What is equal-weight basket volatility with two20%-vol assets at zero correlation?
Reveal the worked answer
Approximately14.142%.
Square-root the variance; do not average volatilities directly.
Advanced Options · ADV-27 · Core
Dispersion and correlation
Why can index volatility differ from component volatility?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Read a contract and its premium, Rights, obligations and expiration, Defined payoff risk is not margin, Read the whole multi-leg ticket
An index aggregates individual returns and their co-movement. Even volatile components can form a less volatile basket when they do not move together. Dispersion strategies compare index and component option exposures, but implementation is much more complex than this identity.
Correlation can rise during stress exactly when diversification is most needed.
Understand the mechanism
For two assets, basket variance includes weighted individual variances plus twice the weighted covariance. Actual index weights, differing vols, rebalancing and more constituents matter.
An institutional dispersion trade is not simply 'buy stocks and short the index.' It concerns volatility exposures with hedge, weighting, surface and jump risks.
Walk through the process
Understand the variance relationship before discussing positions. Use variance-consistent weights and compare implied versus realized quantities. Explain correlation and constituent-event risks.
A theoretical covariance calculation is not an executable strategy payoff or a promise of diversification through a gap.
Model and implementation boundary
These are complete fictional reading examples, not live opportunities. Terminal identities assume the stated common settlement. Multi-expiry values require a surviving-leg model. Costs, assignment and financing can alter realized outcomes; a mathematical bound alone does not guarantee the same operational loss path.
A worked example
Two fictional equal-weight assets each have 20% annual volatility. With correlation 0, basket variance is .5²×.2²+.5²×.2²=.02, giving 14.142% volatility. With correlation 1, covariance raises volatility to20%.
The graph varies correlation with fixed weights and constituent vols. It illustrates the relationship, not a forecast or a live dispersion opportunity.
Open the calculation without leaving this lesson
Dispersion and correlation—worked comparison
Vertical: Basket annualized volatility (%)
Horizontal: Correlation assumption
1. Fictional example
Read the graph as a data table
| Correlation assumption | Fictional example |
|---|---|
| -0.5 | 10 |
| 0 | 14.1421 |
| 0.25 | 15.8114 |
| 0.5 | 17.3205 |
| 0.75 | 18.7083 |
| 1 | 20 |
What would invalidate the reading?
A trader ignores changing weights or assumes low historical correlation persists. One constituent's gap can also dominate a component-option book.
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
A trader ignores changing weights or assumes low historical correlation persists. One constituent's gap can also dominate a component-option book.
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: Why can index volatility differ from component volatility? 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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