SHORT HEDGE : Short a futures contract to hedge against a price decrease in the existing long position.
LONG HEDGE : Long a futures contract to hedge against an increase in the value of the shorted asset.
ADVANTAGE : Leads to less uncertainty regarding future profitability.
The basis in a hedge is defined as the difference between the spot price on a hedged asset and the futures price of the hedging instrument.
Basis = Spot price of asset being hedged — futures price of contracts used in hedge.
The change in basis over the hedge horizon is termed as Basis Risk.
Three sources of basis risk are:
The hedge ratio is the ratio of the size of the future position relative to the spot position.
Hedge ratio, HR = ρs,f x σs/σf [ This is also beta (β) ]
Where, ρ = correlation between the spot & the future prices.
σs = Standard Deviation of spot price
σf = Standard deviation of futures price
The effectiveness of the hedge measures the variance that is reduced by implementing the optimal hedge. This effectiveness can be evaluated with a coefficient of determination (R2) term where the independent variable is the change in futures prices and the dependent variable is the change in spot prices.
The beta of spot prices with respect to futures prices is equal to the hedge ratio (HR), which is also the slope of this regression. The R2 measure for this simple linear regression is the square of the correlation coefficient (p2) between spot and futures prices.
Hedging with Stock index
No. of contracts = β * Portfolio value/ Value of futures contract
To correct the possibility of over-hedging if daily settlement is not accounted for, a hedger can implement a tailing the hedge strategy in which the hedge ratio is multiplied by the daily spot price to future price ratio.
Hedging an existing portfolio with index futures is an attempt to reduce the systemic risk of the portfolio. If the beta of the CAPM is used as the systematic risk measure, then hedging bails down to a reduction of the portfolio beta. To calculate the appropriate number of futures
No. of contracts = (β*– β) * Portfolio value/ underlying asset
Where β* = Target Beta
Β = Portfolio beta
“-” indicates selling futures
“+” indicates buying futures
When the hedging horizon Is long relative to the maturity of the futures used in the hedging strategy, hedges have to be rolled forward as the futures contract in the hedge come to maturity or expiration. This is called rolling the hedge forward.
Hedgers are exposed to the basis risk of the original hedge as well as new position known as rollover basis risk.
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