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The Futures Pricing

Forward Market

• Forwards market
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• How to short
• Nifty futures
• Nifty futures
• Futures pricing
• Hedging with futures
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10.1 – The Pricing Formula

If you were to enroll in a traditional futures trading course, you would presumably learn about the futures pricing formula pretty early on in the program. However, we purposefully chose to discuss it now, at a much later time. The explanation is straightforward: you don’t really need to understand how futures are  if you’re trading them based on technical analysis, which I presume the vast majority of you are. However, having a solid understanding would be beneficial. However, you must be aware of this if you intend to trade futures using quantitative strategies like Calendar Spreads or Index Arbitrage. In reality, we will cover some of these methods in a module on “Trading Strategies,” thus the discussion in this chapter will serve as a basis for the ensuing modules.

If you recall, we occasionally covered the “Futures Pricing Formula” in some of the earlier chapters as the main cause of the discrepancy between the spot price and the futures price. I suppose it’s time to pull the curtain and disclose the “Future Pricing Formula” at this point.

We are aware that the respective underlying determines the value of the futures instrument. We are also aware of the future instrument’s synchronic movement with its underlying. The futures price would decrease if the actual price did, and vice versa.

However, the fundamental price and the futures price are not truly the same and different. As I write this, the Nifty Spot is trading at 8,845.5, while the comparable current month contract is trading at 8,854.7. For context, please see the snapshot below. “Basis or spread” refers to the price differential between the futures price and the actual price. The spread is 9.2 points (8854.7 – 8845.5) in the case of the Nifty sample below.

The “Spot – Future Parity” is responsible for the price discrepancy. The discrepancy between the spot and futures prices that results from factors like interest rates, dividends, a time before expiration, etc. is  as the spot future parity. In a very broad sense, it is just a formula that compares the underlying price to the matching futures price. The formula for futures pricing is another name for this.

The futures pricing formula reads as follows:

Futures Price is equal to Spot Price *(1+ RF)-D.

Where,

The risk-free rate is rf.

d: Dividend

It should be  that “rf” stands for the risk-free rate that you can earn for the entire year (365 days); given that the expiration is at 1, 2, and 3 months, you might want to scale it proportionately for time periods other than the precise 365 days.

Consequently, the following formula is more general:

Futures Price is equal to Spot Price plus [1 + rf*(x/365)].

– d

Where,

x is the number of remaining days.

The 91-day Treasury note issued by the RBI serves as a stand-in for the short-term risk-free rate.

The current rate is 8.3528 percent, as seen in the graphic above. In light of this, let’s work on a pricing example. What price should the current month futures contract for Infosys be set at if Infosys spot is now trading at 2,280.5 with 7 days left till expiration?

Futures Price: [1+8.3528 percent (7/365)] = 2280.5 – 0

Please take note that Infosys is not to pay a dividend over the following seven days, therefore I’ve assumed there would be none. The answer to the preceding equation is 2283, which is the predicted price. This is  to as the future’s “Fair value.” However, as you can see from the figure below, the actual futures price is 2284. The “Market Price” refers to the actual price at which the futures contract trades.

The difference between the fair value and market price mainly occurs due to market costs such as transaction charges, taxes, margins, etc. However by and large the fair value reflects where the futures should be trading at a given risk-free rate and the number of days to expiry. Let us take this further, and figure out the futures price for mid-month and far-month contracts.

Mid-month calculation

Number of days to expiry = 34 (as the contract expires on 26th March 2015)

Futures Price = 2280.5 * [1+8.3528 %( 34/365)] – 0

= 2299

Far month calculation

Number of days to expiry = 80 (as the contract expires on 30th April 2015)

Futures Price = 2280.5 * [1+8.3528 %( 80/365)] – 0

= 2322

From the NSE website let us take a look at the actual market prices –

It is obvious that the determined fair value and the market price are different. This is what I would put down to the relevant expenses. Additionally, the market might be accounting for some dividends paid at the conclusion of the fiscal year. The important thing to remember is that the gap between fair value and market value expands as the number of days till expiration increases.

In reality, this introduces us to the discount and the premium, two crucial terms utilized in the market.

The futures market is  to be at a “premium” if the futures are trading higher than the spot, which, mathematically speaking, is the natural order of events.

Although the term “Premium” is  in the equity derivatives markets, the term “Contango” is preferred in the commodity derivatives markets. The fact that the Futures are trading higher than the Spot, however, is what both contango and premium allude to.

Here is a graphic of the January 2015 series’ Nifty spot and associated futures. As you can see, throughout the entire run, the Nifty futures traded above the spot price.

I wish to focus your attention, in particular, on the following few points:

  1. The difference between the spot and futures is relatively large at the beginning of the series (shown by a black arrow). This is due to the large x/365 component in the futures price methodology and the high number of days till expiration.
  2. Throughout the series, the futures maintained a premium over the spot price.
  3. The futures and the spot have come together at the end of the series (shown by a blue arrow). In actuality, this constantly occurs. On the day of expiration, the futures and spot prices will always converge, regardless of whether the future is at a premium or a discount.
  4. If you have a futures position and don’t close it out by expiration, the exchange will do it for you and settle it at the spot price since both futures and spot prices converge on the day of expiration.

Futures trading is not necessarily more profitable than spot trading. There may be times when the futures trade at a lower price than the corresponding spot, primarily due to short-term imbalances in supply and demand. In this scenario, it is  that the futures are trading at a discount to the spot. A similar circumstance is as “backwardation” in the realm of commodities.

10.2 – Practical Application

Let’s put the formula for futures pricing to work before we wrap up this chapter. As I had previously indicated, the futures pricing formula is highly helpful if you want to trade using quantitative trading strategies. Please be aware that the conversation that follows is just a sneak peek into the realm of trading methods. When we start the module on “Trading Strategies,” we will go into deeper detail about all of these topics and more. Think about this scenario:

650 Wipro Spot

8.35 percent Rf

x = 30

d = 0

As a result, the futures ought to be trading at –

Futures Price is equal to 653*(1+8.35% (30/365)) – 0

= 658

In order to account for market fees, the futures should trade at or near 658. What if the price of the futures contract is dramatically different instead? How about 700? There is definitely a trade going on. In an ideal world, there should only be a 5-point gap between spot and futures, but due to market imbalances, that disparity has increased to 47 points. We can use trade to deploy and capture this spread.

The futures market price is  as being expensive in relation to its fair value since the futures contract is trading over its fair value. Alternately, we may state that the spot is trading less expensively than the futures.

The general rule for any kind of “spread trade” is to purchase the less expensive asset and sell the more costly one. As a result, using this as our guide, we can sell Wipro Futures on the one hand while concurrently buying Wipro on the spot market. Let’s enter the numbers and see what happens.

Purchase Wipro on-site for $653

Offer to sell Wipro futures at 700

Now we are aware that the spot and futures prices converge into a single price on the expiry day (refer to the Nifty graph posted above). Let’s assume a few arbitrary values where the spot and futures converge: 675, 645, 715

As you can see, after you execute the deal at the anticipated price, the spread is basically locked in. Profits are thus assured, regardless of where the market moves by expiry! It goes without saying that it makes sense to close out the bets right before the futures contract expiration. You would have to sell Wipro on the spot market and then purchase it back on the futures market to do this.

The term “Cash & Carry Arbitrage” also refers to this type of trade between futures and spots in which the goal is to extract and profit from the spread.

Spreadsheet Calendars 10.3

The calendar spread is a straightforward development of cash and carries arbitrage. The goal of a calendar spread is to extract and benefit from the spread that results from two futures contracts with the same underlying asset but different expiration dates. Continue using the Wipro example to better grasp this –

Wipro Spot currently trades at = 653.

30 days until expiration, current month futures fair value = 658

Futures for the current month are actually worth 700.

The fair value for mid-month futures (65 days to expiration) is 663

Mid-month futures actually have a market value of 665.

The current month’s futures contract is trading much over its anticipated theoretical fair value, as seen by the example above. The mid-month contract, however, is trading rather close to its real fair value estimate.

Based on these facts, I’ll assume that the basis for the current month’s contract will eventually contract and that the mid-month contract will continue to trade fairly.

The current month contract now seems to be more expensive than the mid-month contract. So, instead of buying the pricey contract, we sell the expensive one. I would therefore need to buy the mid-month futures contract at 665 and sell the current-month contract at 700 in order to execute the deal.

What do you believe the spread is in this case? The spread, or 700 – 665 points, is the difference between the two futures contracts.

The trade is set up as follows to catch the spread:

Sell the futures for the current month at 700

Keep in mind that because this is a hedged trade, the margins are significantly decreased because you are buying and selling the same underlying futures with different expires.

One must now wait for the current month’s futures to expire after starting the trade. We are confident that the spot price and the current month’s futures will converge at expiration. Of course, from a more pragmatic standpoint, it makes sense to close off the deal right before expiration.

Naturally, keep in mind that the crucial presumption we have made in this case is that the mid-month contract would remain relatively close to its fair value. According to my trading expertise, this occurs frequently.

Most importantly, keep in mind that this chapter’s study of spreads is really a brief introduction to the realm of trading methods. These methods will be  in a separate session that will provide you with a detailed examination of how to use them in a professional setting.

CONCLUSION

  1. The formula for calculating futures prices is Futures Price = Spot price *(1+Rf (x/365)) – d.
  2. The basis, also referred to as the spread, is the distinction between futures and spots.
  3. The term “Theoretical fair value” refers to the futures price as determined by the pricing algorithm.
  4. The term “market value” refers to the price at which futures trade on the market.
  5. Theoretically, the market value and the fair value of futures should be about equal. However, there can be a small variation, primarily because of the accompanying expenditures.
  6. Futures are to be at a premium if they are wealthy to spot, otherwise, they are said to be at a discount.
  7. Using commodities lingo Discount = Backwardation and Premium = Contango.
  8. One can buy in the spot market and sell in the futures using the spread as “cash and carry.”

  9. When one buys one contract and simultaneously sells another contract (with a different expiry but the same underlying), this is as a calendar spread.