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How do the prices of derivatives relate to prices of their underlyings?
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How do the prices of derivatives relate to prices of their underlyings?

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How do the prices of derivatives relate to prices of their underlyings?

As someone who has recently become interested in learning to day-trade (perhaps the ES), I am trying to get a better understanding of how the market works. I will expand on my question above with examples. (Note that the numbers in the examples probably won't make sense, but I hope they are still illustrative.)

Example 1: Some news event causes a large institutional investor to sell a good deal of large-cap holdings, causing the S&P 500 to fall 2%. How quickly and to what extent will that change propagate to the ES? Does this affect change as we get closer to the closing date of the derivative?

Example 2: A wealthy day-trader invents a new system that is quite bearish. He shorts 1,000 contracts, causing the price of the ES to fall 5%. How (and why) will this affect the S&P and the underlying equities in the index?


Thanks,

Dave

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dyross View Post
As someone who has recently become interested in learning to day-trade (perhaps the ES), I am trying to get a better understanding of how the market works. I will expand on my question above with examples. (Note that the numbers in the examples probably won't make sense, but I hope they are still illustrative.)

Example 1: Some news event causes a large institutional investor to sell a good deal of large-cap holdings, causing the S&P 500 to fall 2%. How quickly and to what extent will that change propagate to the ES? Does this affect change as we get closer to the closing date of the derivative?

Example 2: A wealthy day-trader invents a new system that is quite bearish. He shorts 1,000 contracts, causing the price of the ES to fall 5%. How (and why) will this affect the S&P and the underlying equities in the index?


Thanks,

Dave

Shorting 1,000 contracts may move the ES by 0.1% during the illiquid night session. During the flash crash it took 200,000 contracts (contract value $ 12 billion) to move the ES down 5%. So that day trader must be pretty wealthy.

The underlying of ES is the S&P 500. If you hold an ES position until expiry, you will not get the basket of underlying stocks. This would be too complicated, as you would get fractional shares. ES is therefore cash settled, and the value of your futures contract is calculated as the index value as determined in the Special Opening Quotation on the Friday when it expires.

Until the settlement day you need to compare the value of the equivalent stock position and futures position by comparing the cash flows. The holder of the futures contract

-> is not entitled to dividend payment prior to settlement date (disadvantage)
-> has little (margin) or no (if margin is held as US treasuries) financing cost(advantage)

You can therefore calculate the fair value of the ES futures contract from the basket of stocks.

fair value (ES) = index value (S&P 500) + interest paid by stock holder - expected dividends received by stock holder

By the way the settlement price on the last business day of the month is determined as the fair value and the close of the stock market. It is not a market price.

Arbitrageurs Stepping In

If the market price of ES diverges from its fair value, arbitrageurs will step in and try ot make a profit. If somebody heavily sold ES and it is below its fair value, the arbitrageur can buy the futures contract and sell the basket of stocks. The arbitrageur can then hold the futures contract until expiry and then repurchase the stock.

So far the theory. During the flash crash the tape was not up-to-date, some stocks were totally illiquid, so it would been impossible to sell them and buy the ES. This also means that during the crash was not trading at its fair value. Arbitrage was limited for technical reasons. The risk for the arbitrageurs was simply to large that they would only get filled on the futures leg, but not on the other leg, which would have required selling the stocks.

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Shorting 1,000 contracts may move the ES by 0.1% during the illiquid night session. During the flash crash it took 200,000 contracts (contract value $ 12 billion) to move the ES down 5%. So that day trader must be pretty wealthy.

I guess that was unavoidable.


Quoting 
The underlying of ES is the S&P 500. If you hold an ES position until expiry, you will not get the basket of underlying stocks. This would be too complicated, as you would get fractional shares. ES is therefore cash settled, and the value of your futures contract is calculated as the index value as determined in the Special Opening Quotation on the Friday when it expires.

Until the settlement day you need to compare the value of the equivalent stock position and futures position by comparing the cash flows. The holder of the futures contract

-> is not entitled to dividend payment prior to settlement date (disadvantage)
-> has little (margin) or no (if margin is held as US treasuries) financing cost(advantage)

You can therefore calculate the fair value of the ES futures contract from the basket of stocks.

fair value (ES) = index value (S&P 500) + interest paid by stock holder - expected dividends received by stock holder

By the way the settlement price on the last business day of the month is determined as the fair value and the close of the stock market. It is not a market price.

I don't quite understand the financing cost / interest advantage. Are you saying that since the underlying stocks (fractions of S&P) are so expensive, anyone who owns them surely financed that purchase and will therefore pay interest in the future? Does this happen in practice?


Quoting 
Arbitrageurs Stepping In

If the market price of ES diverges from its fair value, arbitrageurs will step in and try ot make a profit. If somebody heavily sold ES and it is below its fair value, the arbitrageur can buy the futures contract and sell the basket of stocks. The arbitrageur can then hold the futures contract until expiry and then repurchase the stock.

I wonder how quickly this happens in practice. Surely it depends on the size of the discrepancy, but are we talking seconds, hours, days?

Is it possible for the reverse of this to happen? Perhaps a price difference signals that some (rather intelligent) futures traders know something that stock traders don't, and therefore the stock traders bring the price of the underlying stocks closer to what the ES is signaling. How do futures day traders "move the market?"


Quoting 
So far the theory. During the flash crash the tape was not up-to-date, some stocks were totally illiquid, so it would been impossible to sell them and buy the ES. This also means that during the crash was not trading at its fair value. Arbitrage was limited for technical reasons. The risk for the arbitrageurs was simply to large that they would only get filled on the futures leg, but not on the other leg, which would have required selling the stocks.

According to Wikipedia's entry on the Flash Crash, the price of some S&P 500 companies (Accenture, Exelon) fell to a penny per share, while other companies (Apple, HP) rose to over $100,000 a share (very briefly). How did the selloff of many ES contracts translate to this?

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dyross View Post
I don't quite understand the financing cost / interest advantage. Are you saying that since the underlying stocks (fractions of S&P) are so expensive, anyone who owns them surely financed that purchase and will therefore pay interest in the future? Does this happen in practice?

Two Options to Invest $ 1 million

Let us assume that you are an investor, who has $ 1 million, and you want to invest this amount to get exposure to the stock market, more precisely the S&P 500

Option 1: You buy the S&P stocks according to their relative weight within the index.

Option 2: You get long the ES 06-11. It currently trades at 1,350 points, so one contract equals market exposure equivalent to $ 67,500. To invest one million you will get long 15 contracts.

Now what is the difference between option 1 and option 2?

Option 1: Your money, $ 1 million is now invested in stocks. You are entitled to dividends paid.

Option 2: You need to deposit a margin with your broker. Let us assume that this will be about $ 100,000, which you have to feed into your broker account. The margin is a financial deposit that you are required to make, in case that your position will suffer from a loss. It is adjusted on daily basis. If your broker is nice, you are allowed to invest this money and purchase US treasuries, which are good enough as a guarantee. Now let us assume that you invest both - the $ 100,000 required as a margin and the $ 900,000 in risk-free treasuries, then you will receive interest payments on your $ 1 million at the risk-free rate.

To summarize. If you buy the stocks, you get dividends. If you enter a long futures position, you keep your money and can invest it, so you receive interest. Therefore

fair value (ES) = value of underlying index - expected dividends (unitl expiry of the futures contract) + interest at the risk free rate

This is a simplification, but gives you an approximate relationship between the S&P 500 and its derivative the ES.


The formula does not hold for a Total Return Index

The formula would not apply to a total return index, which is calculated by reinvesting dividends. The DAX 30, on which the FDAX future is based, is a total return index, to the FDAX should always trade above the DAX30, unless you can imagine negative interest rates.

The FDAX is therefore always in contango, while the ES is in backwardation, when interest rates are low. This is currently the case. The interest rate gain is therefore lower than the expected dividends and ES should trade below the S&P 500.

At this moment: ES 1350.25 / S&P 500 1353.50, which is as expected.

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This makes perfect sense. Thanks for the informative reply.

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dyross View Post
I wonder how quickly this happens in practice. Surely it depends on the size of the discrepancy, but are we talking seconds, hours, days?

Is it possible for the reverse of this to happen? Perhaps a price difference signals that some (rather intelligent) futures traders know something that stock traders don't, and therefore the stock traders bring the price of the underlying stocks closer to what the ES is signaling. How do futures day traders "move the market?"

For some futures traders it is quite difficult to move the market. This is the case with index futures and currency futures. Via the fair value formula these are linked to the much larger underlying markets, that is the stock market and the FOREX market. This usually leads to a dampening of price spikes, So when a futures trader tries to move these markets, some arbitrageurs will step in if the differential between the futures and the cash market at fair value becomes large enough to cover the trading cost and the risk of teh arbitrage.

For other markets, such as the oil markets this does not necessarily hold. It really depends on the size of the futures and the size of the cash market to determine which one is dominating. The earth revolves around the sun and not vice-versa. In the end it is the larger market which will dominate.

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For some futures traders it is quite difficult to move the market. This is the case with index futures and currency futures. Via the fair value formula these are linked to the much larger underlying markets, that is the stock market and the FOREX market. This usually leads to a dampening of price spikes, So when a futures trader tries to move these markets, some arbitrageurs will step in if the differential between the futures and the cash market at fair value becomes large enough to cover the trading cost and the risk of teh arbitrage.

For other markets, such as the oil markets this does not necessarily hold. It really depends on the size of the futures and the size of the cash market to determine which one is dominating. The earth revolves around the sun and not vice-versa. In the end it is the larger market which will dominate.

So I guess I'll ask a more general, naive question: What (if any) affect does speculation in futures markets (especially the larger markets like indices and forex) on a macro level? Are traders simply moving money between each other (and taking on hedgers' risk)? The Flash Crash seems like it was a freak incident, but that was an example of ES trading affecting the S&P index and it's underlying companies, right?

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dyross View Post
So I guess I'll ask a more general, naive question: What (if any) affect does speculation in futures markets (especially the larger markets like indices and forex) on a macro level? Are traders simply moving money between each other (and taking on hedgers' risk)? The Flash Crash seems like it was a freak incident, but that was an example of ES trading affecting the S&P index and it's underlying companies, right?

Markets are driven by supply and demand, which depends on investor sentiment. This also applies to futures markets.

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Can't prove anything regarding who had a clear advantage in potentially the most profitable day in trading history. Even if I did I wouldn't have the balls to post it - nor the big (but circumstantial) chunk of the puzzle I saw 10 days later. FWIW it's well known that not all venues of trade were subject to the same (unheard of ?) 30% max profit limitation.

It took a while to come out but Zero Hedge prove the flash crash was a result of quote stuffing (in my book at least).

What I incorrectly said caused it at the time was the high frequency trading algos going from buy to sell. 100's of thousands of HFT's are sent out every second. Almost all of them cancel out but the ones that don't break up big orders which pushes up the buy limit of the order. Not great if it's your order but great if you already owned the equity. If they go from buy to sell that would be reversed and the number of liquidity providing old fashion market makers has gone down a good amount.

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