It is July 16. A company has a portfolio of stocks worth ...

It is July 16. A company has a portfolio of stocks worth $$\$ 100$$ million. The beta of the portfolio is 1.2 . The company would like to use the December futures contract on a stock index to change the beta of the portfolio to 0.5 during the period July 16 to November 16 . The index futures price is currently 2,000 and each contract is on $$\$ 250$$ times the index. (a) What position should the company take? (b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take?

It is July 16. A company has a portfolio of stocks worth $$\$ 100$$ million. The beta of the portfolio is 1.2 . The company would like to use the December futures contract on a stock index to change the beta of the portfolio to 0.5 during the period July 16 to November 16 . The index futures price is currently 2,000 and each contract is on $$\$ 250$$ times the index.
(a) What position should the company take?
(b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take?

Key Concepts

Portfolio Beta

Portfolio beta measures the sensitivity of a portfolio’s returns to the movements of the overall market. It is an indicator of how much the portfolio’s returns are expected to move relative to market movements. A beta greater than 1 implies that the portfolio is more volatile than the market, while a beta less than 1 indicates lower volatility. This concept is key in risk management and is often the target parameter when adjusting a portfolio's market exposure.

Futures Contracts

Futures contracts are standardized agreements to buy or sell an asset, such as a stock index, at a predetermined price and time in the future. They are widely used in financial markets for hedging against risk or speculating on price movements. The specifics of a futures contract, including its multiplier and contract size, directly influence how much market exposure each contract represents, making them a useful tool for adjusting portfolio beta.

Hedging with Index Futures

Hedging with index futures involves taking a position in a future contract to offset or modify the market risk of an existing portfolio. By either buying (going long) or selling (going short) futures contracts, investors can increase or decrease the overall beta of their portfolio. This technique allows for dynamic risk management, enabling investors to align their portfolio’s exposure with their market outlook or risk preferences.

Determination of Contracts for Beta Adjustment

Adjusting the beta of a portfolio using futures contracts requires calculating the desired change in market exposure and matching it to the notional amount of the futures contracts. The number of contracts needed is determined by the difference between the target beta and the current beta, the total value of the portfolio, and the notional value represented by a single futures contract. This calculation is central to effectively implementing a hedging strategy that alters the portfolio's sensitivity to market movements.

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