How to adjust portfolio beta for the CFA Level 3 exam

The Risk Management Application of Derivatives material (Study Session 15 in 2018) is a long, difficult, and important set of readings for the CFA Level 3 exam. 

You need to walk away with a good understanding of how to use forwards, futures, options, floors and caps, and swaps to adjust a portfolio's risk factors. From a calculation perspective, you will need to know how to adjust a portfolio’s beta or duration, switch exposure between stocks and bonds, and create a synthetic cash position. But this material isn't just calculation focused, L3 may have questions probing the advantages and disadvantages of each derivative strategy, including the challenges associated with maintaining a dynamic hedge.

This post tackles arguably the most important of these derivatives, futures, (most important at least for exam purposes). Here we'll build on our post covering modifying portfolio duration to laser in on how to use futures to adjust portfolio beta.

Beta as a proxy for equity exposure

Recall that Beta—the measure of the relationship between a stock (portfolio) and the market portfolio—is the most common risk measure for diversified equity portfolios. 

Beta is the systematic, non-diversifiable market risk which an investor faces. It is calculated as:

Calculating beta (CFA)


When it comes to risk management we can increase or decrease our exposure to beta in much the same way as we adjust a portfolio’s duration.

Let’s start with applying futures to adjusting the market exposure of an equity position which we do by increasing or decreasing our exposure to a market index by buying or selling futures contracts on that underlying index.

In this case we are using beta as the measure of market risk, or systematic risk that cannot be diversified away.

If we expect the market to increase in value we would want to increase our portfolio’s beta to take advantage. If we expected the market to decrease in value we would want to decrease our portfolio beta to minimize this loss.

  • To INCREASE a portfolio’s beta BUY futures contracts
  • To DECREASE a portfolio’s beta SELL futures contracts

We then calculate the number of futures contracts to buy or sell use the following equation:

Note: On the exam the futures price could be given as inclusive of the multiplier. The context should make it obvious if you need to use the multiplier in the equation. You should immediately notice that this equation is virtually the same as that for hedging duration. We are just swapping in Beta for portfolio duration. The most common multiplier is the S&P 500, which = 250.

Now that you have a good understanding of modifying portfolio duration AND portfolio beta its time to turn to using both together to shift portfolio exposure from fixed-income to equities and vice versa