Single-Stock Futures Part 7

Using Fair Value to Predict Market Open

In the last course, we learned about the concept of fair value and how to calculate it. We're now going to turn our attention to a practical use that can keep you from making erroneous trading decisions.

As you invest, you will start to hear the term "fair value" used over and over. In most cases, you will hear about it just before the stock market opening bell, which is 9:30 Eastern Time, as market commentators attempt to determine whether the market will open up, down, or unchanged. Advanced market traders listen to these reports and, in many cases, place pre-market trades based on the information. I have seen many cases where a lot of money is lost or, at a minimum, commissions were spent for nothing because traders misinterpreted what it meant when they heard that the futures were either up or down prior to the open. Now that you have learned the basics of fair value and futures contracts, we can apply it to the stock market and see how to use this information correctly.

To start, understand that the two main indices used to gauge the markets are the S&P 500 and the Nasdaq 100 futures contracts. These are usually the two indices you see reported on financial stations such as CNBC in the mornings. You may hear the commentators say something like, "The S&P futures are down 10 points this morning prior to the opening bell." Even advanced traders get confused as to exactly what this futures quote means. They often associate the change in futures prices (either up or down) as the indication of the market open. For example, if the futures are trading down 10, they mistakenly believe this means a negative indication for the open just because they are down. Likewise, they feel if the futures are trading up 10 that the markets will open positively. While this may sound sensible, it is not necessarily correct; this erroneous interpretation can get you into trouble quickly if you are placing pre-market trades based on that misunderstanding.

When you hear CNBC and other financial sources talking about fair value, they are referring to the fair value of the S&P 500 index futures contract, which is widely regarded as the standard to gauge the overall markets. It is used by about 97% of U.S. money managers with more than $1 trillion in assets being pegged to that index. There are four contract months -- each is the last month of each respective quarter. The contracts are March (represented by the letter "H"), June (M), September (U) and December (Z). Whenever you hear CNBC or other sources quoting fair value, they are always talking about the near-term contract (the contract next in line to expire).

The S&P 500 futures contracts are cash-settled, which means you cannot take delivery of the underlying index. If you could, you would have to provide a portfolio of 500 stocks in the exact proportions of the S&P 500, which is rather tedious. But as we showed in the previous courses, there's really no mathematical difference if a futures contract delivers the underlying asset or is closed out for cash. Settling the futures contract in cash is effectively the same thing as actually buying and selling the actual stocks in the index. It makes no mathematical difference.

Because futures trade on separate markets from the spot market, they are subjected to their own sets of supply and demand, so they may wander off in different directions from the stock market. In fact, the futures trade all night long on GLOBEX, a computerized trading platform at the CME (Chicago Mercantile Exchange), from 4:45 pm until 9:15 am Eastern Time. The U.S. stock market, however, does not open until 9:30 Eastern Time. This definitely leaves room for the two markets to get out of line from the theoretical cost of carry formula we discussed in the last course. But if the futures get too far out of line, the arbitrageurs will correct for that at the opening bell.

Let's make some basic assumptions and then see how to calculate fair value:

• S&P 500 cash index (spot)* 1150
• Interest rate 5%
• S&P 500 dividend yield1.5%
• 75-day S&P futures 1162

* The actual S&P 500 index is often referred to as the "cash" market or the "spot" market since that is where you could "buy" the index with cash today or "on the spot." If you ever hear the financial press referring to the cash (or spot) levels of an index, they are talking about the current level (quote) of that index. For instance, if you want a quote on the S&P 500 cash or spot market, you would simply get a quote on the S&P 500 index, whose symbol is SPX.

The following formula is used to calculate fair valuefor stock index futures or any forward agreement where dividends or other cash forms are paid. It is basically the same formula we used in the last course but with a small twist:

Fair value = Spot price * [1+ (interest rate - dividends) ] ^days/360

Notice how this formula is just a variation of the one we provided earlier, which is:

Fair value = Spot price * (1+interest rate) ^time

Rather than using "1+ interest rate" inside the parentheses in the basic formula, fair value for indexes that include dividends use the term "1+ (interest rate - dividends)," which is the effective interest rate. This is done to reflect the fact that your borrowing cost (interest rate) is reduced by money received (dividends). If you are holding all of the stock in the S&P 500 or in the Nasdaq 100, you can bet that some dividends will likely be paid. This reduces your borrowing cost.

With the above assumptions, we can calculate the fair valueof this S&P futures contract, assuming we had to buy the value of the index and hold it to expiration:

Fair value of futures = 1150 [1 + (.05 - .015) ] ^75/365 = 1158.16

Based on our fair value calculation, the S&P futures "should be" trading for 1158.16. If they are, the index is said to be trading at "full carry." However, we see they are actually trading for 1162. Therefore, the futures are overpriced by 1162 - 1158.16 = 3.84 points. In this example, we would say the futures should be trading for a premium of 8.16 points above the current spot price of 1150 since the fair value calculation of 1158.16 is 8.16 points above that spot price. Rather than trading at the expected fair value premium of 8.16 points, the futures are trading at a premium of 12 points (1162 - 1150).

Because the futures are overpriced, we expect to see arbitrageursuse cash and carry arbitrage. They will buy the underpriced stocks and carry them for future delivery by hedging with a short futures contract. In other words, they will buy the stocks representing the S&P 500and sell the S&P 500 futures contracts. The short futures contract guarantees the sale. This puts buying pressure on the stock market and therefore is an upward indication for stocks at the opening bell. The reason for the upward pressure is because the futures were trading above fair value.

Key Points

If the futures are trading above fair value, it's a positive indication for stocks at the opening bell.

What if the futures were trading at 1152, for example? We determined that fair valuewas 1158.16, which means the futures are now too cheap. Arbitrageurs will attempt to short the stocks representing the S&P 500and hedge by purchasing the futures contract. These actions put selling pressure on stocks at the opening bell.

Key Points

If the futures are trading below fair value, it's a negative indication for stocks at the opening bell.

Here's where traders often get confused. Let's assume that yesterday the S&P 500 futures closed at 1168. This morning, prior to the stock market open, they are trading for 1162, down six points. As we mentioned earlier, many traders think this means a negative indication for the market simply for the fact that the futures are down. However, even though they are down, they are still more than three points above the fair valueof 1158.16, so it is really a positive indication for stocks at the open.

Key Points

Whether stocks are expected to rise or fall off the opening bell has nothing to do with whether the futures are up or down -- it all depends on where the futures are trading in relation to their fair value.

Because of the ease of arbitrage between stocks and futures, the futures contracts usually trade at close to full carry.

By the way, different sources (i.e., brokers, financial media, institutions, etc.) may quote different fair values but that does not mean a mistake has been made. Each firm calculating fair value has different borrowing costs and may have different assumptions about the compounding of interest. Therefore they may use a little different formula, such as the two we discussed in the last course. Regardless, each firm attempts to answer the questions: "How much does the spot asset cost, how long will I hold it, how much interest will I pay, and how much will I receive in dividends?" Because fair value is a cost of carrycalculation, that number changes just slightly on a daily basis. Each new day, fair value will be reduced slightly to reflect one less day's interest.

Market Imperfections

We just showed that arbitrage is theoretically possible if the futures contract is any amount above or below fair value. However, in the real world, there are many imperfections that make arbitrage impossible even though the futures contract may be trading outside of its theoretical cost of carry limit. Some of these imperfections are:

• Transaction Costs
• Bid/Ask spreads
• Restrictions on short sales (Is it allowable to short the underlying asset?)
• Different borrowing/lending rates
• Execution risk (Will you get the execution in time, if at all?)
• Lack of storability (Is the asset able to be stored?)

Because of these imperfections, arbitrage opportunities may disappear even though the futures are not priced at their fair value. For example, let's say there is a 1% transaction cost (commission) to buy or sell the stocks representing the S&P 500. If so, our fair value calculation of roughly 1158 will no longer be the dividing point for arbitrage. Instead, a range of values will be created with no arbitrage being possible inside this range.

Using the same assumptions as before, we can find that range. In order to successfully buy the S&P futures now, we must buy the spot asset plus a 1% commission, which increases the cost by a factor of 1.01. To buy the spot index, it will now cost:

1150 * 1.01 * 1.035 ^75/365 = 1169.74, which is approximately 1170

Note: to make the formula simpler, we're going to use the effective borrowing cost as 3.5%, which represents the 5% borrowing cost less 1.5% dividends.

In order to successfully buy the index and sell the futures for an arbitrage profit now, we must receive more than 1170 for the futures contract.

The transaction cost hurts us on the sell side as well. Because we will receive 1% less from a short sale of the stocks in the index, that results in losing 1%, which is the same as keeping 99% (0.99) of the proceeds.

If we sell the spot index, we will receive 1150 * 0.99 = 1,138.50, which will grow to a value of 1,138.50 * 1.035 ^75/365 = 1146.58 at expiration, which rounds down to 1146.¹

In order to successfully sell the index for an arbitrage profit, we must pay less than 1146 for the futures contract. Prior to transaction costs, arbitrage was possible for any futures value above or below the fair valuelevel of 1158. Now with the introduction of a 1% transaction cost, our fair value calculation is expanded to include a range of values where no arbitrage can occur. Specifically, if the futures trade between 1146 and 1170, arbitrage cannot take place.

If the futures should trade outside of this range, arbitrage will normally bring the futures prices inside this range rather quickly. For example, if the futures are above 1170, arbitrageurs will buy the stocks and sell the futures (cash-and-carry), which tend to bring the futures price below 1170. If the futures fall below 1146, arbitrageurs then buy the futures and sell the stocks, which tend to bring the futures price back above 1146.

These arbitrageurs are usually using computer programs that analyze all opportunities by calculating the price on every stock in the S&P 500, as well as the current futures contract. Then they calculate fair value and enter the corresponding orders to carry out the appropriate arbitrage if one exists. This is known as computer trading, program trading, or simply programs See computer trading" . You may hear that term from time to time in the markets such as in the following excerpt from a 1992 Washington Post article:

Other traders said steep premiums of stock futures to stocks' cash value in late afternoon trading sparked computerized buy programs, after the Dow held a key level at 3240 during a sell-off. "We did not make a new low," that trader said. "Programs took the market up in the last hour."

So there are many forces at work during the trading day on the stock and futures markets. Stocks are free to move independently of the futures but are still joined by the invisible force of arbitrage.

Using the Spread

We just showed that arbitrage would occur if the futures were either above or below 1170 or 1146 respectively. However, that's assuming that the spot index remained at 1150, which would almost never happen. If the futures are above 1170, they will be sold at the same time the underlying asset is being purchased. This means that whether cash-and-carry or reverse-cash-and-carry arbitrage is being used, both the underlying asset and futures will move in price. An invisible force ties the two assets together and one will not sit still while the other one moves.

What's more important for the arbitrageurs is the difference in value between the spot price and futures price, which is called the spreador basis:

Spread = Futures price - Spot price

Using the above example, computers would generate buy programs if the spreadexceeds 20 (1170-1150) and the sell programs if they fall below -4 (1146 -1150). Regardless of where the spot and futures prices are, their differences should not fall outside this invisible fence, otherwise arbitrage will occur. For example, your broker may tell you that "buy programs" are at 20 with "sell programs" at

-4. This means that if the spread ever gets above 20 during the trading day, then the stock market will rise because buy programs will start. Similarly, if the spread falls below -- 4, the stock market will fall because sell programs will start.

While the true cost of carry will change with different levels of the spot market due to low risk-free rates and short terms to expiration for the futures contract, it usually will not have a large impact. For instance, assume the spot market rises from 1150 to 1160 during the day. Now the fair value is 1160 * 1.01 * 1.035 ^75/365 = 1179.91, which 19.91 points above the new cash price of 1160, which is still about the 20 points we stated earlier. No matter where the spot index is trading, arbitrage will usually keep the spreadunder 20, in this example.

So the spread between the futures contract and the underlying index (also called the "cash" or "spot") are allowed to wander within this "invisible fence" around the fair value as shown in the following figure:

We can see that during this hypothetical time period the spreadactually fell below -4 (shown at the lower circled point) at which point the computer programs kicked in with the "sell programs. That's why the lower band is labeled "sell" and is colored red.

Now you may think that looks backwards since the line in the chart rises after that point, which looks like a buy program. However, the line in the chart represents the spread between the futures and the spot. When sell programs start, computers will sell stocks and buy futures (reverse-cash-and-carry), which increases the spread between the futures and the spot.

Likewise, once the point shown in the upper circle was broken, the spread exceeded 20 and was too large. In other words, the futures were now too expensive compared to the underlying stocks. Computers followed with cash-and-carry-arbitrage and bought stocks and sold futures. This puts buying pressure on stocks, which is why the top line is labeled "buy" and colored green.

The cash-and-carry arbitrage reduced the spread between them, and the line (the spread) falls. Just remember that the computerized trading is intended to keep the spread between the futures and the spot price within the fair value range. If the spread gets too wide, computerized trading will automatically reduce that spread. Likewise, if the spread gets too narrow, computerized trading will work to increase that spread.

The above chart is very similar to what you will see if you ever get the chance to look at a computer program that tracks the spread between the cash and futures markets. The top line will be green, the bottom red, and the up-to-the-minute calculations will show whether stocks are about to rise or fall.

Key Points

It is the spread(difference between the futures and spot) that counts and determines whether the "buy" or "sell" programs will start. If the spread gets too wide, buy programswill start (computers will buy stocks and sell futures) and the spread will narrow. If the spreadgets too narrow, sell programswill start (computers will sell stocks and buy futures) and the spread will widen.

Even though the arbitrage should theoretically bring prices inside these boundaries rather quickly, it's possible to stay outside the "buy" or "sell" ranges for extended periods of time, possibly hours at a time. If so, this happens because the futures markets are continually rising or falling at a faster rate than the spot market. If so, arbitrageurs cannot even bring the prices back in line quickly enough.

The concept of fair value is usually of little use for retail investors other than to satisfy their curiosity about the direction of the market at the opening bell. Where many investors get in trouble is when they either buy or sell stocks in the pre-market (such as through Selectnet) based on the futures quote. Before you base your decisions on a futures quote, make sure you know where it is in relation to fair value. It is only then that you will truly know the expectation of the market on the opening bell. Also keep in mind that the effects of the arbitrageurs occur very quickly and the stocks will get back "in line" with the futures prices usually within seconds. This point cannot be emphasized enough. For example, just because you may see that the futures are below fair value prior to the opening bell does not mean we're in for a down day overall. It is possible it may turn out that way, but that obviously cannot be determined prior to the open. Using fair value to determine the direction at the opening bell is just that -- it applies for the first few minutes of the open.

There are occasions where this knowledge could be very profitable though. Indices on futures also have price trading limits, as do most commodities. We learned about this in the last course section when we said that many commodities cannot trade if these boundaries are broken and are said to be either locked limit up or locked limit down. If the futures trade at certain percentages above or below their closing price then trading curbs may be put into place by the exchange. This is often known as a trading halt and is intended for investors to "take a breather" and think about their actions before jumping into the trading frenzy. For example, on the S&P 500contracts at the CME, trading halts will occur during normal trading hours if that contract's price is 5%, 10%, and 20% below the prior settlement price. The lengths of the halts vary depending upon which percentage decline occurs. During after-hours sessions on GLOBEX, those same percentages apply for increases and decreases as well.

On October 19, 1987, "Black Monday the S&P 500 was down more than 20%. Although the S&P 500 futures prices usually sell at a premium (higher price) to the spot index, they were actually below the spot price. Due to the heavy volume on that day, the New York Stock Exchange placed short-term restrictions on the way program trading "See computer trading" could be done the following day. Because of these restrictions, program trading "See computer trading" could not be carried out in the usual fashion and the spreadbetween the S&P 500 futures and the index slipped further. In fact, at its widest point, the futures contracts were trading at an 18% discount to the spot market. Had you known about fair value and program trading "See computer trading" , you would have known to buy the S&P 500 futures contracts. Once the restrictions were removed, arbitrageursand program traders would bid the futures prices to their normal level of spot price plus cost of carry -- and net you a hefty profit along the way.

¹Technically, we would use a 5% cost of carry since we would not get to keep the dividends from a short sale. However, to keep the math easier, we're going to assume equal effective borrowing and lending costs.

Understanding Futures Quotes

Now that you know that basics of futures contracts and how their prices are determined, we can move forward and look at how those prices will be displayed.

We're going to use examples with commodity quotes since, at this time, single-stock futures are still not trading.

In many ways, quotes on futures on not that different from quotes on stocks. You will see bids and offers, last trades, closing prices, highs and lows, and many other terms already familiar to you. The biggest difference is that many commodities will be quoted in cents rather than dollars.

For now, let's take a look at the following table, which shows the way futures quotes may be listed in your local paper or through your online broker:

GOLD (COMEX) 100 troy ounces ; dollars per troy ounce
Contract	Last	Chg.	Open	High	Low	Settle	Lifetime High	Lifetime Low
April	300.9	-1.2	300.7	300.9	300.7	302.1	301.3	300.0
May	302.4	0.0	302.2	302.4	302.1	302.4	303.4	301.8
June	301.2	-1.7	302.6	302.9	300.7	302.9	303.5	300.1
August	301.6	-2.2	302.8	303.8	301.6	303.8	304.2	301.3

The heading in the table identifies the commodity, which in this example is gold. The letters inside the parenthesis designates the exchange at which the commodity is traded. This quote is from the Commodities Exchange (COMEX), which is a division of the New York Mercantile Exchange (NYMEX).

The second line in the heading tells us the contract size, or the multiplier. We see that each contract controls 100 troy ounces and the quotes are in dollars per troy ounce. This is important information since, as we've said before, each commodity has a different multiplier and you need to know the size of the package before you can determine the total value of that package. Remember that single stock futures will be standardized in this respect; they have a contract size of 100 shares per contract and will be quoted in dollars per share.

Below each heading will be the various contract months that are being traded. To reduce space we won't list them all here, but just be aware that the lists are often longer than just the four or so months you may see listed in your newspaper. Additional months will usually be designated by an abbreviated code for their month plus the last two digits of their expiration year. For example, if the chart is for the year 2002 and an August 2003 contract exists, they may display it as AUG 03.

If we look at the quotes under the column labeled "last," we see that the April contract last traded at 300.9 dollars per troy ounce. That last price changed by $1.20 from the previous settlement price, which is shown in the "Chg" column. Because that number is negative, we know the price fell by $1.20. The "open" column shows where the contract opened the day for trading and the "high" and "low" columns show the highest and lowest values that contract made during the trading day. The previous day's settlement price is shown under "settle" and the "lifetime high" and lifetime low" columns tell us the all-time high and low prices for that contract since it first began trading.

Because each contract controls 100 troy ounces, a one-cent move is equal to $1 (.01 * 100 = $1). However, this contract just so happens to have a minimum price variation (tick size) of 10 cents, which simply means that 10 cents is the smallest increment that the price is allowed to move. So while the commodity may theoretically be trading higher or lower at any given time, that price change will not register for this commodity until it is at least a change of 10 cents. Because of this minimum tick size, this gold contract will change in minimum increments of 100 troy ounces * 10 cents = $10. If you've traded stocks, you're already used to minimum price increments, since stocks above $5 must trade in 5-cent increments. This is the same idea that is used for futures. However, once again, it is not a standardized amount for futures -- you will see many different minimum tick sizes as you look at quotes on the various commodities.

From this information, we can also calculate the total contract value, which is 100 troy ounces * 300.9 = $30,900. Keep in mind that you only pay a small portion of this value, the initial margin, if you wish to enter this contract. At the time of this writing, the initial margin for that gold contract is only $1,350. For only a $1,350 deposit, you immediately control $30,900 worth of gold based on these prices.

Other fields you may see printed, although not shown in the table are:

• Bid and Ask prices
• Volume (the number of contracts traded that day)
• Open interest (the total number of long positions or
  the total number of short positions in existence)

The bid and ask prices, as well as open interest, are important to understand if you are actively trading futures or options, so we'll go through both a little more in detail.

More About Bid and Ask Prices

If you have been investing at all, you are undoubtedly familiar with the terms bid and ask. The interpretation of the bid and ask in futures trading is exactly the same as for stocks, bonds, options and any other asset you may have traded. However, if you are new, the bid and ask can be confusing, but it's important to understand what they represent.

The bid price is the highest price someone is willing to pay for the asset, while the asking price (or offer price) is the lowest price someone is willing to sell the asset. The bid price, therefore, represents the buyers and the ask price represents the sellers. If you call your broker for a quote, he may say something like, "It's currently bidding $25.50 and asking $25.75" or, more simply, "It's currently $25.50 to $25.75" where the first number represents the bid and the second represents the ask. Some may shorten the quote even more and just say, "$25.50 to 75," in which case it is assumed that the base number ($25 in this example) is the same and they are just quoting the cents.

If the concept of the bid and ask is confusing, just think about the terms you use when you buy or sell a house. If you wish to buy a house, you put in a bid for it. If you are selling your house, you tell a prospective buyer you are "asking" or "offering" it at a specific price. The same terms apply to financial markets. Just remember that bids represent buyers and asking prices (offer prices) represent sellers. Under normal market operating conditions, the bid price will always be the smaller of the two prices.

Why are only the highest bidder and lowest offer shown in a quote? That's because they are the only prices that are ever of interest to the market. If you are selling your house, you're not concerned who will pay the least for it. If you were, you'd collect lots of $1 bids, $2 bids, and so on. Anybody can bid low. Only the serious bidders will bid high. Likewise, if you are buying a house you're not concerned with who will charge the most for a given quality of home. If a certain quality home is going for $200,000, we're not concerned with the person who is willing to sell it for $300,000, $500,000, or even a million dollars. While high offers will always exist among any group of sellers, they are not of interest to the market. We want to know the prices of the highest bidder and lowest offer. Notice how the highest bid and the lowest asking price create the smallest difference between the two prices, which is called the bid-ask spread. Using the earlier quote of $25.50 to $25.75, the bid-ask spread is 25 cents since that is the difference between them. The more competitive the market, the narrower the spread will become. As you trade futures contracts, you will notice that most are highly liquid (there are lots of willing buyers and sellers), which means lower prices if you are buying and higher prices if you are selling.

Key Points

• The bid represents the buyer(s) willing to pay the highest amount
• The ask represents the seller(s) willing to sell for the least amount

If you look at the April contract in above table, you will see the "last" trade is $300.90. This does not necessarily mean that is the current price, as the last trade could have been several minutes, days, or weeks ago. That is simply the price when it last traded. If you are about to place a trade on a futures contract, it is therefore important to look at the bid or ask depending on whether you are buying or selling. Although they are not shown, let's assume the bid on this contract is $300.75 and the ask is $300.85.

If you wish to buy a contract, you should look at the asking price, as that is the lowest price offered by the sellers. If you are selling a contract, you should look at the bid, as that is the price submitted by the highest bidder. This does not mean that you must buy at the ask or sell at the bid any more than you should buy a house for the asking price or sell it to your first bidder. It does mean, however, that those prices are more relevant to your trade at that time and are better representations of value as opposed to the last price, high, low, or other prices you may see quoted.

The bid and ask prices are often a source of confusion for new traders since they are used to buying at the asking price and selling for the bid price. Because of this, they incorrectly feel that the asking price represents buyers and the bid represents sellers. Upon closer examination, you should see that this is not possible. In order to trade a futures contract (or any product, for that matter) you need a buyer matched with a seller. The reason you can buy at the asking price is because that person is a seller and the trade can be matched and executed. Likewise, you can sell at the bid price since that bid price represents a buyer, which again matches the opposing sides of the trade and allows an execution.

The bid and ask prices are rarely shown in newspapers or other printed publications to conserve space. However, if you are trading online or getting a quote from your broker, you can bet that you will see or hear the terms bid and ask. You need to be sure you understand what each one represents.

If you still don't feel up to speed with bids and offers, we have a fun exercise at the end of this course you can try

Thought Questions: Why can you buy at the asking price and sell at the bid price?

More About Open Interest

Open interest is a term unique to futures and options. It is simply defined as the total number of long or the total number of short positions. It is not the total number of long and short positions. That's because for every long position there must be a short position. Counting the total number of long and short positions would double-count them.

If you are familiar with options trading, you know that you must specify whether a trade is either "opening" or "closing." With futures contracts you do not need to specify whether your trade is opening or closing, because it will be determined and reported by your brokerage firm. If you are entering into a contract, it will be reported as opening. If you are closing it by entering an offsetting position, it will be reported as closing. The clearinghouse will pair all "open" positions together, and it is this number that is reported in "open interest." The fact that you do not need to specify "open" or "close" with each transaction really adds to the speed at which futures contracts can be used to change your directional bias. If you are long 10 contracts and now want to be short 10 contracts, you simply enter an order to sell 20 contracts. With options and stocks, you'd need to enter two separate orders. The first would be "sell to close" 10 contracts and the second order would be "sell to open" 10 contracts.

This should give you just a little insight into the power that futures will have for those who actively invest or trade. We've covered a lot of material on futures, so now we're going to run through an example in the next course from the very beginning. We'll place a trade and then track it through the various daily changes so that we're sure you understand marking-to-market and maintenance margin calls.