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# Selling Naked Strangles: The Math

Selling short (naked) strangles is heavily promoted by some options "gurus". Is it a good strategy? It might have an unlimited (theoretical) risk, but what about the return? Is the return worth the risk? We decided to do some math, based on real prices, not some theoretical "studies".

Assumptions:

1. \$100,000 account.
2. Sell SPY 10 delta calls and 10 delta puts.
3. Use options expiring in 30 days.
4. Base the number of contracts on "notional﻿ exposure﻿", not margin.
5. Hold till expiration, then open the next trade.

Notional value speaks to how much total value a security theoretically controls. For example, with SPY around \$290, that means selling 1 SPY strangle per ~\$29,000 of capital.

With SPY around \$288 on August 12, 2019, we will be selling the following strangle:

• Sell 4 Sep.11 2019 264 put
• Sell 4 Sep.11 2019 302 call

Those strikes are the closest to 10 delta. 4 contracts give us notional﻿ exposure﻿ of \$115,200 (\$288*100*4), which means 1.15 leverage. This is fairly conservative exposure.

This is how the P/L chart looks like:

Please note that our total credit is \$676 (assuming we can get filled at the mid point).

Now lets do the math.

If ALL trades expire worthless and we keep all credits, we will collect \$676*12=\$8,112. This is 8.1% on \$100,000 account. But this is the best case scenario. This is probably not going to happen. Based on the deltas of the options, this trade has around 80% probability of winning. Which means that statistically, 2-3 trades per year will be losers.

Now, lets be conservative and assume that 2 trades per year will be losers, and the losing trades will lose the same amount as winners (\$676 per trade). In reality, when the markets move against you, even with the best risk management, your losers are usually larger than your winners when you trade a high probability strategy. But again lets be conservative.

Note: The theoretical probability of winning is based on deltas and implied volatility, while the actual win rate is slightly higher because of the volatility risk premium (IV exceeding RV over time). But it doesn't have material impact on the results.

This assumption gives us total P/L of \$676*10-\$676*2=\$5,408. That's total annual return of 5.4%. You can use T-bills as a collateral, which might add 2-4% to the annual return.

In no way this single example can represent the whole strategy, and this calculation might not be very "scientific". Different dates or parameters might provide slightly different results, but this is a ballpark number. We estimate the range to be around 5-7% per annum.

Of course fund managers like Karen Supertrader who use similar strategies realize that those returns probably would not attract too many investors, and also would not get her a spot in tastytrade show. What's their solution to get to the 25-30% annual return they advertise? The answer is: leverage. To get from 5% return to 25%, you need 5x leverage, or 20 contracts.

To see how the leveraged trade would perform during market meltdown, lets assume it was initiated on Dec.3, 2018, with SPY at 280. Three weeks later, SPY was around 234, 16% down. This is how the trade would look like:

That's right, the \$100k portfolio would be down 50%. This is how you blow up your account.

In this case, the 16% market decline took 3 weeks. What if it was 25% decline happening in one week? You can only imagine the results.

Of course we could change the parameters, use 20 delta options, different time to expiration etc. This would not change the results dramatically. With 20 delta options, you would get more credit, but also higher number of losers per year.

Does it mean the selling naked strangles is a bad strategy? Not necessarily. In fact, according to CBOE Volatility Risk Premium and Financial Distress, 1x notional strangle on SPX has historically returned about the same as SPX with 3x the Sharpe Ratio:

But the strangle itself produced around 6% annualized return, which is pretty close to the performance we calculated. Rest of the return came from the collateral.

The bottom line is: selling naked strangles on indexes is a good strategy if used with a sensible amount of leverage. But you should set your expectations correctly. I suspect that most traders would probably base their position sizing on margin, not notional﻿ exposure, which is like driving a Ferrari 190 MPH down a busy street...just because you can. This would increase the return, but also the risk. If you base your position sizing on notional﻿ exposure﻿, the risk is pretty low, but so is the potential return.

Naked options by themselves are not necessarily a bad thing. The problem is leverage and position sizing. If implemented correctly, naked options can make money in the long term. But if you overleverage, you just cannot recover from the inevitable big losses. We warned our readers about the dangers of naked options and leverage on several occasions. It's not the strategy that killed Karen Supertrader, James Cordier, Victor Niederhoffer and others. It's the leverage and lack of risk management.

What about selling naked strangles on individual stocks? Personally, I would never do it, especially not before earnings. The risk is just too high. But lets leave something for the next article..

“The problem with experts is that they do not know what they do not know.”
― Nassim Nicholas Taleb.

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VERY good article. I know some traders are really feeling some pain out there right now. Conservative position sizing is one sure way to give yourself a little edge and confidence to be able to do this long term.

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You are right that leverage is a solution but not in the way you think:

- own capital (i.e. from investors) 10,000\$ ;

- borrow the equivalent of 90,000\$ in the Eurozone at monthly rates of say 0.2% over EURIBOR - that would be -0.2%;

- perform a swap transaction of the currency into US\$ which includes eliminating the currency risk - this will have a variable cost but lets put that at 1% - it can be more or less.

Now lets take your assumption that they can make 5% on a 100K. That would now look like this:

•  +5,000\$ income from the SPY strategy
• - 720\$ Total cost of swap/interest
• +4,280\$ profit for investors

That is a 42.80% return on an annual basis. You could be less sophisticated and just borrow monthly US\$ which costs around 2.5% tops - the strategy remains the same and the return would be 25% annualised. There is still huge risk involved in this transaction even though its mitigated somewhat by the fact you trade monthly SPY. There can be a refinancing problem or interest rates could rise which would eat into your return like there is no tomorrow.

Obviously this isnt happening wholesale and so the premise of your article that you wont lose more than you win on your two losers is at fault here. Whilst you can mitigate the losers somewhat taking them at least at the triple value of a 'regular' win is already more realistic. You then have a 3% or less return which means that unless you go the sophisticated way of foreign currency swaps and the whole shebang you will find it hard to get to where you need to be.

If there was a strategy yielding standard 5% (without additional risk) today all the big money in the market would be into it. Big fortunes fear above all to make big losses and do very well on modest growth.

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Totally agree about the "gurus" pitching option selling as some great alternative to buy and hold without really addressing the risks (including the risk of under-performing buy and hold which is likely the case over the past 10 years).

On the positive side,  my father who is in retirement mode may be fine with a 5% annualized return that has less volatility that holding SPY and provides a diversified income stream.   I think it just depends on your goals and tolerances for risk.

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19 hours ago, TrustyJules said:

You are right that leverage is a solution but not in the way you think:

- own capital (i.e. from investors) 10,000\$ ;

- borrow the equivalent of 90,000\$ in the Eurozone at monthly rates of say 0.2% over EURIBOR - that would be -0.2%;

- perform a swap transaction of the currency into US\$ which includes eliminating the currency risk - this will have a variable cost but lets put that at 1% - it can be more or less.

Now lets take your assumption that they can make 5% on a 100K. That would now look like this:

•  +5,000\$ income from the SPY strategy
• - 720\$ Total cost of swap/interest
• +4,280\$ profit for investors

That is a 42.80% return on an annual basis. You could be less sophisticated and just borrow monthly US\$ which costs around 2.5% tops - the strategy remains the same and the return would be 25% annualised. There is still huge risk involved in this transaction even though its mitigated somewhat by the fact you trade monthly SPY. There can be a refinancing problem or interest rates could rise which would eat into your return like there is no tomorrow.

Obviously this isnt happening wholesale and so the premise of your article that you wont lose more than you win on your two losers is at fault here. Whilst you can mitigate the losers somewhat taking them at least at the triple value of a 'regular' win is already more realistic. You then have a 3% or less return which means that unless you go the sophisticated way of foreign currency swaps and the whole shebang you will find it hard to get to where you need to be.

If there was a strategy yielding standard 5% (without additional risk) today all the big money in the market would be into it. Big fortunes fear above all to make big losses and do very well on modest growth.

I believe the over a long time, you can make 5% with this strategy. But it doesn't mean you will make it every year - it is still possible (and expected) to have 20-30% drawdowns (which is still better than S&P). What happens if the drawdown happens right after you took the loan? The 30% loss means 30k which is 3 times your initial capital. And you have no idea how long will it take to recover.

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10 hours ago, FrankTheTank said:

Totally agree about the "gurus" pitching option selling as some great alternative to buy and hold without really addressing the risks (including the risk of under-performing buy and hold which is likely the case over the past 10 years).

On the positive side,  my father who is in retirement mode may be fine with a 5% annualized return that has less volatility that holding SPY and provides a diversified income stream.   I think it just depends on your goals and tolerances for risk.

Options selling strategies are likely to underperform in strong bull markets. But what will happen to your father's retirement funds if the markets tank 50% tomorrow?

The whole point of options selling strategies (like our Steady Momentum strategy) is to reduce volatility, while still producing market like returns over the long term. After all, you never know when the next bear market will come.