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 26^th 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 30^th 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.