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# Volatility Rules, Not Size: It’s Not Price, But Vol That Counts

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July 5, 2016
Max Broden

Of all the cool things options give us, perhaps none is more useful than implied volatility. Aside from being used to calculate options prices and deltas, we also use implied "vol" to gauge how much a stock might move in the future. Best of all, there’s a simple vol calculation that can help us estimate a stock’s expected range in a single day.

With that info, we can start to see that big, scary, expensive stocks may not be that big and scary after all. It turns out, certain high-dollar stocks are often nothing more than teddy bears that actually move less (relatively speaking) than other stocks trading at a fraction of their price. In other words, monster stocks from big companies don’t necessarily always equal more risk. And the key to understanding this is implied vol.

Here’s a closer look. Take the implied vol of a stock’s options (you can use the vol of the at-the-money [ATM] 30-day options), multiply that by the stock price, then divide by 16 (which is the square root of 256—the number of trading days in a year). For example, if FAHN is trading at \$530 and the implied volatility is 29%, the stock can be expected to have a daily range of about \$9.60, because .29 X 530 ÷ 16 = 9.60. So FAHN could move up or down by that amount, and any trading within that range would be expected. (Just bear in mind that the stock could also move outside the standard vol range, too, as nothing is guaranteed.)

Going further, if you take two stocks with the same vol, the expected dollar moves would be the same percentage of their prices. This helps you compare stocks with widely different prices on more of an “apples-to-apples” basis. And this means you can allocate your cash accordingly to better spread the risk. Here’s how.

### Fear Not the Price Tags

If a \$500 stock and a \$50 stock each have the same volatility, you’d equate the risk in the \$500 stock with the risk in the \$50 stock by trading the \$500 stock at one-tenth the size of the \$50 stock. Simple enough.

Let’s say that Gavorin.com’s stock GVRC is trading for about \$700 with an option implied volatility of about 35%. Another stock, Phystil.com (PHYL), is trading for approximately one-tenth of Gavorin’s price at \$71, and it also has options with an implied vol of about 35%.

Using the formula, you can see that GVRC’s daily price range is about \$15.31. PHYL’s expected range is about \$1.55—or about one-tenth the range of GVRC. Is GVRC really any more volatile than PHYL? No. They’re both expected to move by the same percentage.

So, this information might help you more accurately spread your risk because you won’t automatically avoid the GVRCs of the world while unwittingly adding too much risk with lower-dollar stocks that only seem “safer,” but may actually have larger expected moves.

### Calculating Options Risk

Time for another example. Let’s start with a simple long call where the risk is equal to the purchase price. The GVRC 700 call costs \$35.80. In a perfect world, the PHYL 70 call with the same-month expiration would cost \$3.58, but at these prices, it’s going for \$3.85. Although the volatility of each isn’t exactly the same, it’s pretty close. So you’ll risk about the same buying 10 PHYL calls versus buying one GVRC call. If you’re comfortable buying the PHYL calls, then you may be comfortable with the GVRC trade as well, at least from a risk standpoint.

###### FIGURE 1: Calculating Margin Requirements. Even though the margin requirement (multiplied by 100 for each contract) for PHYL is less than that of GVRC, it doesn’t mean it’s less risky. The risk for both is at about the same percentage of the stock price. For illustrative purposes only.

Let’s apply the same logic to a different trade, this time using a short out-of-themoney (OTM) put. We’ll use TD Ameritrade margin requirements for this example—20% of the stock value, less the OTM amount, plus 100% of the option’s current market value.

Keep in mind that options don’t match exactly to the penny, but they can be close. And with PHYL at \$71, the 65-strike put is 8.5% OTM. With GVRC, the 640-strike put is roughly the same percentage OTM. Now, take a look at the option pricing and the margin requirement for both trades in Figure 1.

The margin requirement for the GVRC put, on a per-share basis, comes to \$94. Multiply that by 100 for each option contract, and the margin requirement for one short put option comes to \$9,400. The margin requirement for the PHYL put comes to \$96, or \$960 per option. Again, this highlights how GVRC isn’t necessarily any more “risky” than PHYL, nor is PHYL necessarily less risky than GVRC. The risk for either is about 13.5% of the stock’s price. Trading 10 PHYL puts is roughly the same amount of risk as trading one GVRC put.

### Still Not Convinced?

Let’s slice this up one more way to show that dollar value doesn’t always describe a stock’s risk as much as its vol does. Instead of looking at a short put and dealing with all the margin issues, let’s look at something similar, and perhaps easier to understand—a short put vertical spread.

###### FIGURE 2: Looking at the Short Put Vertical Spread. Comparing “apples to apples,” you’re equalizing your risk by trading the same ratio of spreads as the ratio of the two stock prices. For illustrative purposes only.

Here, there’s no margin required, and you know your risk up front. Potentially the full value of the spread, less your credit, is the amount you could lose. So using this amount as the max risk, let’s compare GVRC to PHYL to see how they stack up to each other (Figure 2). Again, you’re looking at the PHYL 65–60 put spread, where the long 60 put is approximately 15.5% OTM. In GVRC, a similar spread turns out to be the 640–590 put spread, where the long 590 put is likewise just about 15.5% OTM.

The \$5-wide PHYL spread is also one-tenth the width of the \$50-wide spread in GVRC, just as the PHYL stock is one-tenth the value of GVRC. Notice that the credit of the PHYL spread equates to the GVRC spread but again, at the 1:10 ratio.

The biggest takeaway is that spreads that are similarly distanced OTM are priced at roughly the same percentage of the stock price. And other than the stock price, they’re often pretty much the same. So, risk can be equalized by trading the same ratio of spreads as the ratio of the two stock prices. At the end of the day, it’s not necessarily stock price that dictates risk, but the volatility.

That’s why volatility can be a critical measure when you’re looking for innovative ways to spread your risk. Putting all your eggs into low-priced, potentially high-vol stocks might well turn out to be far riskier than trading the gentle giants.