## HEDGING WITH FUTURES #

**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.

## ADVANTAGES & DISADVANTAGES OF HEDGING #

__ADVANTAGE__** : **Leads to less uncertainty regarding future profitability.

__DISADVANTAGE__** : **

- 1.Can lead to less profitability if the asset being hedged ends up increasing in value.
- Questionable benefit that accrues to shareholders. Shareholders can hedge risk on their own.
- If price In an industry frequently adjust for changes in input prices & exchange rates, not hedging will give more stable return than hedging frequent changes.

## BASIS RISK #

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.

- When spot increases faster than futures Basis increase = Strengthening of basis.
- When futures increases faster than spot Basis decrease = Weakening of basis.

The change in basis over the hedge horizon is termed as *Basis Risk.*

Three sources of basis risk are:

**Interruption in the convergence of the futures & spot price :**If the position is unwound prior to maturity, the return to the futures position could be different from the return to the cash position.**Changes in the cost of carry :**Changes in the component of the cost of carry (storage, interest, insurance etc. ) can lead to basis risk.**Imperfect matching between the cash asset & the hedge asset :**Sometimes it may be more efficient to cross hedge or hedge a cash position with a hedge asset that is closely related but different from the cash asset. However, if there is a structural shock that changes the close relationship of these two assets, the position may not be hedged as effectively as originally believed. This is the most common form of basis risk. Other forms of mis match include maturity or duration mismatches, liquidity mismatches, and credit risk mismatches.

## OPTIMAL HEDGE RATIO #

The hedge ratio is the ratio of the size of the future position relative to the spot position.

**Hedge ratio, HR = ****ρ**_{s,f}_{ }**x**_{ }**σ**_{s}**/σ**** _{f }**[ This is also beta (β) ]

Where, ρ = correlation between the spot & the future prices.

σ_{s } = Standard Deviation of spot price

σ_{f} = 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 (R ^{2})** 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 R^{2} measure for this simple linear regression is the square of the correlation coefficient (p^{2}) between spot and futures prices.

__Hedging with Stock index__

**No. of contracts = ****β**** * Portfolio value/ Value of futures contract**

## TAILING THE HEDGE #

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.

## TYPES OF ORDERS #

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

## ADJUSTING THE PORTFOLIO BETA #

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.**