Okay bear with me while I lay out the obvious definitions and uses of volatility so I can better explain the charts below, instead of just presenting them as if I understand them fully. Which I can assure you is not the case.

**Volatility**: is a market-based signal that reveals past or expected price action in a given security. More specifically, it reveals a market’s variation in price or returns. Along with studying and sequencing deltas in price, volatility can signal where and when market opportunities are ripe for the plundering.

Volatility, can be broken down into two categories, **Realized Volatility** and **Implied Volatility. **

**Realized Volatility: **** **measures volatility in the past. A stock can go from Price A to Price B a million different ways. Realized volatility tells us the path it took to get there. In other words, what trading ranges (ATR) and volatility did it take to arrive at the current market price. The path any particular instrument has taken tells us a lot about investor behavior and sentiment.

**Implied Volatility: ** gives us insight on what investors believe will happen in the future. Implied Volatility (IV) is derived from the publicly traded price of options contracts that expire in the future. Implied Volatility tells us about the market’s expectation for price or * return variance* in a given security. The price of options, and thus the price of implied volatility changes by the second throughout the trading day just like the price of a. security.

**Return Variance**

Or, if variance was calculated using forecasted data,

*(Source: Columbia Business School, Risk and Return: Variance and Standard Deviation) *

**Implied Volatility Premiums: ** Compares implied volatility to realized volatility. A “premium” measures by how much implied volatility trades over realized (30D realized volatility compared to volatility over 30D.

**Volatility Skew:** Compares the implied volatility assumption embedded in different contract strikes. For example, looking at the relative changes in the price of downside puts to upside calls (25-delta risk reversal).

After the aforementioned price definitions and relative performances are identified across asset classes, the next step is to observe trends in different tickers under the same umbrella (asset class).

The goal is to find setups where volatility and options markets price-in-expectations that are different from your our personal views on an asset within a certain optimal exposure predilection.

Looking at a graphical representation of volatility, along the x-axis we can see a normal distribution curve that can represents an ITM (2SD), ATM(1SD), & OTM(3SD). Then, imagining the y-axis along the left side of the normal distribution curve, will in this case represent an options extrinsic value.

All else equal, if you want to bet the price of a stock will move from point A to point B, it will be more expensive the higher the volatility assumption.

That being said, we all know or should know markets don’t distribute themselves over a normal distribution curve, however, this is a good framework for conceptualizing further volatility concepts.

The chart below shows the Historical Return Distribution for the S&P 500 Index over a one-year period. Compared to the graphical representation of volatility (normal distribution curve) they look quite similar. Therefore, overtime price’s will generally group around their mean averages.

However, the actual distribution of 30D realized volatility is one of higher peaks and fatter tails than a normal or lognormal distribution behind a standard model (*Black-Scholes*). In regard to the meaning “higher peaks” and “fatter tails”, Ben Ryan of Hedgeye Risk Management states, “there is a lot of chop between 10%-15% even though outsized moves are perpetually priced in.”

We can see this here.

At the extremes in volatility the market usually bets on mean reversion. When realized volatility gets to an all time low nobody is going to sell you insurance assuming that continues.

**Bottom Line **

- Implied volatility is a measurement used in the Black-Scholes Model, used to calculate option prices.
- Volatility measures the magnitude of a potential price change in an underlying.
- High Implied Volatility = Stock Price is Less Stable, increases extrinsic value of option prices across the board.
- Low Implied Volatility = Stock Price is More Stable, decreases extrinsic value of option prices across the board.
- Implied volatility rank (IVR) allows you to put context around current implied volatility levels.

- Normal volatility skew occurs when put options are priced more expensive than equidistant call options in the same expiration cycle.
- Option implied volatility is calculated by inputting option prices into an option pricing model.
- If put options are priced more expensive than call options, the option chain has a normal volatility skew.
- A normal volatility skew means the put options have higher implied volatilities than their call counterparts.
- If call options are priced more expensive than put options, the option chain has a reverse volatility skew.
- Volatility smile refers to implied volatility increasing for far OTM options.

-R.W.N II

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