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What Do Implied Option Volatilities Have to Do With Actual Volatility?

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We’ve spoken a fair amount recently about implied volatilities in options, mostly with the intention of designing trades that allow us to purchase options that are relatively cheap and sell those that are relatively expensive, tipping the odds in our favor.

The CBOE VIX index – a measure of the implied volatility of a basket of 30 day options on the S&P 500 – hovered around 10% for the past few years, but has climbed into the mid-teens this year due to big moves in the level of the index. 

To explain how actually movement in the stock translates (or in some cases doesn’t seem to translate) to changes in the implied volatility in options prices, we’re going to expand upon our discussion of Option Greeks. (Read the original article here)

There are hundreds or thousands of options each listed on thousands of stocks, and the normal forces of supply and demand can’t provide the liquidity necessary for orderly markets, so most bids and offers for options in the marketplace are provided by professional market makers.  These market makers are willing to provide two-sided quotes in many options at once in the hopes of earning the bid-ask spread on their transactions.

There are many market-making strategies in use at any given time, but in general, the goal of market-makers is to be “delta-neutral” - or have little to no exposure to movements in the underlying stock. 

Recall that “delta” is an option price’s sensitivity to movement in the underlying. Because they were simply seeking to earn part of the spread and don’t have an inherent bullish or bearish opinion about the stock (and in some cases may even be at an informational disadvantage to their counter-parties in this regard), they would prefer to be agnostic about which direction the stock moves.

Hedging

After making an options trade, a market maker will typically make a trade in the underlying stock in the opposite direction to mitigate risk.  Known as a “hedge”, this involves buying or selling an equivalent number of shares to offset the total delta of the option trade.

Example:

If a trader buys 10 calls with a strike price of 100 on a stock that’s trading $100, since at-the-money options have a delta of .50, the trader now has a position delta of 500 – that is, in terms of price, this position will behave as if he is long 500 shares of stock. If he were to then sell 500 shares of stock, the position would be delta-neutral.  For small movements in the stock, all value that the options gained, the stock position would lose and vice-versa.

Notice that this is true only for small movements. Why? because of the second Greek value we discussed – Gamma.  Gamma is the sensitivity of an option’s delta to movements in the underlying.

Adjusting the Hedge

Let’s assume our option from the above example has gamma of .01, which would mean that for every dollar the underlying moves, the option gains or loses 0.01 delta.  So if this stock were to decline to $90, the 100 strike call would have a delta of only 40.  Since the trader is still short 500 shares of stock, but is now long only 400 deltas worth of options (10 calls * 0.40 delta) if he intends to be delta neutral, he will need to buy 100 shares of stock to balance to position.  Because the original hedge was initiated at a stock price of $100 and the hedge adjustment involves buying back stock at the current market price of $90, this is a profitable trade.

If, later in the day,  the stock were to rally all the way back to $100, the trader would once again need to adjust the hedge since the long calls would again be 50 delta and he would need to sell 100 shares to be once-again delta neutral.

Even though the stock is now in exactly the same place as it started the day, the trader has booked $1000 in profits because he was able to re-hedge the trade at advantageous prices.

The same would be true if the stock rallied to $110 and then turned around and went back to $100, allowing the trader to sell 100 more shares higher and buy them back lower.  Movement in the stock is advantageous to an position that is long options – if they are hedged – regardless of the direction of the movement.

The opposite would be true for a trader with the opposite position (short 10 calls and long 500 shares) who undertook the opposite hedge trades – a loss of $1000.

While owning options gives a trader the opportunity to re-hedge at profitable prices, recall that the third Greek we discussed is Theta – an option's sensitivity to the passage of time.  When time passes, the trader’s long options will be worth less, regardless of whether he has made profitable hedge or re-hedge trades.  This effect will accelerate as the option has less time remaining to expiration until ultimately, the option has zero time value and is worth either the amount it is in the money – or worthless.

Implied vs Actual Volatility

How does the market arrive at implied volatilities used to price options? There is a supply and demand effect at work, as market makers sell options, they raise implied volatilities (and option prices) to try to either buy them back and be flat again or to sell more only at a higher price.  The opposite occurs when market-makers buy options.

Movement in the underlying determines whether owning options represents an opportunity for profitable hedge trades.  More movement means more opportunities for hedge trades and leads to higher option values. Whether the implied volatility matches the observed volatility depends on the time period used to make the observation.

In the above example, if observed volatility were measured daily based on closing prices, the measurement would be zero, because the stock closed on the same price it had closed the day before.  But the intraday volatility was much higher, making profitable re-hedge trades possible.  This would likely keep implied volatility high because it is profitable for market makers to own options.

Putting Higher Implied Volatilities to Use

2018 YTD has been basically 4 months of this phenomenon.  The S&P 500 is basically unchanged on the year, yet there have been several big moves in the index and in many individual stocks.  Consequently, implied volatilities are higher than they have been in several years.

This means a conservative option selling strategy like selling covered calls (selling out of the money calls against stock you already own) makes more sense than it has in a while.  With implied volatilities on the rise, savvy investors can enhance the return of their portfolios by selling calls against long stock at higher volatilities (and thus higher prices) than 2016 or 2017. 

 

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