a past window and is not stable; a hedge sized on it is only as good as that estimate. Does not account for basis risk between the portfolio and the index, margin, roll cost, commissions, dividends on the index, or the fact that a futures or options hedge carries its own profit and loss. It sizes a hedge and does not evaluate one.
A portfolio with a beta above 1 moves more than the index it is measured against, so hedging it needs more index exposure than its dollar value. Multiplying the value by the beta gives the index-equivalent exposure, and dividing that by what one contract controls gives the contract count.
A $1,000,000 portfolio with a beta of 1.15 carries $1,150,000 of index-equivalent exposure. Against an index at 5,000 points, an E-mini contract at $50 a point controls $250,000, so a full hedge takes 4.6 contracts. Only whole contracts trade, so 5 sold leaves the position slightly over-hedged at a beta of -0.10.
Sizing on the dollar value and ignoring the beta. At a beta of 1.15 that under-hedges by 15% of the portfolio, and the shortfall only shows up in the move being hedged against.