A company has a 20 million portfolio with a beta of 1.2 ....

A company has a $$\$ 20$$ million portfolio with a beta of 1.2 . It would like to use futures contracts on a stock index to hedge its risk. The index futures price is currently standing at 1080 , and each contract is for delivery of $$\$ 250$$ times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6 ?

Key Concepts

Hedging Strategy Adjustment

Hedging strategy adjustment involves modifying the number of futures contracts used in the hedge to achieve a specific risk profile. For example, if the goal is to reduce the portfolio beta, the hedging position can be adjusted so that the effective beta of the hedged portfolio aligns with the desired lower level of market exposure. This strategy is vital for tailoring the risk-return characteristics of a portfolio to meet specific investment objectives.

Hedge Ratio

The hedge ratio is the proportion of the portfolio that is hedged with futures contracts, calculated using the portfolio’s beta, market value, and the size of the futures contract. It helps in determining the optimal number of futures contracts required to reduce the portfolio's exposure to market risk to a desired level. This concept is essential for achieving effective hedging, whether aiming for a full hedge or a targeted adjustment of the portfolio’s beta.

Futures Contracts

Futures contracts are standardized financial instruments that obligate the buyer to purchase, or the seller to sell, an asset at a predetermined price at a specified time in the future. In the context of hedging an equity portfolio, index futures are used as a tool to mitigate market risk by taking positions that offset potential losses arising from adverse market movements.

Beta

Beta is a measure of a portfolio's or asset's sensitivity to overall market movements. It indicates the degree to which the portfolio's returns are expected to move in relation to the market. A beta greater than one implies more volatility than the market, while a beta less than one suggests less volatility. This concept is crucial in determining the amount of market risk that needs to be hedged using derivatives such as futures.

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