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Relationship between CAC40 index and CAC40 September futures index.
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Relationship between CAC40 index and CAC40 September futures index.

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Relationship between CAC40 index and CAC40 September futures index.

Hello all,

I am studying the shares on the CAC40 index in Paris, France.

I am trying to understand if there is any relationship between the CAC40 index and the CAC40 Futures index. The Futures index is currently lagging below the CAC40 index.

Is it possible to infer anything from the relationship between the 2?

Thanks

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I'm not sure lagging is the correct word: there is a small difference between the cash and the futures, which is stable, and decrease while the expiry date approach.
The cash index is a simple math computation: a weighted average price of the CAC40 stocks.
The futures index has an expiry date, the dividend payed for a stock (the stock price will decrease after that), the splits, ..., are used to evaluate the futures price, which is mechanically different from the index value.

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sam028 View Post
I'm not sure lagging is the correct word: there is a small difference between the cash and the futures, which is stable, and decrease while the expiry date approach.
The cash index is a simple math computation: a weighted average price of the CAC40 stocks.
The futures index has an expiry date, the dividend payed for a stock (the stock price will decrease after that), the splits, ..., are used to evaluate the futures price, which is mechanically different from the index value.

Okay Thanks for this reply but can I infer anything from the difference between the 2 - change in futures will have an impact (maybe delayed) on the cash?
People moving out of (selling) futures (futures price goes down) to go into cash (buying and pushing cash prices up)??

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rsksmiles View Post
Okay Thanks for this reply but can I infer anything from the difference between the 2 - change in futures will have an impact (maybe delayed) on the cash?
People moving out of (selling) futures (futures price goes down) to go into cash (buying and pushing cash prices up)??

I don't think you can do anything useful, watching the spread between the two. It would have been too easy .

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rsksmiles View Post
Okay Thanks for this reply but can I infer anything from the difference between the 2 - change in futures will have an impact (maybe delayed) on the cash?
People moving out of (selling) futures (futures price goes down) to go into cash (buying and pushing cash prices up)??

A direct comparison is not fruitful. However, if you were an arbitrage trader (don't try to do this with a retail account, as you would need ultra-low commissions and considerable purchasing power to buy the basket of 40 stocks) you could benefit from the difference between the futures price and its fair value.


Calculating Fair Value

To calculate the fair value of a future, you would first want to know whether the index is a total return or a price index. A total return index (such as the DAX) has the dividends reinvested, so somebody who buys the DAX future has the same right to dividend payment as somebody who holds the underlying basket of stocks. This means that the FDAX always trades at a premium to the index, as it benefits from lower interest rates. As far as I know the CAC40 is a price index, which means that dividends are not reinvested but taken away (by the way there is also the total return index CACR see Bloomberg here : CACR Quote - CAC 40 Total Return Index - Bloomberg). You will see this confirmed, if the futures contract trades at a discount to the index price.

For a price value, the simplified formula (assumptions here are zero transaction costs, equal marginal borrowing and lending rates) for the relationship between index price and fair value is

fair value = spot index price * ( 1 + (interest rate - projected dividend rate) * days until expiry / 360)

The interest rate is the money market yield prior to expiry of the futures contract, the projected dividend rate is calculated from the dividends that are attributed to the holder of the component stocks prior to the expiry of the futures contract. The formula shows the difference between a long futures position and a long stock position. If you are long the futures

-> advantage: you do not have to invest the money to pay for the stocks (you don't have to pay interest or can receive interest on the margin for your futures contract and the remaining amount)
-> disadvantage: you are not entitled to any dividend payment prior to the expiry of the futures contract

Currently the money market yields are pretty low, which explains that the advantage of not having to pay interest is worth less than the disadvantage of not receiving dividends (which also depends on the ex- dividend date). This explains that the CAC40 futures contract should trade at a discount to the index. We are now close to expiry, so the difference should be small.


Theoretical Arbitrage Opportunities

Now you can try to chart the fair value of the index and the futures price. When the futures price deviates by a few points from the fair value, there is an arbitrage opportunity. Let us say there is a panique and the selling of the futures has driven down the futures price considerably below fair value. Then you would love to by the futures and sell the stocks. Short selling stocks is not easy, so you should actually own those stocks

-> requirement No.1 for arbitrage: own a huge amount stocks or have those stocks in your customer's portfolio, so that you can short them

Then you can sell them quickly. This requires that you sell them via market orders, best you have some purchase orders from customers

-> requirement No. 2 for arbitrage: slippage should be taken into account

Now you can sell the future and pocket the arbitrage gain.

But let us come back to the fair value formula. Do you really have access to money market rates

-> requirement No. 3 for arbitrage: have access to the lowest interest rates possible for financing

and do you really have the lowest transaction costs?

-> requirement No. 4 for arbitrage: have the lowest transaction costs of all market participants

Not really enticing.


What can you do?

You can watch the differential between the futures contract and the fair value. When they deviate by a certain amount arbitrage will be kicking in, and slow down the futures contract(which usually moves faster than the stocks, as liquidity is higher and it is a less complex construct than a basket). Mayne a widening spread may even indicate a climax type situation such as a high tick reading.

You can also chart the futures contract against the index and try to find those extrema. You may even assume that a long period moving average of the differential is similar to fair value and use the deviation from that moving average to chart the spread. I have not done this yet.

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