2.2.10. Fare Future Value
Assets which have future contracts negotiated must be arbitrated, that is, does not exist difference between positions at spot or future, except the load and store cost.
In case of future index of exchange, does not have any storage cost, being that index must be arbitrated according to the at spot index and to interest rate for the period until the index settlement.
This future index, arbitrated according to interests rate, it's the fare index. If the future index differ from the future fare index, it has chance to arbitrate the market.
2.2.10.1. Function CC.INDJUSTO
Access:
- Menu - Insert | Function | Calculus
 - Toolbar Default | Calculus
Description:
Return the fare value for the future index in the stock exchange, considering the yield curve and the settlement of the future index.
For calculating the interest rate relative to the settlement of the future index, this function do the interpolation by the exponetial method. Does not been effected extrapolations. If the future index expires after the last point on the yield curve, will be used the rate of the last point. Also does not have extrapolation befroe the first settlement in the yield curve.
A same yield curve can't have more than one information for the same point in time (in example a future interest and other of swaps). If it occur, will prevail the bigger rate.
Important:
The interpolation method used for calculate the fare future index it's exponential interpolation, without doing extrapolations!
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Call: CC.INDJUSTO (Spot Index, Workdays, Yield Curve)
Argument |
Type |
Description |
Spot index |
long integer |
Spot index for an asset - Stock index for example.
|
Workdays |
integer |
Workdays till settlement of the future contract.Must be bigger than 1.
|
Yield Curve |
range |
Range (n rows and 2 columns) describing yield curve - base 252 and workdays.
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The result for the future spot index is:
- Future spot index: valor futuro do incide à vista projetado pela curva de juros. Este valor é arredondado.
- Fare index:
With Pint equal to the interest rate by year(base 252) interpoled for the settlement Dint of future index and considering Pi and Pi+1 as point in the yield curve, Di and Di+1 as the number of workdays corresponding to this points, being Dint between Di and Di+1, have:
Important:
If the payment day is previous to the the first settlement on the yiled curve, the interpoled rate will be equal to the interest rate on the first point of yield curve! If it's after the last settlement, the interpoled rate will be equal to last rate of the yield curve (without extrapolations).
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Usage example deducting the interval:
This is the most common case, where the midday interval is considered as an interruption on negotiations, the actual volume makes reference to the negotiated volume in stock exchange until the time now.
- IBOVESPA spot index 10,000 point
- Days to index settlement 25 (workdays)
- Curve: A2:B11 (11 points not sorted)
| 18.75% | 20 |
| 20.65% | 220 |
| 20.70% | 300 |
| 20.40% | 140 |
| 19.15% | 40 |
| 19.75% | 80 |
| 20.71% | 350 |
| 20.60% | 180 |
| 19.40% | 60 |
| 20.00% | 100 |
= CC.INDJUSTO( 10000, 25, A2:B11)
Results:
Considering the yield curve, the fare future index for IBOVESPA its 10,173 points.
2.2.10.2. Function CC.INDTAXA
Access:
- Menu - Insert | Function | Calculus
- - Toolbar Default | Calculus
Description:
Return the interest rate (base 252) implicit in the future index from the stock exchange negotiated in the market.
The calc of the interest rate inlaid or implicit in the exchange future index its complementary to the calculation of the fare index and presents, however, the same result: an oportunity for arbitrating or not.
The interest rate implicit in the future index must be, considering an arbitrated, to the same rate obtained by the interpolation of the yield curve for the settlement of the future contract.
Call: : CC.INDTAXA ( Future Contract, Workdays, Spot Index)
Argument |
Type |
Description |
Future Contract |
long integer |
Future contract quotation of the chosen index.
|
Workdays |
integer |
Workdays till settlement of the future contract.This number must be bigger than 1.
|
Spot Index |
long integer |
Spot Index.
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The result for the rate implicit in the future index is:
- Implicit rate: interest rate effective base 252 implcit in the future index from IBOVESPA, where Vcto (settlement) represents the workdays for the future settlement:
- Implicit rate:
Usage example for BOVESPA:
This is the most common case, where the midday interval is considered as an interruption on negotiations, the actual volume makes reference to the negotiated volume in stock exchange until the time now.
- Future index 10,210 points
- Workdays to index settlement 25 (workdays)
- IBOVESPA spot index 10,000 points
= CC.INDTAXA( 10210, 25, 10000)
Results:
The interest rate implicit in the future index in the stock exchange its 23.30%. If this rate is different from the rate apointed in the yield curve for the same period, there is an arbitrating oportunity.
2.2.10.3. Function CC.INDDIF
Access:
- Menu - Insert | Function | Calculus
- - Toolbar Default | Calculus
Description:
Returns the difference between the future fare index and the negotiated. Returns negative for the "cheap" and positive future index for teh "expensive" future index.
The differential its a tool of absolut reference (independing from index level) of market bias.
Call: CC.INDDIF ( Spot Index, Future Contract, Workdays, Yield Curve)
Argument |
Type |
Description |
Spot index |
long integer |
Spot index for an asset - Stock index for example.
|
Future Contract |
long integer |
Spot index for an asset - Stock index for example.
|
Workdays |
integer |
Workdays till settlement of the future contract.Must be more than 1.
|
Yield Curve |
range |
Range (n rows and 2 columns) describing yield curve - base 252 and workdays.
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The result for the differential is:
- Differential: difference between the fare future index and the negotiated in the market:
- Differential:
Important:
For calculate the fare index used in the differential use previous observations for interpolations on the function CC.INDJUSTO!
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Usage example for IBOVESPA:
This is the most common case, where the midday interval is considered as an interruption on negotiations, the actual volume makes reference to the negotiated volume in stock exchange until the time now.
- IBOVESPA spot index 10,000 pontos
- Future index 10,210 points
- Index settlement days 25 (workdays)
- Curve: A2:B11 (11 points not sorted)
| 18.75% | 20 |
| 20.65% | 220 |
| 20.70% | 300 |
| 20.40% | 140 |
| 19.15% | 40 |
| 19.75% | 80 |
| 20.71% | 350 |
| 20.60% | 180 |
| 19.40% | 60 |
| 20.00% | 100 |
= CC.INDDIF( 10000, 10210, 25, A2:B11)
Resultados:
As the return is positive, the negotiated future index in the market is "expensive" or with agio of 37 points in relation to the fare future index.
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