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S&P500 index and S&P500 index futures correlation
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S&P500 index and S&P500 index futures correlation

  #1 (permalink)
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S&P500 index and S&P500 index futures correlation

Can someone explain to me the mechanism that keeps the s&p500 futures pegged to the s&p500? From what I gather it is primarily arbitrageurs who perform this function. Also, I believe that contango is playing a role. I just haven't figured it out totally in my head yet.

It's sort of embarrassing as I've traded the es and I don't completely understand the fundamentals.

Thanks.

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  #3 (permalink)
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ocmsrzr View Post
Can someone explain to me the mechanism that keeps the s&p500 futures pegged to the s&p500? From what I gather it is primarily arbitrageurs who perform this function. Also, I believe that contango is playing a role. I just haven't figured it out totally in my head yet.

It's sort of embarrassing as I've traded the es and I don't completely understand the fundamentals.

Thanks.


The futures contract relates to the future price of the asset at the expiry date / settlement of the contract.


Arbitrage and Structural Contango

An investor, who wants to invest a sum of money until the expiry date of ES can either

(a) purchase the underlying stocks of the S&P 500 and sell them at the expiry date or

(b) enter the equivalent long position by buying the appropriate number of ES contracts

If he buys the stocks, he has to pay for them, which is a disadvantage. If he enters a long futures position, he does not need to pay anything, because he will enter the position on a margin. So he has the advantage that he can place the money at the risk-free rate, for example by buying government bonds, which his broker will accept as margin for ther transaction.

The fact that the holders of the futures contract has this advantage, is translated by a higher price of the futures contract compared to the cash index. The difference is the interest received on the amount invested in government bonds calculated with the risk-free rate. This is the contango situation you refer to: the price of the futures must be higher than the cash index. The cash price is the futures price, discounted at the risk-free rate.

Now this is not always true, because I have omitted other factors.


Total Return Index and Price Level Index

Above I did not tale into account, that the investor has an advantage, when purchasing the stocks. He is entitled to the payment of dividends. The holders of the futures position is not entitled to dividend payment. This clearly reduces the advantage and - if interest rates are low and dividends are high - can transform the contango into backwardation. If I look at yesterday's close at 4:00 PM Est, ES 12-10 was at 1120 while the SPX index was at 1126. This is a mild backwardation. This means that current dividend expectations for the period until settlement of ES 12-10 in the third week of December are higher than the interest earned on the investment at the risk-free rate for the same period. This happens, if current interest rates are quite low. Do not expect backwardation during a period of higher interest rates.

The S&P index is a price level index, which means that the dividends paid are not reinvested.

However, there are indices such as the FDAX, where the index calculation assumes that dividends are being reinvested. This type of index is called a total return index. As a consequence the holder of the long futures position is entitled to receive a higher number of shares after each payment of dividends. So the holder of the FDAX futures position does not have any disadvantage as the holder of the ES position , and the only difference between the futures and the cash position is the interest received.

A futures contract on a total return index should therefore always show a contango, and indeed, yesterday the DAX index closed at 6210, while the FDAX futures contract closed at 6222.


Convenience Yield and Storage Cost

If you actually own the shares you can rent them out to short sellers and generate fee income. In case of a commodity you have an insurance in case of a physical supply shortage. This additional advantage is called convenience yield. The convenience yield shifts the futures position further into backwardation, while disadvantages linked to the physical position, such as storage costs for commodities shift the futures contract back into contango.


Last edited by Fat Tails; September 20th, 2010 at 05:49 PM.
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  #4 (permalink)
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Thanks a lot Fat Tails. That explains a lot.

The only question that I still have in my mind relates to the character of an ES buyer as either an investor/trader.

As an investor, you are clearly looking into things such as dividends, reinvestment, storage cost, ect. I'm not sure about the percentage of spoos buyers that are investers/traders, but I assume that the percentage of traders is higher than negligible.

As a trader, you are buying off of a myriad of indicators such as technicals, news, ect. My assumption is that arbitrageurs are looking at what they think the price should be given your pricing analysis and the spot price and taking advantage of the price difference.

Perhaps i've answered my own question.


Fat Tails View Post
The futures contract relates to the future price of the asset at the expiry date / settlement of the contract.


Arbitrage and Structural Contango

An investor, who wants to invest a sum of money until the expiry date of ES can either

(a) purchase the underlying stocks of the S&P 500 and sell them at the expiry date or

(b) enter the equivalent long position by buying the appropriate number of ES contracts

If he buys the stocks, he has to pay for them, which is a disadvantage. If he enters a long futures position, he does not need to pay anything, because he will enter the position on a margin. So he has the advantage that he can place the money at the risk-free rate, for example by buying government bonds, which his broker will accept as margin for ther transaction.

The fact that the holders of the futures contract has this advantage, is translated by a higher price of the futures contract compared to the cash index. The difference is the interest received on the amount invested in government bonds calculated with the risk-free rate. This is the contango situation you refer to: the price of the futures must be higher than the cash index. The cash price is the futures price, discounted at the risk-free rate.

Now this is not always true, because I have omitted other factors.


Total Return Index and Price Level Index

Above I did not tale into account, that the investor has an advantage, when purchasing the stocks. He is entitled to the payment of dividends. The holders of the futures position is not entitled to dividend payment. This clearly reduces the advantage and - if interest rates are low and dividends are high - can transform the contango into backwardation. If I look at yesterday's close at 4:00 PM Est, ES 12-10 was at 1120 while the SPX index was at 1126. This is a mild backwardation. This means that current dividend expectations for the period until settlement of ES 12-10 in the third week of December are higher than the interest earned on the investment at the risk-free rate for the same period. This happens, if current interest rates are quite low. Do not expect backwardation during a period of higher interest rates.

The S&P index is a price level index, which means that the dividends paid are not reinvested.

However, there are indices such as the FDAX, where the index calculation assumes that dividends are being reinvested. This type of index is called a total return index. As a consequence the holder of the long futures position is entitled to receive a higher number of shares after each payment of dividends. So the holder of the FDAX futures position does not have any disadvantage as the holder of the ES position , and the only difference between the futures and the cash position is the interest received.

A futures contract on a total return index should therefore always show a contango, and indeed, yesterday the DAX index closed at 6210, while the FDAX futures contract closed at 6222.


Convenience Yield and Storage Cost

If you actually own the shares you can rent them out to short sellers and generate fee income. In case of a commodity you have an insurance in case of a physical supply shortage. This additional advantage is called convenience yield. The convenience yield shifts the futures position further into backwardation, while disadvantages linked to the physical position, such as storage costs for commodities shift the futures contract back into contango.


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  #5 (permalink)
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ocmsrzr View Post
Thanks a lot Fat Tails. That explains a lot.

The only question that I still have in my mind relates to the character of an ES buyer as either an investor/trader.

As an investor, you are clearly looking into things such as dividends, reinvestment, storage cost, ect. I'm not sure about the percentage of spoos buyers that are investers/traders, but I assume that the percentage of traders is higher than negligible.

As a trader, you are buying off of a myriad of indicators such as technicals, news, ect. My assumption is that arbitrageurs are looking at what they think the price should be given your pricing analysis and the spot price and taking advantage of the price difference.

Perhaps i've answered my own question.

At the expiry date, the futures price and the price of the underlying converge. This is what makes arbitrage possible. Indeed, you can calculate the futures price at "fair value", which would be

futures price = underlying + interest received + strorage cost - expected divends - convenience yield

If the future price deviates from the fair value, arbitrageurs will buy the futures contract and sell the stocks, or sell the futures contract and buy the stocks. As it is difficult to purchase or sell all 500 components of the S&P, they may only do this with the most active stocks. If such a buy or sell program hits the market, you will likely see that it causes extreme readings of the NYSE Tick.


Last edited by Fat Tails; September 21st, 2010 at 10:30 AM.
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  #6 (permalink)
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Got it.

I think the only question i'm left with is: why is the price action, not just the price, so similar?

It must be arbitrage.

??

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  #7 (permalink)
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ocmsrzr View Post
Got it.

I think the only question i'm left with is: why is the price action, not just the price, so similar?

It must be arbitrage.

??

Of course it is arbitrage. If the futures contract deviates from the fair value you can make a risk-free profit.

Let us say ES trades 1 point (4 ticks) above its fair value. Sell ES and buy the stocks, and you have made 1 point of profit. The profit is guaranteed by the price adjustment at expiry (the underlying stocks of index futures are not deliverable).

If you want to access this profit you need

(1) to build a model to replace the 500 component stocks of the S&P with a smaller portfolio that is correlated to the original portfolio to the tick, possibly by selecting all stocks that have a higher market capitalization and are well behaved

(2) buy this portfolio via the available exchanges *)

(3) sell the equivalent number of ES contracts

(4) have low transaction costs, because they will reduce the profit

*) it helps, if you have larger customer who wants to sell the components

We cannot do that because

(1) we do not have that model
(2) our accounts do not have the necessary size
(3) our transaction costs are too high compared to those that are members of the exchanges

We are not competitive to play this type of game, but we can watch the NYSE Tick, and conclude, that the futures price may have overshot or undershot its fair value, when the NYSE Tick shows extreme readings.

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Here's the evolution of the premium during the day, it's eSignal EPREM A0 symbol.
It tracks SP500 index - ES.

You can see the values oscillates around the fair value of the day, approx -5 points.

Oscillation today was +/- 0.5 point during the day, +/- 1 point after FOMC.

You can get fair value of the day here
Today's Program Trading Buy/Sell Execution Levels

or for all days before expiration here
Program Trading Values vs. Time S&P 500 DEC 2010 Futures - indexArb.com

Attached Thumbnails
S&P500 index and S&P500 index futures correlation-prem.png  
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Thanks Gomi, that programtrading.com site is very interesting. Have you tried either their delayed or realtime chat services?

Are you finding PREM useful in your trading?


gomi View Post
Here's the evolution of the premium during the day, it's eSignal EPREM A0 symbol.
It tracks SP500 index - ES.

You can see the values oscillates around the fair value of the day, approx -5 points.

Oscillation today was +/- 0.5 point during the day, +/- 1 point after FOMC.

You can get fair value of the day here
Today's Program Trading Buy/Sell Execution Levels

or for all days before expiration here
Program Trading Values vs. Time S&P 500 DEC 2010 Futures - indexArb.com


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