What is the modeled basis under these inputs?
Reveal the worked answer
About 31.35 points.
Subtract 5,000 cash from the computed future.
Equity Index Futures · FUT-11 · Core
Fair value and basis
Why need futures and cash not display the same number?
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?
Basis is the difference between a future and the relevant cash price under a stated sign convention. Here basis means F−S. Nonzero basis need not be sentiment or mispricing: financing, dividends and maturity explain much of the relationship.
Always label the convention because some sources reverse it.
Understand the mechanism
A simplified continuous-yield model gives F=S×exp((r−q)T). Financing the basket adds carry while dividends offset some of it. This is not the same as a discrete-dividend or simple-interest formula.
Actual supply, financing access, dividend uncertainty and transaction costs can create deviations. The modeled reference is not a guaranteed executable arbitrage.
Walk through the process
Align timestamps, underlying definitions and expiry. Use expected dividends over the actual holding window rather than a historical yield without thought. Check contract month and data delay before interpreting a discrepancy.
A longer-dated future can have a larger level difference without predicting a larger market rally.
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
For fictional S=5,000, continuous r=4%, q=1.5% and T=0.25, modeled F is 5031.347860. Basis is 31.347860 points.
The graph increases maturity while holding all economic assumptions fixed. It shows carry, not an expected path of the stock index. A different dividend forecast would change the line.
Open the calculation without leaving this lesson
Fair value and basis—worked comparison
Vertical: Model basis F−S (points)
Horizontal: Years to expiry
1. Fictional example
Read the graph as a data table
| Years to expiry | Fictional example |
|---|---|
| 0 | 0 |
| 0.05 | 6.25391 |
| 0.1 | 12.5156 |
| 0.15 | 18.7852 |
| 0.2 | 25.0626 |
| 0.25 | 31.3479 |
What would invalidate the reading?
Calling positive basis automatically bullish confuses carry with direction. Wrong dividends or stale cash can also manufacture apparent mispricing.
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
Calling positive basis automatically bullish confuses carry with direction. Wrong dividends or stale cash can also manufacture apparent mispricing.
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 need futures and cash not display the same number? 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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