# Synthetic Long and Arbitrage Strategies in Nifty Futures with Options

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Synthetic Long & Arbitrage: Background

You need to open both long and short positions on Nifty Futures, with the same expiration date. How could you possibly accomplish this? And why would it be necessary?

In this chapter, we will answer both of these questions. Let’s begin by understanding how to do it and follow up by exploring the reasoning behind it (hint: arbitrage is the key).

Options are highly flexible derivative instruments, and it is possible to generate any kind of payoff with them, including that of long or short futures.

In this chapter, we will learn how to use options to replicate a long Futures’ payoff. Before moving on, take a moment to refresh your understanding of its linear return here.

The long futures position has been started at 2360 and this is the breakeven point: no gains nor losses are made here. Profits arise if the futures rise higher than it, and losses occur when it moves lower. The 10 point up or down move grant equivalent financial results. Owing to this linearity in return, a future is also called a linear instrument.

The idea with a Synthetic Long is to build a similar long Future’s payoff using options.

– Strategy Notes

Executing a Synthetic Long is fairly simple; all that one has to do is –

1. Buy the ATM Call Option
2. Sell the ATM Put Option

When you do this, you need to make sure –

1. The options belong to the same underlying
2. Belongs to the same expiry

Let us look at an example to get a better understanding. Let’s say Nifty is at 7389- this would put 7400 as the ATM strike. A Synthetic Long position here implies going long on 7400 CE for Rs.107, and shorting the 7400 PE at 80.

The net cash outflow would be the difference between the two premiums i.e 107 – 80 = 27.

Let us consider a few market expiry scenarios –

Scenario 1 – Market expires at 7200 (below ATM)

At 7200, the 7400 PE would have an intrinsic value of Rs.107/-, which is the same as the premium that was paid for it. This means we would not lose out on any money.

Intrinsic value of Put Option = Max [Strike-Spot, 0]

= Max [7400 – 7200, 0]

=Max [200, 0]

= 200.

Clearly, since we are short on this option, we would lose money from the premium we have received. The loss would be –

80 – 200 = -120

Total payoff from the long Call and short Put position would be –

= -107 – 120

= -227

Scenario 2 – Market expires at 7400 (At ATM)

If the market expires exactly at 7400, both the options would expire worthless and hence –

1. We lose the premium paid for the 7400 CE option i.e 107
2. We get the retain the premium for the 7400 PE option i.e 80
3. Net payoff from both the positions would be -27e 80 – 107

Do note, 27 also happens to be the net cash outflow of the strategy, which is also the difference between the two premiums

Scenario 3 – Market expires at 7427 (ATM + Difference between the two premiums)

7427 is an interesting level, this is the breakeven point for the strategy, where we neither make money nor lose money.

1. 7400 CE – the option is ITM and has an intrinsic value of 27. However we have paid 107 as premium hence we experience a total loss of 80
2. 7400 PE – the option would expire OTM, hence we get to retain the entire premium of 80.
3. On one hand we make 80 and the other we lose 80. Hence we neither make nor lose any money, making 7427 the breakeven point for this strategy.

Scenario 4 – Market expires at 7600 (above ATM)

At 7600, the 7400 CE would have an intrinsic value of 200, we would make –

= 200 – 107

= 93

The 7400 PE would expire worthless; hence we get to retain the entire premium of Rs.80.

Total payoff from the strategy would be –

= 93 + 80

= 173

With the four scenarios described above, it is evident that the strategy earns money when the market rises while making losses as it falls, a behavior akin to futures. However, this does not necessarily guarantee that its payoff is of the same type. In order to confirm linearity in payoffs, as in futures, we must analyze the returns at 200 points on either side of our break-even point. If identical outcomes are seen, then linearity can be established.

So let’s figure this out.

We know the breakeven point for this is –

ATM + difference between the premiums

= 7400 + 27

= 7427

The payoff around this point should be symmetric. We will consider 7427 + 200 = 7627 and 7427-200 = 7227 for this.

At 7627 –

1. The 7400 CE would have an intrinsic value of 227, hence we get to make 227 – 107 = 120
2. The 7400 PE would expire worthless, hence we get to keep the entire premium of 80
3. In all we experience a payoff of 120 + 80 = 200

At 7227 –

1. The 7400 CE would not have any intrinsic value, hence we lose the entire premium paid i.e 107
2. The 7400 PE would have an intrinsic value of 7400 – 7227 = 173, since we have received 80 as premium the net loss would be 80 – 173 = -93.
3. In all we experience a payoff of -93-107 = -200

Clearly, there is payoff symmetry around the breakeven, and for this reason, the Synthetic Long mimics the payoff of the long futures instrument.

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