How many contracts reduce example Beta from 1.2 to 0.4?
Reveal the worked answer
Sell 32.
(0.4−1.2)×10,000,000/250,000=−32.
Equity Index Futures · FUT-02 · Core
Institutional portfolio hedging
How can broad risk change without selling the holdings?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: What is an equity index future?
A manager may want to reduce market Beta while retaining individual investments. A short index future can offset part of the portfolio's common-market sensitivity. It does not remove company-specific risk or guarantee a matched return.
Understand the mechanism
A simple estimate is N=(target Beta−current Beta)×portfolio value/(futures price×multiplier). It assumes a suitable proxy and a stable Beta estimate. Sector concentration, funding, basis and unexpected company events remain.
The hedge target and its statistical uncertainty should be stated separately. A precise contract count does not make the estimated Beta precise.
Walk through the process
Define what risk to reduce and for how long. Choose an economically relevant index. Calculate contracts, round deliberately and record residual exposure. Then stress how cash and margin behave if the hedge moves against the account.
An index hedge cannot substitute for deciding whether individual holdings still deserve ownership.
Operational boundary
All prices, portfolio values and account balances are fictional. Real contract calendars, broker requirements and available liquidity must be checked for the instrument actually traded. The example's mathematical hedge or payoff is not an execution guarantee.
A worked example
A fictional portfolio is worth 10 million with estimated Beta 1.2. The future is 5,000 with a 50 multiplier, or 250,000 per contract. Targeting Beta zero implies selling 48. Targeting Beta 0.4 implies selling 32.
The chart varies target Beta under these fixed assumptions. It is a sizing illustration, not evidence that the portfolio's actual returns will follow the model exactly.
Open the calculation without leaving this lesson
Institutional portfolio hedging—worked comparison
Vertical: Target signed futures contracts
Horizontal: Target portfolio Beta
1. Fictional example
Read the graph as a data table
| Target portfolio Beta | Fictional example |
|---|---|
| 0 | -48 |
| 0.2 | -40 |
| 0.4 | -32 |
| 0.6 | -24 |
| 0.8 | -16 |
| 1 | -8 |
| 1.2 | 0 |
What would invalidate the reading?
An idiosyncratic earnings shock can damage holdings even while the broad hedge behaves as expected. Beta can also change during stress.
Check your understanding
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
What is the critical failure to avoid?
Reveal the worked answer
An idiosyncratic earnings shock can damage holdings even while the broad hedge behaves as expected. Beta can also change during stress.
Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome.
Return to the question: How can broad risk change without selling the holdings? State the observed facts, the assumptions and the failure condition separately.
Sources, assumptions and downloadable script
External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.
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