**Target portfolio beta**

Futures contracts on equity indices can be used to decrease the beta of a portfolio by shorting them, and long positions can be used to increase the beta of a portfolio. A portfolio’s beta equals the weighted average of the betas of the individual stocks in the portfolio. On this page, we discuss how to calculate the **hedge ratio**, i.e. the necessary number of contracts to change the beta of an existing portfolio to a certain target. The target portfolio beta is often changed dynamically by global macro hedge funds.

A spreadsheet that implements the approach is available for download at the bottom of the page.

**Target portfolio beta formula**

The number of contracts needed to change the beta of an existing portfolio can be calculated using the following formula

where **betaT** is the target beta, **betaP** is the current portfolio beta, **betaF** is the futures beta (beta of the stock index), **MVP** is the market value of the portfolio, and **F** is the futures contract value (i.e. futures price times multiplier).

If we wish to fully hedge the portfolio, then the target beta equals 0.

**Target portfolio beta example**

Next, let’s consider a simple numerical example that implements the above concepts. The following table shows the results of a fund manager that wishes to achieve a target beta using index futures. Notice that the beta of the futures contract is 1 by definition

Note that if the number of required contracts is negative, then we have to sell futures contracts. The Excel spreadsheet can be downloaded at the bottom of this page.

**Summary**

We discussed how fund managers can alter their portfolio beta using a target beta and futures contracts.

### Download the Excel spreadsheet

Want to have an implementation in Excel? Download the Excel file: Target Beta calculator