## Use Implied Volatility to Discover Stock Price Expectations

In the previous article, What is Implied Volatility in Options?, we introduced implied volatility and how it is calculated. Implied volatility is one of the most important factors used to assess the affordability or the luxury of an option. The judgment of option traders and investors in determining their best buying and selling strategies for a particular option depends on their analysis of that option’s implied volatility. Below are the key takeaways on the dynamics behind implied volatility (IV):

- Option prices are dependent on implied volatility.
- A higher IV means higher option prices.
- When big moves occur in implied volatility in just a short period of time, there are big changes in option prices as well.
- Buyers must aim to buy options with a low implied volatility to pay less.
- Sellers must aim to sell options with a high implied volatility to gain more.

We said that understanding implied volatility, as well as the basic knowledge on how it is computed, can help traders and investors avoid committing poor investment decisions when options are involved. Accounting for it is extremely necessary to ensure that you are not overpaying or underpaying. When one does not consider this seriously, he is up for a huge error. Both new and experienced traders should not fall into this trap.

Aside from that, we introduced you to the Implied Volatility Rank (in percentage terms). It is used by many financial institutions to measure a stock’s implied volatility. As an example, when a stock has an IV Rank as high as 90%, this means that it has a lower implied volatility than the current one 90% of the time over the past year. This means that the current implied volatility is high, since it sits at least at the 90th percentile over the past year. Many financial advisors can help you with looking into implied volatility charts through their online screening systems, so you may see the expected range for an underlying asset in a particular period of time.

**This brings us to another question.**

If the implied volatility of an underlying asset helps investors evaluate the affordability or luxury of an option, how then can they assess the possibility of a stock’s price moving up or down? How do we calculate stock price expectations using the implied volatility of an underlying asset?

Implied volatility gives us the expected price movement of an underlying asset (we’ll dive into this shortly). That’s one of the factors that scare or excite us when it comes to options trading.

Let us go deeper again with implied volatility for a minute.

Of course, we have markets where options are trading. Variables such as the stock price, strike price, time to maturity, and the risk free rate (usually the 10 year treasury yield is the benchmark) are widely available in these public markets. Stock market prices fluctuate based on various factors: big market events; employee strikes; entrepreneurial errors; unfavorable litigations; political and legal policy changes that affect the business; bad management; changes in business location or succession; and other company or industry specific events. Prices fluctuate based on supply and demand. The change in stock prices directly affects implied volatility.

You can use a pricing model to come up with a theoretical option price. In the previous article, we used the Black-Scholes pricing model. One of the inputs in this pricing model’s formula is volatility (or implied volatility). Implied volatility can be calculated as a plug in the Black-Scholes formula. We can use Excel’s Goal Seek Function to calculate the correct implied volatility number given all the other variables in the formula are widely available using the market data. We won’t go into too much details on this again since this was already introduced in the previous article. If you haven’t read it, please read “What is Implied Volatility in Options and How is it Calculated?”

## Standard Deviation Vs. Volatility

Standard deviation is one way to measure volatility and for our purposes, standard deviation and volatility are essentially two ways of saying the same thing. It’s the probability for a stock to move up or down by certain amounts in a given time of period.

However, there are certain differences that you should be aware of.

Volatility is a percentage that tells us how much something (not just a stock) tends to move. It is not always standard deviation since there are other measurements of volatility. For example, average true range, which is a measure of volatility that has nothing to do with standard deviation.

Whereas, standard deviation is a statistic that describes variability in a data set. It’s the square root of variance. Variance is the average of all squared deviations away from the mean in a data set.

Therefore, these standard deviation and volatility go beyond finance and investing. But if we were to focus on our topic of stock and option trading, standard deviation is the measure of volatility we’ll be using. Therefore, these two terms will be used interchangeably in this article.

Let’s dive into calculating a stock’s price range below.

## Calculating a Stock’s Estimated Price Range Using Implied Volatility

Let us now take a look at how we can calculate stock price expectations. The expected move of an underlying asset can be determined in three steps:

- Standard Deviation. As discussed above, for our purposes, implied volatility derived from the Black-Scholes formula is the same as standard deviation. So the first step is finding implied volatility, which we’ll substitute for standard deviation.Here’s how the generic bell curve graph, the most common type of distribution for a variable, looks like. This graph is often used by financial analysts and investors when looking into the possible returns of a security.Source: http://www.optionstradingsignals.com/understanding-implied-volatility-when-trading-options-part-1/You should be aware that in a normal distribution, roughly 68% of observations (potential stock price movements) fall within one standard deviation away from the mean (in our case, current stock price). 95% of potential stock price movements fall within two standard deviations. 99.7% of potential stock price movements fall within three standard deviations.
- Next, we need to multiply the standard deviation by the current stock price. You’d also want to take into account the number of days for which you’re estimating the stock price movement for. This will give you the increase and decrease of the stock price you can expect in a given time period. Here’s the formula:Where:
- S is the stock price.
- σ is the annual volatility of the stock (also referred to as standard deviation).
- n is the number of days for which you’d like to find out the expected stock price move for.

Let’s say that the stock price of an underlying asset is $62.25, and the implied volatility (standard deviation) is 20%. The number of days for which you’d want to know the range of stock price movements is 45 days. By using the formula you get:

What this says is that the stock price is likely to move $4.37 up or down in the next 45 days, given a 68% probability (we’re only looking at one standard deviation for now).

- Add the increase and decrease of the stock price you can expect in a given time period to the current stock price.The resulting stock range is between $57.88 and $66.62 in the next 45 days. By default, this is given a 68% probability, since we only used one standard deviation. What this means is that the stock price will be between that range in the next 45 days with a 68% probability.If we were to use two or three standard deviations, the formula would look like this:Two standard deviations:Three standard deviations:This would increase the range of potential future stock prices. For instance, with two standard deviations, the range increases in the next 45 days to between $53.51 and $70.99 with a 95% probability. And with three standard deviations, the expected range is between $49.14 and $75.36 in the next 45 days with a 99.7% probability.Here’s the work done in an Excel file:

## Advantages of Getting a Stock’s Estimated Price Range Using Implied Volatility

Why do investors use this formula to get the stock’s estimated price range? The bottom line is that any investor would like to make investing portfolio decisions that will earn returns. With the help of this formula, forming our assumptions on a stock’s price potential can largely benefit investors when making buy and sell decisions.

By looking into the __+__4.37 value from the example earlier, investors can assess whether or not that estimate is large or small. If your belief is that this value is too small and you expect greater potential for stock movement, then you’ll definitely that the option is a great buy. Whereas, if that value seems large, then you may be inclined to sell the option of that stock.

If your assumptions are correct and you utilized the formula, then you ultimately benefit from your return on investment.

Lastly, while it is important that we know about IV Rank which we can easily access from online screeners or through the assistance of your financial advisor (if you have one), it is equally important to understand what actually went into that IV Rank, by understanding the above formula.

## Making Decisions between Price Trends and Volatility

We have covered the importance of implied volatility in a pricing model when making wise investment decisions. But, how about looking into price trends?

Trends change when there are events that affect investors’ minds about the stock. Some of the factors that constitute these events could be supply and demand; earnings of a company’s stock; an industry’s trend; investors’ sentiments of certain breaking news within or outside of the country; company changes; and many more.

Stock charts show us that there is no one single stock with prices that go up continuously or in a straight line. They zigzag in a general upward direction in a bull market and down in a bear market. The general direction of a stock’s price is the trend. In essence, you need to be able to properly distinguish normal volatility in the context of a trend so that you can make effective investment decisions.

## Volatility Indices

Today, investors have more means to stay updated with the current and expected volatilities of their chosen portfolios implied by options prices. Some benchmarks are the Volatility Indexes provided by the Chicago Board Options Exchange (CBOE). The Board calculates and updates the prices of several volatility indexes which are designed to measure the volatility expectations by the market, implicit in the option prices. The indexes are leading measurements of investor sentiment and market volatility related to listed options.

As you can see, most investors don’t really have to make all the calculations themselves when it comes to figuring the expected volatility of a security. With various stock charts and volatility indexes available today, investors don’t have to spend a lot of time manually calculating Implied Volatilities, Call or Put Options prices, and Expected Stock Range, unless they don’t have tools that allow them to do this effectively and provide an edge over the market. We here at OptionParty go one step further by calculating probabilities on the entire market so individual investors don’t have to. Try it for yourself using our free 14 day trial here.

The most popular Volatility Index is the CBOE Volatility Index ($VIX). It measures the implied volatility for a group of out-of-the-money put and call options for S&P 500 stocks.

There is generally an inverse relationship between the VIX and the stock market. This is because markets go down a lot faster than they go up, which means volatility is higher during down markets. Also, investors are more cautious during uncertain times when prices drop, which increases price fluctuations, and therefore volatility.

Let’s look at an example of the VIX chart.

In this chart, as of Aug. 11 2016, we see that the implied volatility as measured by the VIX was 11.55%. By just looking at the chart, how are our investment decisions driven? When we see that there is a decline in the implied volatility, there is a decrease in option prices. It’s one of many good indicators to help investors decide when to buy or sell options. If you believe the VIX is overstated or overvalued, you should be selling options. If you believe the VIX is undervalued and that more implied volatility can be expected, this is one indicator to suggest that it’s a good option buying opportunity time.

## FINAL WORDS

Implied volatility is an important aspect for determining a stock’s potential future price movement, especially for short-term option sellers. While it may have its limitations, many investors rely on factors other than implied volatility, such as Implied Volatility Rank (IVR), expected stock price ranges, and Volatility Indexes as well.

While trends and indicators in the stock market help you achieve investment returns in the stock market and options trading, remember not to neglect your financial goals, risk appetite, and investment constraints.