Other contenders for this installment’s title were:
“Viva la risk”
“Is Le Pen Mightier?”
“Je ne sais pas”
But then we remembered an earlier promise to talk about implied volatility. First and foremost, this post isn’t going to make you an expert on options, volatility, or the math involved in pricing derivatives. However, we do hope it’s somewhat informative and entertaining. Our intended learning outcome — to steal a phrase from the lexicon of military flight training — is for our readers to understand what an option is (and what it does) and where implied volatility comes into play.
Thales and his olive presses
Thales of Miletus was a Greek philosopher, mathematician, astronomer, and all-around interesting guy. You may be familiar with his theorem involving an inscribed angle, but if you’re not, don’t worry… Thales’ supposed forays into business provide an interesting history of optionality. As the story goes, Thales made a prediction about the weather one year that led him to believe the olive harvest was going to be a good one. Instead of buying olive presses outright, Thales apparently reserved them early in the year for a discount. If his weather prediction was accurate — and led to a large olive crop — he could rent out the presses for a high price as the demand rose. If he was wrong on his prediction, he was only on the hook for the discounted cost of the presses that he paid for upfront. So Thales paid for the right — but not the obligation — to use the olive presses.
A simple contract
Options are contracts that give the buyer the right (but not the obligation) to buy or sell a security (called the underlying) at a predetermined price. A call option allows the purchaser of the contract to buy the underlying at a predetermined price, while a put option allows the purchaser of the contract to sell the underlying at a predetermined price.
There’s a cost associated with the option contract as well as an element of time. Options have expirations, so they’re technically a wasting asset… their value erodes as time passes.
So what determines the price of an option? The pithy answer is simply “the market,” but there’s more nuance to it. The academic answer involves the current price of the underlying security, the predetermined price at which the option contract allows the purchaser to buy or sell the underlying security (called the strike price), the time until expiration, the risk free rate of return, and the volatility of the underlying security.
Academia doesn’t mean reality
Armed with the academic answer, we can theoretically determine the price of any option given the aforementioned components. As an example:
Amazon is currently trading at $920 per share. I want to purchase a put option (that allows me to sell my shares of Amazon at a predetermined price) that has a strike price of $850 and expires in 30 days. The risk free rate is .75% and Amazon’s historical volatility for the last 60 days is 27.5%.
I plug the values into my option pricing calculator and come up with an expected cost of around $5.40… but wait…
The market price is $6.35. What gives?
The wrong number in the wrong formula to get the right price
The market price of $6.35 in our example uses the same underlying security price ($920), the same strike price ($850), the same time to expiration (30 days), and the same risk free rate (.75%). However, it uses a different value for the volatility of the Amazon stock. That is, it uses a volatility that is implied by the market price of the option, holding all other variables the same. As such, our desired put option contract has an implied volatility of about 29%.
Why is that?
From a supply and demand perspective, let’s consider the following:
Investing, by definition, involves holding an interest in a security. We call this being “long” the security, and the vast majority of folks have long positions… that is, you own shares of GE, or Amazon, or a S&P 500 exchange traded fund, or your favorite mutual fund. How can an investor protect a portfolio from downside risk? Well, one option (pun intended) is to purchase put contracts to limit the loss if the market goes down. Remember, our put contract allows us to sell a security at a predetermined price… even if that price is significantly higher than the current price of the stock during a bear market.
So investors buy put contracts as insurance against losses.
Just like anything else, an increase in demand has a resulting effect of driving up the price. As such, the efficient market reflects a higher price for this “insurance.” To make the equation work out to the market price (instead of the academic price), we adjust the volatility… the wrong number in the wrong formula to get the right price.
The fear gauge
You may have heard of the VIX, or the CBOE Volatility Index, referred to as the “fear gauge” because as investor anxiety rises, the value of the VIX typically rises with it. The VIX simply measures the implied volatility of options on the S&P 500. We’re probably doing a disservice with that explanation, but it will work for this post.
Let’s practice what you’ve learned so far.
The VIX measures implied volatility. If the VIX is rising, then implied volatility is rising. Why is implied volatility rising and what does that have to do with investor anxiety?
If you came to the conclusion that anxious investors are buying more “insurance” in the form of put contracts, thereby driving up the implied volatility by way of supply and demand, then nice work!
Barely scratching the surface
We’ve only done a very shallow dive into the world of options and volatility, but we hope you learned something along the way. Options can help define risk, but at the cost of the contract. Options can also be used to express views on direction, volatility, and other higher order elements. Volatility has also been considered an asset class, although we would side with PIMCO’s terminology of volatility being an “opportunity class.”
Finally, if you ever figure out how Thales did with his olive press options, please let us know.
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