Let's look at a concrete example to understand how beta adjusted hedges work in principle. An investor is looking to completely hedge their current long portfolio position in S&P 500 companies with a current market value of $100 million. Let's assume that the portfolio beta is 1.2. The relevant E-mini S&P 500 futures contract is trading at 4,565.75, and with a multiplier of $50 has a contract size of $228,287.50.

A beta of 1.2 indicates that the portfolio is expected to move 1.2 times the market movement. So a 1% increase in the index would lead to an anticipated 1.2% increase in the portfolio's value and vice versa for a decline. Since the investor is hedging, they must be expecting a market correction. They would need the hedge to reflect the portfolio's beta. The beta adjusted hedge ratio calculates the number of future contracts to be traded by dividing the equity portfolio value to be hedged 100 million here by the futures contract size, £228,287.50, and then multiplied by the portfolio beta of 1.2. This gives 525.65 rounding to the nearest contract indicates that 526 contracts would have to be sold to hedge this position.

This means the investor is effectively setting up a futures position with a total value of around $120 million, which is 228287.50 multiplied by 526. Over hedging the portfolio size in order to compensate for the higher beta in the portfolio. Essentially, a $100 million portfolio with a beta of 1.2 is hedged by selling $120 million in equity index features, which have a beta of one.

If the index declines by say 1%, the cash portfolio is expected to decline by 1.2%, resulting in a 1.2% loss, but the future's hedge sized at 1.2 times the portfolio would gain 1% offsetting the portfolio's decline and resulting in a net neutral position.

However, calculating an accurate beta can be challenging.

Beta is typically derived from historical data through regression analysis of the portfolios and indexes returns. It can vary depending on the timeframe making it data history dependent. A beta calculated over a short period may differ significantly from one calculated over a longer period.

Additionally, beta is a historical measure, which means that while it provides insights into past sensitivity, it may not accurately predict future movements, changing market conditions, economic factors, and even alterations in the portfolio's composition can cause realized beta to diverge from the historical figure.

Given these challenges, investors must approach beta adjusted hedges cautiously. It's generally wise to regularly update beta calculations to reflect the most current data and market conditions. Some investors may even use a range of beta values calculated over different periods to gauge the potential sensitivity of the portfolio under varying market conditions. Is this hedge likely to be effective? That depends on the realized beta over the hedging period. Historical beta can serve as a useful guide, but it's not a guarantee. If the portfolio's actual beta during the hedging period differs from its historical beta, the investor may experience net losses or gains in the combined position.