"THE ROAD GOES ON FOREVER AND THE PARTY NEVER ENDS"
-Robert Earl Keen
Equity markets are enjoying one of the longest running bull markets in history right now as the S&P 500 has not had a 20% correction in (the technical definition of a bear market) since the end of the financial crisis of '08-'09. Furthermore, since the US Presidential election of 2016, the index has yet to experience a single month of negative performance. If this continues through December, 2017 will be the first year in the index's history to not have a single down month. Simply put, this market is unprecedented.
Given the duration and magnitude of the current rally, professional investors are beginning to voice concerns about how much stamina the bull market has left. It seems like every day a new headline appears about the latest headwind that will ultimately break the rally; whether it's new struggles in tech stocks, the quickly-flattening yield curve, equity vol falling below fixed income vol or a likely Bitcoin bubble.
MESS WITH THE BULL AND YOU'LL GET THE HORNS
It's one thing to talk about shorting a bull market but it's another thing all together to actually do it. One popular shorting strategy is to buy put options on the S&P; options carry low price tags, have a defined down-side and carry significant leverage benefits. However, successful long options trading is notoriously difficult because the manager has to be right on three dimensions of the trade: direction, magnitude and timing. First, the market actually has to move in the direction of the bet. Second, to be profitable, the magnitude of the move has to exceed the premium paid to purchase the option if it's held to expiration. Lastly, given the fixed life of an option, the previous two elements have to happen before it expires. Failing to be right on all three aspects of the trade will almost certainly produce a loss.
A TOTAL AND COMPLETE UNDERSTANDING OF OPTIONS PRICING IN JUST 3 PARAGRAPHS
Implied volatility is the option pricing component that represents the market’s assumption of the behavior of the underlying security during the life of contract. The higher the expected volatility, the more expensive the option and vice versa.
Option prices also depend on a concept called 'moneyness' which is the distance the strike price is from the underlying's current price. An option whose strike price is equal to the underlying security’s current price is said to be ‘at-the-money’. Near-the-money options will generally have the lowest implied volatility pricing assumptions and away-from-the-money will generally have higher volatility pricing assumptions. The difference in pricing assumptions is due to a statistical phenomenon known as ‘Extreme Value Theory’ which examines the behavior of extreme events known as ‘tail risk’.
Contract quotes are listed by strike prices across time to expiration; this two-dimensional format creates a pricing plane. Implied volatility varies by each of these variables and, when added to the two-dimensional plane, creates a three-dimensional volatility surface.
THE ARBITRAGE OF VOL SKEW
Now that we know a little about implied volatility, let's examine its behavior in the real world. At the time of this writing, the S&P 500 ETF, SPY, is currently trading at roughly $265 and January's options expiration date is 31 market days away. Below, is a chart of the implied volatilities for January SPY put options:
The differences in implied volatility levels across the strike prices create a curve that that is colloquially called a 'volatility smile' or 'volatility skew'. As said before, the higher the implied volatility, the greater the expected move in the underlying security over the life of the contract.
Even if we assume the lowest projected return for the SPY over the life of the option (-0.35%), the implied volatility of the at-the-money put creates a return distribution that looks like this:
In contrast, if we use the implied vol from the January $230 put (trading at $0.29 bid with a -3.4 delta) which is 22.4%, the return distribution looks like this:
For the sake of context, here's the historical distribution of 31 day SPY returns over the last 2 years (which have seen unusually low volatility):
To better understand equity price forecasting, see the blog titled 'Projecting Equity Prices Using Exponential Trends and Stochastic Simulations':
http://tancockstradingblog.blogspot.com/2015/08/projecting-equity-prices-using.html
The difference in the distributions illustrates the arbitrage opportunity created by the vol skew as we see the $230 put is being valued with aggressive pricing assumptions.
TRADE STRUCTURE
To set up our market short, we can capture the richness of vol skew by shorting the $230 put and using the proceeds to purchase puts with higher absolute deltas. For this example, I structured the following trade:
To get an idea of the magnitude of a -14.37% move over 31 trading days, let's revisit the projected return distributions with an indicator of the breakeven point:
At-the-money vol:
$230 put vol:
2-year historical:
To illustrate the arbitrage opportunity provided by vol skew one more time, let's revisit the January $230 put. Bid at $0.29, the option has a delta of -3.4; this loosely means that the option is expected to finish either at or below the strike price 3.4% of the time. However, when we look at the history of the SPY 31 day returns going back to January of 1993, the index ETF has only experienced a move of this magnitude a total of 1.23% of the time... the 2.2% difference here represents a sizeable advantage.
The expected value of the trade under the three original vol scenarios are as follows:
PROS & CONS:
The pros and cons of this strategy are as follows:
Pros:
-Robert Earl Keen
Equity markets are enjoying one of the longest running bull markets in history right now as the S&P 500 has not had a 20% correction in (the technical definition of a bear market) since the end of the financial crisis of '08-'09. Furthermore, since the US Presidential election of 2016, the index has yet to experience a single month of negative performance. If this continues through December, 2017 will be the first year in the index's history to not have a single down month. Simply put, this market is unprecedented.
Given the duration and magnitude of the current rally, professional investors are beginning to voice concerns about how much stamina the bull market has left. It seems like every day a new headline appears about the latest headwind that will ultimately break the rally; whether it's new struggles in tech stocks, the quickly-flattening yield curve, equity vol falling below fixed income vol or a likely Bitcoin bubble.
MESS WITH THE BULL AND YOU'LL GET THE HORNS
It's one thing to talk about shorting a bull market but it's another thing all together to actually do it. One popular shorting strategy is to buy put options on the S&P; options carry low price tags, have a defined down-side and carry significant leverage benefits. However, successful long options trading is notoriously difficult because the manager has to be right on three dimensions of the trade: direction, magnitude and timing. First, the market actually has to move in the direction of the bet. Second, to be profitable, the magnitude of the move has to exceed the premium paid to purchase the option if it's held to expiration. Lastly, given the fixed life of an option, the previous two elements have to happen before it expires. Failing to be right on all three aspects of the trade will almost certainly produce a loss.
A TOTAL AND COMPLETE UNDERSTANDING OF OPTIONS PRICING IN JUST 3 PARAGRAPHS
Implied volatility is the option pricing component that represents the market’s assumption of the behavior of the underlying security during the life of contract. The higher the expected volatility, the more expensive the option and vice versa.
Option prices also depend on a concept called 'moneyness' which is the distance the strike price is from the underlying's current price. An option whose strike price is equal to the underlying security’s current price is said to be ‘at-the-money’. Near-the-money options will generally have the lowest implied volatility pricing assumptions and away-from-the-money will generally have higher volatility pricing assumptions. The difference in pricing assumptions is due to a statistical phenomenon known as ‘Extreme Value Theory’ which examines the behavior of extreme events known as ‘tail risk’.
Contract quotes are listed by strike prices across time to expiration; this two-dimensional format creates a pricing plane. Implied volatility varies by each of these variables and, when added to the two-dimensional plane, creates a three-dimensional volatility surface.
THE ARBITRAGE OF VOL SKEW
Now that we know a little about implied volatility, let's examine its behavior in the real world. At the time of this writing, the S&P 500 ETF, SPY, is currently trading at roughly $265 and January's options expiration date is 31 market days away. Below, is a chart of the implied volatilities for January SPY put options:
The differences in implied volatility levels across the strike prices create a curve that that is colloquially called a 'volatility smile' or 'volatility skew'. As said before, the higher the implied volatility, the greater the expected move in the underlying security over the life of the contract.
Even if we assume the lowest projected return for the SPY over the life of the option (-0.35%), the implied volatility of the at-the-money put creates a return distribution that looks like this:
In contrast, if we use the implied vol from the January $230 put (trading at $0.29 bid with a -3.4 delta) which is 22.4%, the return distribution looks like this:
For the sake of context, here's the historical distribution of 31 day SPY returns over the last 2 years (which have seen unusually low volatility):
To better understand equity price forecasting, see the blog titled 'Projecting Equity Prices Using Exponential Trends and Stochastic Simulations':
http://tancockstradingblog.blogspot.com/2015/08/projecting-equity-prices-using.html
The difference in the distributions illustrates the arbitrage opportunity created by the vol skew as we see the $230 put is being valued with aggressive pricing assumptions.
TRADE STRUCTURE
To set up our market short, we can capture the richness of vol skew by shorting the $230 put and using the proceeds to purchase puts with higher absolute deltas. For this example, I structured the following trade:
- Short 23 January $230 puts at $0.29 to generate $667 in proceeds - total delta points: 78.2
- Long 1 January $265 put at $4.17 - delta points: -50.08
- Long 1 January $260 put at $2.42 - delta points: -32.46
To get an idea of the magnitude of a -14.37% move over 31 trading days, let's revisit the projected return distributions with an indicator of the breakeven point:
At-the-money vol:
$230 put vol:
2-year historical:
To illustrate the arbitrage opportunity provided by vol skew one more time, let's revisit the January $230 put. Bid at $0.29, the option has a delta of -3.4; this loosely means that the option is expected to finish either at or below the strike price 3.4% of the time. However, when we look at the history of the SPY 31 day returns going back to January of 1993, the index ETF has only experienced a move of this magnitude a total of 1.23% of the time... the 2.2% difference here represents a sizeable advantage.
The expected value of the trade under the three original vol scenarios are as follows:
- 2-year historical vol assumption: +$305
- At-the-money implied vol assumption: +$268
- $230 implied vol assumption: -$50
PROS & CONS:
The pros and cons of this strategy are as follows:
Pros:
- By financing the purchase of at-the-money and near-the-money options, a manager removes the 3 requirements of a profitable long only option trade: direction, magnitude and timing.
- Using the vol skew arbitrage, a manager can maintain a hedge and not have to time the placement of a protective position
- A manager can optimize the structure of the trade by maximizing delta points at inception (at-the-money options were used for this example to illustrate implied vol pricing)
- The downside of this trade - beyond the breakeven point - although unlikely, is not impossible and can certainly be costly
- By loading up on short options, a manager will be exposed to vega - the sensitivity of an option price due to a change in volatility
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