A FUTURES CONTRACT is a legal contract in the US under the Commodities Exchange Act of 1850. The futures contract allow market participants to take or make delivery of a commodity on some date in the future at a price agreed to today. In many cases businesses plan their raw supply needs and/or their production ahead of time. Often businesses can make contracts between each other, but the benefits offered by the futures markets centralized trading standard contract terms and the risk mitigation of the Clearinghouse made futures well in demand as our country grew.
By having a central marketplace (electronic bulletin board) where buyer and seller can meet and transact also begets liquidity. Then, the investment Managers will tend to get interested in a products along with the speculator & arbitrageur. Futures are OBLIGATIONS. Both buyer and seller are obligated to perform to the terms of their contract. Futures contracts are standardized with respect to all terms and conditions:
|Symbol:||CL_7 <comdty> P [go] (for the price of the __month* (7=2017) on Bloomberg|
|Quantity:||1,000 barrels of WTI Crude Oil|
|Quality:||WTI describes the area in West Texas where the crude oil a very light & very sweet|
|Delivery Point:||Cushing, Oklahoma|
|Contract Value||WTI trading @ $50 per barrel * 1,000 barrels = $50,000 CONTRACT VALUE WTI trading @ $51 per barrel * 1,000 barrels = $51,000 CONTRACT VALUE CHANGE IN CONTRACT VALUE FROM $50 TO $51 = $1,000|
|Execution||Futures contracts trade on an “exchange”, electronic or telephone. Futures Options still trade on exchange floors due to the complexity of order types.|
|Clearing||All Futures contracts are cleared at a Clearinghouse In the US futures exchanges had their own clearinghouses. Each futures contract traded and cleared on the same exchange. As trading moved to electronic market and a wider range of types of crude oil’s trading, Clearinghouses for each product are not as connected to the execution location.|
Clearinghouses are Organization of Mutuality that is the risk belongs to the owners of the Clearinghouse. If a client defaults on a trade, i.e., cannot post more margin, the introducing broker has a choice: they can cover the loss themselves, or if they’re unable to afford the loss they can bring it to the clearinghouse committee. Each member will share in the loss on a pro-rata basis.
As mentioned above, futures contracts clear at a clearinghouse. Long & Short both post INTIAL MARGIN or a good faith deposit. Thereafter the positions are marked to the market: the counterparty making money receives more margin. The counterparty losing money pays more margin. This additional margin is called variation margin. Initial Margin acts as a cushion and variation margin allows for the settlement of P&L daily. This system allows clearinghouses to mitigate the counterparty risk.
Initial Margin = $3,190 Both long and short post $3,190 for each contract they want to keep open overnight. While they may choose to get out of the trade when Asia or Europe are trading, they will have to post $3,190 to their US-based clearinghouse. Variation or Maintenance Margin = $2,900 Maintenance margin is a trigger. The client will be called for additional margin if the account falls below the maintenance level. During the credit crisis, Maintenance Margin wasn’t used and some firms have chosen to maintain that policy. Herefore a client must always have the initial margin for the contract set aside in a segregated account as a good-faith or performance bond. Check with your broker prior to trading so you know their specific guidelines.
Using the Futures Margin Example above, FOCUS ON THE TWO RIGHT MOST COLUMNS TO SEE HOW Volume & Open Interest Work. Volume and open interest are specific to contract markets. But by measuring the volume relative to the open interest a trader can glean a lot of clues as to:
Volume: Contracts traded during the trading day. Volume is additive throughout the day. Open Interest: Open Contracts held in position. Open Interest measures the net OPEN contracts. If a market has very high daily volume, but open interest remains stable, one could surmise that market has more speculators involved in that market. By contrast, a futures market with high volume sporadically but where open interest grows on those days and progressively over the life of the contract, one could surmise that market has more hedgers involved than speculators.
Any market we look at, we need to understand who uses the product and why. It’s worth saying at the outset that derivatives contracts, in general, have four participants. Viewing the diagram below, you will see two participants on top labeled HEDGERS. These are your participants needing futures contracts to hedge their actual business risk. A scan to the bottom of the diagram will show you the speculator and arbitrageur. These participants are our leveraged players. They use the derivatives market for the leverage it offers and provides liquidity to the hedgers. Going forward you may want to look at the type of participants in a specific product you’re viewing to see if all four participants are in the market. Without all four participants actively trading the product, the contract is unlikely to provide significant liquidity and transparency.
Unleveraged players, a.k.a. “commercials” are corporations with market risk of crude or corn or any future contract. We differentiate between their risk and other types of market participants because these corporations are hedging their business risk to the end product they use or produce:
An end user of grains and sugar such as Kellogg & Co. doesn’t buy & store their corn, wheat & sugar all at once. Rather they make their purchases periodically over the course of the year. This way they don’t bear the risk of spoilage or the cost of storing the raw products. If the price of their commodity goes up, they will have to pay a higher price to make their product. Companies can choose to take this risk or they can choose to hedge it. Companies can hedge their price risk directly with the producers of the products or they can choose to hedge using futures. Futures, cleared through a central clearinghouse provides anonymity, price transparency and the mitigation of counterparty risk. The trade-off of using futures & central clearing is the company doesn’t get the exact product they use, delivered to the exact location they need. They take “basis risk”, which we’ll discuss in a moment.
End producers create a product or make a raw product usable. For example, refiners buy crude oil and refine it into gasoline & heating oil. Kellogg’s purchases grains from farm consortiums. The farmers are the End Producers of corn. End producers are at risk to the price going down. To hedge their market risk they could contract directly with the end user when it’s ready for sale, or they can use futures to hedge their price risk. The end producer, such as the farm consortium choosing to sell futures makes the same trade-off as the End User. By using a central clearinghouse, their advantages include anonymity, price transparency and the mitigation of counterparty risk. The trade-off is that the futures contract may not call for delivery of the exact product they create or delivered to the same location where they are located. The producer takes “basis risk”, which we’ll discuss in a moment.
“Leveraged players” in any derivative market describe those people who will borrow money to express their trade. Futures contracts are leveraged due to the low margin cost relative to the contract value. Recall our crude oil contract, with crude @ $50 per barrel = $50,000. Yet our initial margin is only $3190.
Margin levels can and will change as prices rise or the commodity becomes more volatile. Generally speaking, clearinghouses want initial margin to cover 3 times the average daily move. Or the average volatility of the most recent 3 days, whichever is higher.
Speculators love leverage and with good reason. For a relatively small investment, they can reap great returns. Of course, the ever optimist living within us rarely chooses to look at the double edge sword. In a futures contract, you can LOSE MORE THAN YOU INVEST.
Arbitrageurs take advantage of price anomalies between similar products when the price between the products reaches a level outside of normal range. The arbitrageur enters a trade, looking to reverse the trade when the prices between the products normalize. In effect, a market maker is also an arbitrageur. A market maker is a liquidity provider to the market. Their mandate is to provide a bid and an offer, prices at which market participants can trade. There is a misconception that arbitrage is exploiting an obvious mispricing in the market. There Ain’t No Such Thing As A Free Lunch (TANSTAAFL). Typically arbitrageurs are simultaneously buying and selling similar contracts.
For example, an arbitrageur buying US crude oil and selling UK Brent crude oil will profit if US crude rises more or falls less than Brent Crude.
This arbitrageur is still assuming risk on their trade and will lose money if Brent rises more or falls less than US Crude.
Arbitrageurs look for anomalies in relationships between two. assets.
In the typical futures market, it’s the End User & End Producer that create the need for the futures product. Consider crude oil:
In the last section we covered market risk: we learned that end users of a commodity are at risk to the price of the commodity going up if they choose not to hedge. The end producer of a commodity has price risk of the commodity going down.
Because they don’t need to purchase or sell the crude oil today, but rather on specific dates in the future. They can hedge directly with the company who buys (sells) the underlying commodity. But the futures contract offers several advantages. Since all futures contracts are cleared at a central clearinghouse the advantages are:
If they hedge directly with the buyer (seller) of their commodity, they will receive (deliver) the exact commodity at the exact location they need. But they lose the advantages of the clearinghouse and the price discovery/liquidity of active futures contracts.
The contract specifications for crude oil called for delivery of a certain quality of crude oil. Specifically, the crude must have a Sulphur content of .42% of less; and the API gravity between 37-42 degrees. The crude oil must be delivered into Cushing Oklahoma. Basis risk is the differences between the WTI crude oil (“THE DELIVERABLE GRADE”) and the EXACT crude oil our client is hedging. The exact crude oil the client is hedging can be quite different. The hedger will adjust the number of contracts to account for this risk. But they still use the futures contract as their choice for hedging because of the reasons mentioned above:
Volume & open interest statistics show that many hedgers prefer to use futures. For example in crude oil only ~ 3% of contracts are still open & go through the delivery process. Further, as the open interest of the maturing futures contract goes down, the open interest of the next available futures contract rises.
This shows the hedgers are “rolling” their positions into the next delivery month to maintain their price hedge.
To price a futures contract, we start by calculating the Future Value of the spot price of the commodity and adjust from there. The Deliverable grade of crude oil futures “WTI” has Sulfur: 0.42% or less by weight, and Gravity: Not less than 37 degrees nor more than 42 degrees (measured by API)
|UNDERLYING||WTI Crude Oil (deliverable grade )|
|MATURITY||one month Crude Oil Futures Contract|
|SPOT PRICE OF CL||$50 per barrel|
|INTEREST RATE||30 day LIBOR is 5%|
Other costs or income associated with the underlying asset adjust the Future Value number above.
Transportation by Sea requires a bit of background, so this example will keep us on dry land. Due to larger tankers, investment in canals and other issues, historical numbers skew the cost of transporting oil. To get our futures Price and presume our oil will travel by pipeline from Calgary to Cushing, Oklahoma and stored for the remaining days. The total cost of storage and transportation for 30- days will be $3.78 per barrel. To make our calculation easier, convert it to an annual percentage figure: $3.78/$50.00 = 7.56%.
Hedging using futures is done using the SIMPLE HEDGE RATIO or the OPTIMAL HEDGE RATIO. The simple hedge ratio is more focused on the timing of the hedge. The Optimal Hedge Ratio also wants to adjust for the difference in volatility & correlation between the futures & the exact grade/location of crude oil the hedger buys (sells).
Example: Let’s assume a refiner is looking to hedge his crude oil purchases beginning in April 2017. Recall the refiner buys crude oil to convert it into gasoline and heating oil. Our refiner needs to purchase a total of 150 million barrels of crude oil over four months from May to August 2017. REFINER’S SIMPLE HEDGE = 150,000,000/1000 = 37,500 contracts each month from May, June July & August. REFINER’S SIMPLE HEDGE: BUY 37,500 May, June, July & August Crude Oil Futures.
Let’s continue with the same example used to calculate the simple hedge ratio and introduce the concept of optimal hedge ratio. Our refiner still needs to purchase 150 million barrels over four months beginning in May 2017. But in reality, the crude he will purchase is Gulf Coast crude oil. His refinery is along the gulf coast and it’s easier for him to take delivery at that port. To hedge using the futures contracts we need to adjust for two major variables.
We need to adjust for both of these variables because even though we expect all oils to move in the same direction, if the two oils are less than +.985 correlated, the futures are not likely to be the most efficient hedge. Volatility measures something very different. Volatility measures the magnitude of price returns. If we buy too many contracts we will be over-hedged. If the price of WTI goes down more than we expected we will lose money using futures as our hedge. Adjusting for both of these variables the futures will mimic the performance of Calgary Crude.
|Relative Volatility =||89.7%|
|Positive Correlation =||+.99|
If you’d like to learn more about Commodities forward curves, physical versus futures arbitrage and others topics, they will be covered in Our Learning Center
An interest Rate Swap is a contract whereby each counterparty gets to transform the type of risk management they run. Specifically, it’s a contract where the counterparties exchange a fixed cash flow, which will remain unchanged for the duration of the swap for a floating rate cash flow which will change at pre-defined times and using a pre-defined rate at periodic dates over the duration of the swap.
There are three ways to illustrate an interest rate swap. The first is called a box & arrow diagram.
The timeline Diagram. The timeline diagram show the payment of cash flows over the passage of time:
The third way is called the cash flow diagram. We will discuss this diagram in greater detail in the SWAPS PRICING section.
To An interest rate swap is a contract where one type of interest rate is applied to one leg of the swap while the other leg’s cash flow is calculated using a different type of interest rate.
For example: Fixed Pay for 5 yrs & Received 3 Month LIBOR The fixed leg will be paid for 5 years at the same rate The floating leg (LIBOR) will change every 3 months, for 5 years. If interest rates go down, this swap will lose money as the floating rate heir receiving is going down.
When we speak about swaps, we speak in terms of the fixed leg. “I’ll pay fixed on $100 million for 5 years” It’s already implied I’m receiving the floating leg. PAY FIXED = make money if rates go higher RECEIVE FIXED = makes money if rates go lower.
If you’re long a bond, you receive a coupon and make money if rates go lower. If you’re receiving fixed on a swap you make money if rates go lower. If you’re short a bond you pay the coupon and make money if rates go higher. If you’re paying fixed on a swap, you make money as rates go higher.
To convert the language from futures to Rates, recall with crude oil futures we spoke of End Users & End Producers as participants who would use Crude Oil Futures as Hedges against price risk.
When speaking about other debt instrument relative to interest rate swaps, we speak in terms of the spread between the two products. Below is a corporation bond trading at 4.50%. Today, since interest rate swaps are so liquid, we would say the bond is trade +50 bps over swap rates. The 150 bps is partially the credit rating spread. But relative liquidity between the bond and the swap, the relative duration etc would also be taken into account. Another spread tracked closely is the swap spread. In the illustration below, the swap spread is 100 bps, the swap rate is 4.00% (US Treasuries + Swap Rate).
With respect to interest rate hedgers, it may be worthwhile to discuss how corporations raise capital. Corporations can either borrow money from a bank, or if their credit rating is high enough and they are well known in the market can issue bonds in the public bond market. The determination will be which market they receive a lower rate.
In the Interest Rate Swap Market the concept of Comparative Market Advantage is useful to understanding why each market participant uses swaps. As we go through the hedger examples, we’ll speak to this comparative advantage with respect to each player.
A AA-rated Corporation typically can borrow in the public bond market (fixed rate) at a lower rate than they would pay to a bank on a bank loan. They will issue a bond and pay a fixed coupon to bondholders. If the Higher Rated Corporation wants to pay fixed and it fits their asset-liability management, their fixed-floating mix and cash flow then they will remain in a fixed rate liability. If not, they will enter into a swap, swapping from a fixed rate liability to a floating rate liability. Let’s take a look.
|5 yr BOND ISSUE||2.25%|
|5 YR BANK LOAN||LIBOR + 100 BPS|
|5 YR SWAP RATE||2.50%|
This AA corporate could have remained a fixed rate borrower for 5 yrs. There are several reasons why corporations choose to swap.
A BBB Corporation borrows from a bank (floating rate loan) at a lower rate than the public would lend them money, they will take out a bank loan and pay LIBOR plus a spread. If a Lower Rated Corporation wants to pay LIBOR and the bank loan fits their asset-liability, fixed-floating and cash flow mix, they will remain in a bank loan. If a Lower Rated Corporation would prefer to pay a fixed rate, they will enter into an interest rate swap to PAY FIXED AND RECEIVE LIBOR.
|5 yr BOND ISSUE||4.00%|
|5 YR BANK LOAN||LIBOR + 100 BPS|
|5 YR SWAP RATE||2.50%|
It’s worth noting that the interest rate swap provides flexibility for corporations to separate their source of funds from the way they manage their interest rate risk. As we saw with our AA borrower, they borrowed in the market which provided them the lowest rate. But due to the speed of their asset conversion cycle, as a subscription company, they can better manage their interest rate risk by borrowing LIBOR.
Asset managers can also be seen as Lenders of money by buying bonds from corporations. The type of asset buyer we’re speaking about in the upper right hand portion of our participants circle is an unleveraged buyers of assets. Asset managers use Swaps to create an asset swap. In an asset swap, the asset buys a fixed rate note or bond and enters into a swap to PAY FIXED AND RECEIVE LIBOR. The end result is the asset manager receives LIBOR plus a spread. Effectively they own a synthetic floating rate note. The asset manager can purchase the bond and enter into the swap on their own, as in the diagram below.
Asset Managers also use interest rate swaps as a hedge. Asset managers are paid by client to outperform some pre-agreed bond index. That index has an average maturity or duration of the bonds included in the index. An asset manager can outperform their index in several ways. They can buy more long dated bonds if they think the market will go up or purchase more bonds of the corporations they like. Conversely, an Asset Manager may choose not to buy some of the bonds in the index because they don’t like the credit risk. However once a portfolio of bonds has been put in place, if the manager thinks the market will trade lower, managers don’t want to pay the slippage (bid-ask spread) of selling the bonds and rebuy them later. So they take an alternate route to hedging their rate risk. Asset managers will overlay an interest rate swap to shorten the duration of their portfolio. For those unfamiliar with DV01, it’s the amount the bond will change for a 1 basis point change in rates.
Down the second column of the matrix, you’ll note an increasing column of numbers. Taking a look at the 5 yr row, the present value for each number of years at the rate in force when the matrix was built shows a 5 yr bond portfolio has a DV01 = $481.96. To illustrate the most extreme hedge, we’ll use the following illustration:
By putting on the hedge 1:1, we’ve turned the portfolio into one similar to our asset swap. But for an asset manager whose index has a 5 yr average maturity, we need to look at the difference in risk to see the hedge. Earlier we saw the average risk was $481.96. With the hedge, the portfolio’s DV01 is now only$25!! if rates go up as expected, this portfolio manager will only lose $25 per basis point (for each $ 1 million invested). The unhedged portfolio manager will lose $481.96 per basis point (for each $1 million invested).
This is NOT A LONG TERM HEDGE. This hedge will be in place for two weeks but not much longer. Once the market goes down, the hedge will be taken off. This type of brute force hedging, without refinement for the credit spread risk, etc. is not elegant, but it works. Particularly in fast markets.
Leveraged funds use swaps as synthetic financed bond positions. To a hedge fund, they view swaps as synthetic bonds which they’ve repo’d to purchase and have the credit quality of swap dealers.
To understand this in greater detail let’s look at how a long bond position would look like the following diagram: A client calls and buys a bond, Calls the repo desk to lend the bond and borrow money, Uses the money to pay for the bond. (N.B.: leverage)
Hedge funds use swaps to create synthetic bond positions. The following diagrams show the logic behind this:
Looking just at the coupon flows, the position is receiving the fixed coupon on the bond and paying the repo rate on the financing of the bond position.
But looking at just the cash flows, perhaps we don’t need to use bonds or “real assets” unless they better fit our goal. When ee view this diagram
It doesn’t have anything different than this diagram
On the short side, where the trader is also taking on delivery risk, the bond gets tight in repo, the trade takes on a different angle:
Again focusing on the cash flows:
The above doesn’t look much different with respect to the cash flows below.
The differences between the bond position and the swap position are:
Before we delve into swaps pricing, this section reviews the Time Value of Money, introduces compounding & continuous compounding. Then we’ll have all of the math necessary for this section and your further studies at MH.
1. FUTURE VALUE calculates the value of a cash flow in the future for an investment made today.
Image here: future value
2. PRESENT VALUE calculates the value of a cash flow today, presumed to be paid in the future.
Image here: present value
To calculate the compounded future value, we use the following calculation where R = the annual rate, C = compounding periods per year & t = time to maturity.
Image here: future value calculation
Image here: diagram of compounded cash flows
We use continuous compounding to price derivative products so we can convert all rates & compounding periods to compare them apples to apples. The last column shows the future value continuously compounded. To calculate a continuously compounded cash flow, we use the Exponent e notated as EXP where r = rate per year & t = time to maturity.
Image here: EQUATION FVc
The spreadsheet below shows the compounded future value of an initial investment of $100. The first column lists the maturity of the cash flow. The second row of the table lists the number of cash flows per year or the numbers of compounding periods per year.
Image here: Future value spreadsheet
Compounded Present Value presumes a cash flow will be paid sometime in the future. It presumes the rate will be paid and reinvested more than once during the calculation period. To calculate the compounded PV, we use the following calculation:
EQUATION PV COMP and TIMELINE PV COMP
We use continuous compounding to price derivative products so we can convert all rates & compounding periods to compare them apples to apples. The last column shows the present value continuously compounded. To calculate a continuously compounded cash flow, we use the Exponent e as follows:
Image here: EQUATION PVcc
The spreadsheet below shows the compounded present value of an initial investment of $100. The first column lists the maturity of the cash flow. The second row of the table lists the numbers of compounding periods per year.
Image here: value of compounded rates spreadsheet
“First Commandment” of Derivatives pricing is using the most liquid instrument whose terms and conditions mostly closely resemble what you’re trying to price. The logic is:
This diagram shows the dates the floating leg resets as well as the dates the net cash flow (fixed vs. floating) is paid.
Forward Rate Agreements are agreements to pay a fixed rate of interest at some time in the future, in return to receiving whatever that maturity rate is trading at maturity. FRA’s are really single period interest rate swaps. Eurodollar Futures are FRA’s with a fixed date of maturity since it trades as a futures contract. In a payer FRA the payer agrees to pay a fixed rate at some date in the future, in exchange for receiving whatever rate is in force for that term to maturity. In a payer FRA you make money as rates go higher (prices fall). We’ll see shortly that an FRA is a single period interest rate swap.
In a Receiver FRA the payer agrees to receive a fixed rate and pay the rate in force for that term at maturity. You make money on a receiver FRA as rates go DOWN (price goes up)
|Using the following 12 ML%|
We have our LIBOR rates so we can calculate the Forward Rate Agreements:
The first FRA is the 12 x 24
Then we need to price the 24 x 36 FRA
Now we have all of our rates & forward rates to price the swap. Here’s the resulting timeline showing the Rate Agreement (rate reset today) an the 2 forward rates 12 x 24 & 24 x 36.
Now we’ll put the forward rates into a cash flow diagram and continue on with pricing each cash flow and then solving for the fixed rate on the swap. We use the FRA’s to get the correct forward rates for the swap, but for the swap to be priced fairly, we need all of the cash flow to come back to a NET PRESENT VALUE OF ZERO.
Here’s a snapshot of the whole swap. Now we’ll go through the columns piece by piece.
The first several columns are for Forward Rate Calculations. The forward rates can be seen in the right hand column with their title to the left. i.e. , 7.755% = 1 yr. LIBOR, 1 year forward. The next four columns are used to calculate the present value of the floating leg of the swap.
The future Value is the notional &1,000,000 * the forward rates. The present value brings these cash flows back using the LIBOR rate for 1, 2 & 3 years. Not the sub-diagram Discount Factors. A Discount factor is the zero coupon rate or present value of one unit of currency. The discount rate used is the same as above 1, 2 & 3 year LIBOR deposit rates.
The next two columns calculate the Present Value of the fixed leg of the swap, followed by the last column showing the NPV (Floating PV – Fixed PV).
Notice, the YELLOW highlight around the cell atop the FIXED FV Column. Also note the column NET PV. To solve for a Par swap, use Goal Seek (Data > what if analysis) the second choice down should be Goal Seek, if you don’t see this choice you will need to install your analysis toolkit. Using the goal seek functions as shown above, will give you the fixed rate at which all of the cash flow solve for an NPV of zero.
Here is the spreadsheet in one piece. Note the forward rates are on the row above the cash flow. This tells us the floating rate is set in advance and paid in arrears.
Both cleared and un-cleared derivatives are repriced the same way, using the OIS curve & the LIBOR Curve.
During the Great Credit Crisis and the reporting dealers forced the LIBOR reset rate lower, Since the LIBOR reset rate is used to reset all swaps & loans resetting that day, the rate impacts a large dollar amount. Market Participants decided, given the volatility of LIBOR a more stable rate should be used. The OIS Swap (LIBOR minus Effective Fed Fund) was chosen as the rate for COLLATERAL POSTING. Please note the difference: LIBOR curve is used to calculate Profit & Loss, but the OIS Spread to calculate the collateral one counterparty needs to post.
The OIS Spread or OIS Swaps is the spread between LIBOR and the effective fed funds rate (EFF).
First, recall the Fed Funds are loans made between banking institutions CAN ONLY LEND THEIR FREE RESERVES IN THE FED FUNDS MARKET, and the market is short dated, it’s only liquid out 270 days.
We use the OIs Swaps Market rates. Why? Because they’re so liquid. However there are other sources in the links section is you prefer to do your own work on the curve.
The OIS swap is a floating for floating swap, LIBOR versus Effective Fed Funds. As with most floating – floating swaps, the maturity of the swap is long (i.e. , 5 yr swap) but the two floating rates are observed very frequently, with a net cash flow periodically.