# Fair value and basis

**FUT-11 · Equity Index Futures · Core**

**Lesson question:** Why need futures and cash not display the same number?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.

**Prerequisites:** FUT-01

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.

## Calculation popup: Work the example

```text
F=S×exp((r−q)T)
```

Use matching units and the explicitly hypothetical inputs.

1. r−q=0.025; T=0.25.

2. F=5,000×exp(0.00625)=5031.347860019.

**Result:** Basis 31.347860 points.

## Graph: Fair value and basis—worked comparison

**Horizontal:** Years to expiry  
**Vertical:** Model basis F−S (points)

Fictional data from the written example. The chart organizes the comparison; its shape is not a forecast.

Complete numerical data are embedded in `scripts/equity-futures/FUT-11.js` and displayed as an accessible table in the HTML lesson.

## 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

### What is the modeled basis under these inputs?

**Answer:** About 31.35 points.

**Why:** Subtract 5,000 cash from the computed future.

### What is the critical failure to avoid?

**Answer:** Calling positive basis automatically bullish confuses carry with direction. Wrong dividends or stale cash can also manufacture apparent mispricing.

**Why:** Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome. **Critical risk check.**

## Takeaway

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.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [CME Calculating Fair Value](https://www.cmegroup.com/trading/equity-index/fairvalue.html)