# Optionalysis: Using Standard Deviations to Build Strategies Targeting 2% to 3% per month

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You can use options for many things, and usually we think of options as highly leveraged plays to trade with extreme volatility. Options, however, have many facets, and if you’re comfortable deploying higher capital to write options, you can actually trade with reduced volatility.  There’s multiple uses of options:

• As a leveraged position through only long options (we do this at Options with AP and with MA20 for instance)

• As a hedge – to protect a portfolio from downside

• As an income generating strategy, playing probability numbers – through writing straddles or strangles, or spreads

It’s the third piece we will explore today: How can you generate income while keeping risk at bay? We’ll study the use of Standard Deviations to build strategies that generate between 2% and 3% a month, with lesser need of constant monitoring.

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### There is no return without risk, and it’s about probabilities

Let’s get this straight – “defined” risk through long options is ok, because you can’t lose more than the premium you pay. But if you write options the first thing that comes to mind is: there’s unlimited risk! And a capped return! How can you earn money like this?

The answer lies in evaluating probabilities. There is always a small chance – say 1% – that you will get hit by a car when you cross the road. But you don’t stop crossing the road, do you? On a busy road, you keep a watch in all directions (this is India) and readjust as you move along – but you don’t say that you will not cross the road. There will be risk, no matter what. And in the options world, you work with risk and probability all the time.

Will the Nifty go up 10% tomorrow? In the next 20 days? Before this next expiry date? How do you know if it will?

You will never know for sure, but you can tell what other people are thinking by looking at the option data.

### The Standard Deviation Range

What the market expects is built into the implied volatility of options. Take a call option of Nifty at strike 8000 when the Nifty is at 7915. It trades at Rs. 103 (See Nifty option chain) with animplied volatility (IV) of about 13%. (You can see the IV column there)

The IV itself is calculated using the Black-Scholes or Binomial formula. Let’s now use that to calculate how much the Nifty is expected to move.

So given the IV, the number of days left to expiry and the price of the Nifty we can calculate what market players expect the Nifty to move in. How?

Expected 1 Standard Deviation Move = Nifty value x Implied Volatility x SQRT( Days to Expiry / 365)

so 1SD = 7915 x 13% * SQRT(30/365) = 295

That means Nifty is expected to move 295 points – up or down – as a one standard deviation range. That’s a range of 7620 to 8210.

Note: 1 SD means that the Nifty will be within 1SD about 68% of time. This is about 2 times out of 3. This means that 32% of the time, the Nifty will go outside the range. Therefore the probability of falling below 7620 is 16% (half of 32%) and above 8210 is another 16%.

Which means, the market thinks there is an 84% chance that the Nifty will remain above 7620. That triggers a thought.

### Option Spreads at 7600 or below?

Let’s say the idea is to be play for the chance that the Nifty will not close under 7600. We don’t want unlimited risk, so we won’t write the 7600 Put naked; we could build a position that’s lower in terms of risk:

Sell 1x 7600 put at Rs. 30 and Buy 1x 7400 put at Rs. 13 = a net credit of Rs. 17 per Nifty.

(1x means whatever quantity you sell on the 7600 put, you buy the same quantity on the 7400 put)

The risk is 200 points if the nifty goes to 7400 or below. But the chance of that is very remote – even lower than the 16% probability of 7620. In mathematical terms there is only 4% chance of 7400 – using similar SD calculations. (7400 is 515 points away, which is a 1.75 SD on the downside, which is a 4% chance)

A 4% chance means that you’ll be wrong once in 25 times. If you make 17 points each time, and win 24 times, but lose 200 points once, you win 408 points, but lose 200. That’s still a positive.

(Note: this is simplified math. In reality, the market behaves very differently and can easily do this 1.75 SD move much more frequently! This is called tail risk because the market doesn’t really follow the normal distribution that is expected of it. However, as markets get more volatile, Implied Volatilities go up and markets tend to go into “fear” mode and overestimate the moves. That’s why it makes more sense to write options when IVs are high.)

### What Return?

The put spread (7600-7400) for one lot of 75 Nifty will require Rs. 37000 as margin. (SeeZerodha’s margin calculator) Assume another 8,000 for extra margin for a total of Rs. 45000.

For a lot of 75, the Rs. 17 max gain is a return of Rs. 1275. That, on Rs. 45K, is 2.8% for one month.

More importantly, you might not have to wait the entire month. If the market is at the same level in 10 days, you will see that the spread will collapse to about Rs. 8 (from Rs. 17) which means you can lock a 1.4% return in 10 days and move to a different strategy for the rest of the time.

While this sounds exciting, there are more spreads you could do.

### Hitting Both Sides: The Condor

If the range is 7600 to 8200: Why can’t we play on either side? We could sell a call spread on the higher side. Let’s consider this:

• Write the 8200 CE and buy 8300 CE: At 37/21 the net spread is Rs. 15

• Write the 7600 PE and buy 7500 PE: At 30/19.6 the net spread is Rs. 10.4

• The total credit is Rs. 25.4

For one lot of 75 Nifty, the net investment is Rs. 74,000 (margin). The credit of Rs. 25.4 x 75 = Rs. 1905. That’s a 2.5% return if the index stays in the 1 SD range.

This is a “condor” because the payoff diagram  looks like one.

This is risky in the sense that if the Nifty breaches the levels mentioned, you lose money. If the Nifty is at 8300 at expiry you lose 100 point minus the 25.4 you got as credit earlier, for a loss of 74.6 points. It’s practically not that high though. But how much? Let’s say the Nifty jumps to 8250 in five days. The puts will be close to zero, but the 8200 call will be around 155 and the 8300 call will be at 102. (Assuming 25 days left to expiry then)

That means you will lose Rs. 53 to close the trade out right now. Since you had a credit of Rs. 25.4 to begin with, your net loss is 28 points, much lesser than the 75 points you th
ought you would “theoretically” lose.

You can make an adjustment by say writing a different put spread) – at 8000-7900, or by moving the call spread “up” – to say 8500-8600. There are a lot of adjustments you can easily make to option positions!

If you’re playing probabilities, why define risk? Take the same concept and

• Buy one 7650 put at 37

• Write two 7600 puts at 30 (total Rs. 60)

• Net credit of Rs. 23

• On a Rs. 80,000 outlay, this is a potential profit of Rs. 1650 if the market stays above 7650, or2% in one month.

Again, here if the market is above 7575 you’re profitable. In fact at 7600 the profit is huge at 73 points. Any thing above 7650 yields a profit (since all options will expire worthless and you have the net credit of Rs. 23).

If the market goes against you you always have the ability to adjust – by, say, buying a 7550 put (to limit your overall loss, and by converting to what is called a “butterfly”). You can take out one put after some time and leave a put spread on instead, after booking a bit of a profit through time decay. The possibilities are endless, and that’s the real power of using options strategies.

### The Point: Useful if you must trade less, Use SDs

If you can’t be in front of a terminal all day it’s better to use such strategies to get 2.5% to 5% on your capital in a calculated manner. We’ve used the Nifty, but we could use stocks (only about 10-15 have liquidity), or other indexes like a BankNifty.

Use Standard Deviations to find out where the market expects the underlying stock to move, and write outside that range. 1 Standard Deviation implies that the market will stay inside the 1SD range 68% of the time, 2SD is 95% and 3SD is 99%. If you take a directional strategy, the 1SD probability bumps up to 84%.

What you must do however is wait to build these spreads when the time is ripe. The best time to create such spreads is to build to an expectation (say 3% a month) and then work it when the Implied Volatilities are high. IVs are not always high – for the Nifty, IVs are represented by the VIX, but for other stocks you have to see the option chain to see IV values.  With a higher IV, your return can be even higher, and you can write options further away to get the same 3% return.

(For example, Bank Nifty implied volatilities were very high before the RBI policy, compared to its own history. That would be a great time to build a strategy on the Bank Nifty – and we had build a short strangle on Slack. We also expect implied volatilities to spike up on the week of the US Fed Policy, which is around Dec 16, 2015)

The idea is to write options along with buying them, and here, unless you have big gap moves,you don’t have to look at the market every day. Condors are even better in the sense they are non directional – you don’t have to care if the market isn’t moving.

We’ll explore more in real trades as we move along. But do let us know your questions! (Reply to this post, or use the Slack #options channel.)

## Disclaimer

Nothing in this newsletter is financial advice and should not be construed as such. Please do not take trading decisions based solely on the matter above; if you do, it is entirely at your own risk without any liability to Capital Mind. This is educational or informational matter only, and is provided as an opinion.

Disclosure: The authors at Capital Mind have positions in the market and some of them may support or contradict the material given above, or may involve a direction derived from independent analysis.

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