## Background

The Call Ratio Back Spread is an interesting options strategy. I call this interesting keeping in mind the simplicity of implementation and the kind of pay off it offers the trader. This should certainly have a spot in your strategy arsenal. The strategy is deployed when one is out rightly bullish on a stock (or index), unlike the bull call spread or bull put spread where one is moderately bullish.

At a broad level this is what you will experience when you implement the Call Ratio Back Spread-

- Unlimited profit if the market goes up
- Limited profit if market goes down
- A predefined loss if the market stay within a range

In simpler words you can get to make money as long as the market moves in either direction.

Usually, the Call Ratio Back Spread is deployed for a ‘net credit’, meaning money flows into your account as soon as you execute Call Ratio Back Spread. The ‘net credit’ is what you make if the market goes down, as opposed to your expectation (i.e market going up). On the other hand if the market indeed goes up, then you stand to make an unlimited profit. I suppose this should also explain why the call ratio spread is better than buying a plain vanilla call option.

So let’s go ahead and figure out how this works.

## Strategy Notes

The Call Ratio Back Spread is a 3 leg option strategy as it involves buying two OTM call option and selling one ITM Call option. This is the classic 2:1 combo. In fact the call ratio back spread has to be executed in the 2:1 ratio meaning 2 options bought for every one option sold, or 4 options bought for every 2 option sold, so on and so forth.

Let take an example – assume Nifty Spot is at 7743 and you expect Nifty to hit 8100 by the end of expiry. This is clearly a bullish outlook on the market. To implement the Call Ratio Back Spread –

- Sell one lot of 7600 CE (ITM)
- Buy two lots of 7800 CE (OTM)

Make sure –

- The Call options belong to the same expiry
- Belongs to the same underlying
- The ratio is maintained

The trade set up looks like this –

- 7600 CE, one lot short, the premium received for this is Rs.201/-
- 7800 CE, two lots long, the premium paid is Rs.78/- per lot, so Rs.156/- for 2 lots
- Net Cash flow is = Premium Received – Premium Paid i.e 201 – 156 = 45 (Net Credit)

With these trades, the call ratio back spread is executed. Let us check what would happen to the overall cash flow of the strategies at different levels of expiry.

Do note we need to evaluate the strategy payoff at various levels of expiry as the strategy payoff is quite versatile.

Scenario 1 – Market expires at 7400 (below the lower strike price)

We know the intrinsic value of a call option (upon expiry) is –

Max [Spot – Strike, 0]

The 7600 would have an intrinsic value of

Max [7400 – 7600, 0]

= 0

Since we have sold this option, we get to retain the premium received i.e Rs.201

The intrinsic value of 7800 call option would also be zero; hence we lose the total premium paid i.e Rs.78 per lot or Rs.156 for two lots.

Net cash flow would Premium Received – Premium paid

= 201 – 156

= 45

Scenario 2 – Market expires at 7600 (at the lower strike price)

The intrinsic value of both the call options i.e 7600 and 7800 would be zero, hence both of them expire worthless.

We get to retain the premium received i.e Rs.201 towards the 7600 CE however we lose Rs.156 on the 7800 CE resulting in a net payoff ofRs.45.

Scenario 3 – Market expires at 7645 (at the lower strike price plus net credit)

You must be wondering why I picked the 7645 level, well this is to showcase the fact that the strategy break even is at this level.

The intrinsic value of 7600 CE would be –

Max [Spot – Strike, 0]

= [7645 – 7600, 0]

= 45

Since, we have sold this option for 201 the net pay off from the option would be

201 – 45

= 156

On the other hand we have bought two 7800 CE by paying a premium of 156. Clearly the 7800 CE would expire worthless hence, we lose the entire premium.

Net payoff would be –

156 – 156

= 0

So at 7645 the strategy neither makes money or loses any money for the trader, hence 7645 is treated as a breakeven point for this trade.

Scenario 4 – Market expires at 7700 (half way between the lower and higher strike price)

The 7600 CE would have an intrinsic value of 100, and the 7800 would have no intrinsic value.

On the 7600 CE we get to retain 101, as we would lose 100 from the premium received of 201 i.e 201 – 100 = 101.

We lose the entire premium of Rs.156 on the 7800 CE, hence the total payoff from the strategy would be

= 101 – 156

= – 55

Scenario 5 – Market expires at 7800 (at the higher strike price)

This is an interesting market expiry level, think about it –

- At 7800 the 7600 CE would have an intrinsic value of 200, and hence we have to let go of the entire premium received i.e 201
- At 7800, the 7800 CE would expire worthless hence we lose the entire premium paid for the 7800 CE i.e Rs.78 per lot, since we have 2 of these we lose Rs.156

So this is like a ‘double whammy’ point for the strategy!

The net pay off for the strategy is –

Premium Received for 7600 CE – Intrinsic value of 7600 CE – Premium Paid for 7800 CE

= 201 – 200 – 156

= -155

This also happens to be the maximum loss of this strategy.

Scenario 6 – Market expires at 7955 (higher strike i.e 7800 + Max loss)

I’ve deliberately selected this strike to showcase the fact that at 7955 the strategy breakeven!

But we dealt with a breakeven earlier, you may ask?

Well, this strategy has two breakeven points – one on the lower side (7645) and another one on the upper side i.e 7955.

At 7955 the net payoff from the strategy is –

Premium Received for 7600 CE – Intrinsic value of 7600 CE + (2* Intrinsic value of 7800 CE) – Premium Paid for 7800 CE

= 201 – 355 + (2*155) – 156

= 201 – 355 + 310 – 156

= 0

Scenario 7 – Market expires at 8100 (higher than the higher strike price, your expected target)

The 7600 CE will have an intrinsic value of 500, and the 7800 CE will have an intrinsic value of 300.

The net payoff would be –

Premium Received for 7600 CE – Intrinsic value of 7600 CE + (2* Intrinsic value of 7800 CE) – Premium Paid for 7800 CE

= 201 – 500 + (2*300) – 156

= 201 – 500 + 600 -156

= 145

Here are various other levels of expiry, and the eventual payoff from the strategy. Do note, as the market goes up, so does the profits, but when the market goes down, you still make some money, although limited.

## Strategy Generalization

Going by the above discussed scenarios we can make few generalizations –

- Spread = Higher Strike – Lower Strike
- Net Credit = Premium Received for lower strike – 2*Premium of higher strike
- Max Loss = Spread – Net Credit
- Max Loss occurs at = Higher Strike
- The payoff when market goes down = Net Credit
- Lower Breakeven = Lower Strike + Net Credit
- Upper Breakeven = Higher Strike + Max Loss

Here is a graph that highlights all these important points –

Notice how the payoff remains flat even when the market goes down, the maximum loss at 7800, and the way the payoff takes off beyond 7955.