How the VIX is Calculated

Level: Advanced

Overview

The VIX (Volatility Index) is a benchmark of implied volatility for thirty days in the future. It was created by the Chicago Board Options Exchange, or CBOE, in 1993. This article will focus on what the VIX is, how it is calculated, and how it can be applied. This is a concise version of CBOE’s white paper report for the VIX, which is quite a long and mathematical read.

What is the VIX?

The VIX is a measure of implied volatility in the market. Implied volatility is simply the expectation for how much an underlying asset will move within one standard deviation.

The VIX originally was calculated based on the S&P 100 index at-the-money calls. However, it was revised a decade after it was introduced so that it was based on a wide range of strike prices for options on the S&P 500. We will be focusing on the newer calculation method.

VIX Formula

This is the formula for calculating the VIX:

σ is the VIX/100. That means that the VIX is σ * 100. Notice that the formula gives you the square of σ.
T is how much time there is until options expiration. More on this below.
∑ means summation (addition many times, don’t be scared). The i underneath means that i is a variable within the summation.
F is the forward index level. This is basically what people are predicting the S&P 500 index will be at in the future, based on options prices.
Ko is the first strike below the forward index level.
Ki is also a strike price, but of the ith out-of-the-money option. Remember the summation? For each value of i, Ki will change too. Ki is the strike of a call option if Ki is greater than Ko, a put option if Ki is less than Ko, and if they are equal it is the strike of both the put and call.
∆Ki is just the interval or difference between strike prices around Ki.
R is the risk-free interest rate until expiration. This is not determined by options but rather by bonds. This is for the U.S. Treasury Bill maturing closest to the options contract.
Q(Ki) is the quote or the price of the Ki option. It is the average of the bid and the ask.

That’s all! The raw equation is quite simple, but some of the values used in the calculation require more in-depth analysis.

Keep in mind that the VIX measure expectations for 30 days, or a month, in the future. The time to expiration is calculated as follows:

T = {M_(Current day) + M_(Settlement day) + M_(Other days)} / Minutes in a year

M_(Current day) is how many minutes are left until midnight today.
M_(Settlement day) is how many minutes are from midnight on the settlement day to 8:30 AM for standard options, and till 3 PM for weekly options.
M_(Other days) is how many minutes are in the days between today and expiration

As we can see, T is just a fraction of the year representing how long it is until settlement of a contract.

VIX Calculation Process

This information is a simplified version of CBOE’s white paper on VIX calculation. The steps CBOE uses to calculate the VIX figure are outlined here:

Select the options to be used in the VIX calculation. For EACH month:
1. Take the the strike price at which the difference between prices for calls and puts is the smallest (price is the average of bid and ask). Do this for both the near term (or current term) expiration and the next term expiration.
2. F = Strike Price from above + e^(RT) x (Call Price – Put Price). Recall that this is the forward index level, or F. You will get F1 for the near term and F2 for the next term options.
3. Take Ko as the strike price below F. You will get two of these for each value of F: one for the near term, one for the next.
4. Start iterating through the put options with strike prices less than Ko, and go down from there. Skip ones with bid prices of zero. If two consecutive strikes have bids of zero, stop. Select all of the options iterated through here for use later.
5. Start iterating through the call options with strike prices greater than Ko, and go up from there. Skip ones with bid prices of zero. If two consecutive strikes have bids of zero, stop. Select all of the options iterated through here for use later.
6. Select both the call and put with strike Ko. This will be treated as a single contract in the formula, with the prices for the call and put averaged.
Calculate volatility or the σ values using the above formula for both near-term and next-term options (these are the contracts and values calculated in the outer step 1). The weighting of any contract to the VIX value is proportional to ΔK (the difference between strikes) and the price of the option. It is inversely proportional (negatively affected by) to the square of the option’s strike price.
Calculate the 30-day weighted average of σ1 squared and σ2 squared. Square root that value and multiply it by 100 to get the VIX (look back at the VIX Formula section).

How the VIX is Used

The VIX itself is just a number used to gauge the amount of “fear” in the market. The nature of the VIX’s usefulness arises from the formula above, and is essentially provided by looking at how much people are paying for options (protection) from a market move. In terms of raw values, values above 32 are times of fear, and options pricing is generally more conducive toward premium sellers. On the other hand, values below 16 reflect a calmer market in which premium buyers get a better deal.

Over the years, the VIX has evolved from being just a number. Futures on the VIX index itself trade also, and multiple ETFs are plays on where the VIX will move.

Summary

The VIX is a powerful tool that uses a simple formula to calculate the amount of “fear” in the market. Although the raw calculation process is a bit dreary, understanding it will allow you to realize from where the VIX derives its meaningfulness. Of course, computers now track the index and its value is widely accessible on the web. Hopefully, this article has provided you insight on the inner workings of the CBOE Volatility Index.

Volume

Level: Beginner

This is a beginner level education blog, which means that this is a topic that is introductory and has been covered by our club long before. These should be review and an easy read. Intermediate level articles might contain content intriguing to officers, but not too advanced topics. Advanced blogs are reserved for Michael Trehan for now.

Volume is a powerful tool used by many technical analysts to measure other traders’ level of interest in a particular stock. In addition, it can be used to confirm trend continuations or reversals. It is calculated as follows:

Volume = Shares Traded / Time period

Now let’s further simplify some of the terms here.

Shares Traded: The number of shares that were either bought or sold (it does not matter which you use, the number will be the same) throughout the time period
Time Period: The amount of time being tracked (e.g. 1 hour, 1 day, 1 week)

For example, if 5,000,000 shares of ABC were sold over the week, then its average volume for each day would be 1,000,000. Keep in mind that the number of sellers must equal the number of buyers. If it does not, the price will move up or down until it does.

Technical analysts regularly use volume to determine the strength or weakness of a market move. As an example, one day XYZ shares increased considerably. If the volume for that day was high, it means that tons of buyers wanted the shares. This buying pressure created a strong uptrend which was difficult for bears to fight. However, if the volume was low, it means that buyers did not want ABC shares that badly. The only reason the stock moved up that day was because there were few sellers to keep the price down. This created a very weak trend which could easily be reversed if some sellers enter the market. With this in mind, several events can cause tremendous buying or selling pressure: an earnings report, a manufacturing recall, etc. This pressure then causes the volume to spike.

Many websites like FINVIZ and StockCharts automatically display the volume when a ticker is viewed. The volume appears as a bar chart at the bottom of the display. In addition, the volume bar will be either green or red, depending on the performance of the underlying stock that day.

-Ken Croker

Greeks

Level: Intermediate

I will be bringing you more advanced education blogs that are outside the scope of the club currently.

What are your Greeks? Take a peek.

Delta: Your option price moves by DELTA amount for each dollar the underlying moves. However, even delta can change…

Gamma: Your DELTA moves by GAMMA amount for each dollar the underlying moves. This is the derivative of DELTA.

Vega: Measures how much the option price moves in relation to volatility.

Theta: Each day, how much your option price decays. This could be good or bad depending on whether you are a buyer or seller.

Rho: How much the option price is affected by interest rates. Not that commonly used.

Use these in conjunction with implied volatility and theoretical pricing tools like the Black Scholes model (more on that later) for the best success in choosing strike prices and expirations.

– Michael

P/E Ratios

Level: Beginner

Michael: Welcome to our third issue of the education blog! Notice that there is a line above that tells you the level of the education blog. Beginner means that it is intended for everyone, and usually the topics stay in line with our meetings. Intermediate is for officers and anyone else who is ahead in the meetings, while Advanced is for me to introduce or discuss topics that are currently out of the scope of the club. Our topic this time around is the P/E ratio. Ken will explain to you in simple language what the P/E ratio tells you, how it is calculated, and how it is used.

Ken: The Price-to-Earnings (P/E) ratio is a powerful tool that we can use to determine, on a basic level, how other investors feel about a certain company. To be more specific, it is a fundamental analysis ratio that measures how much money investors are willing to pay for one dollar of earnings. Low P/E ratios suggest that other investors are not as confident in a company as they should be and have therefore oversold the stock. On the other hand, high P/E ratios suggest that investors are overconfident in a company and have therefore overbought the stock. However, a single company’s P/E ratio by itself is useless. In order to gain insight on a company, we must compare its P/E ratio to that of other companies operating in the same sector (type of product or service). The P/E ratio is calculated as follows:

P/E ratio = Share Price divided by Earnings Per Share (EPS)

EPS = Net Income divided by Number of Shares

Translating that financial jargon into English:

Net Income: The amount of money the company earned (usually in the past year)
Average Outstanding Shares: The total number of a company’s shares owned by investors, whether retail or institutional

For example, XYZ had a net income of $200 million last year. XYZ has 100 million shares of stock, each priced at $50. The EPS for XYZ Inc. would be $200 million / 100 million = $2. Since the price is $50 and the EPS is $2, the P/E ratio would be 25. Let’s compare them to ABC, who operates in the same sector. ABC, with 50 million shares, made $150 million last year. Its EPS would therefore be $150 million / $50 million = $3. Each share is currently trading at $45, giving ABC a P/E ratio of $45 / $3 = 15. The P/E ratios of XYZ and ABC show that investors are willing to pay more for XYZ’s earnings than ABC’s earnings. Investors could also be valuing XYZ more than they should, causing XYZ’s stock to fall when the market corrects itself.

Therefore, P/E can be a powerful tool determining when a stock is overvalued or undervalued. However, just because a company’s P/E ratio is relatively low or high does not mean it is undervalued or overvalued. A company could be reporting outstanding earnings, but if it is taking on massive amounts of debt to get there, investors will not be as excited. This lack of confidence will drop the price, thus lowering the P/E ratio. When making trading decisions, use the P/E ratio in accordance with other fundamental ratios for the best result.

– Ken Croker

Candlesticks

First of all, what is a chart? A chart of a stock graphs a stock’s price on the y-axis, and time on the x-axis. You probably are familiar with simple line charts, but candlestick charts provide more information and are more commonly used.

Look at the diagram of the chart below. The box, or “candle” is the body of the candle. Each candle represents a certain amount of time, usually a day. The wicks of the candle are technically referred to as the “wicks,” but they are referred to by their purpose (high or low) in common language. The ends of the body are formed by the opening and closing prices of the security during this time period. If the body is filled with a color like white, green, or a light color, then the security was up in that period of time, and the bottom of the body is the opening price and the top is the closing price. On the other hand, if the body is filled with a color like black, red, or some other dark color, then the security was down in that period of time, and the top of the body is the opening price and the bottom is the closing price.

Candlesticks The wick shows the extremes of price action during the time period. The upper wick is the line extending from the top of the body to the highest price ever reached (during the specified time period), and the lower wick is the line extending from the bottom of the body to the to the lowest price ever reached. Sometimes, one or both of the wicks are not seen because the opening or closing price is also the highest or lowest price.

Here is some more terminology: Let’s say that we have a chart where each candle represents a day, and there are enough candles to show the past year. That would be called a one-year daily chart. If each candle represented an hour, and there are candles going back 180 days, then it would be a 180 day hourly chart.

Also, be careful not to confuse candlesticks with OHLC (open-high-low-close) charts. Candlesticks have a rectangular body, while OHLC charts are lines with tick marks on the vertical line. The candlestick has many advantages over the traditional line chart. When we get into more analysis, we will see that candles can show buying and selling pressure throughout the day and provide earlier indications of market reversals. As a result, many traders use them and some even base strategies off of them. However, candlesticks do not always tell the sequence in which events happened (e.g. whether the high or low came first). Many websites, like FINVIZ and TradingView, use candlestick charts by default.

– Michael Trehan

What is Shorting?

Hello from the Finance Club 2014 Officers!

President: This is the education blog, which is written by our VP. Usually, this one will be published on Sundays. So, for our first issue… what does SHORTING a stock mean?

Vice President: Shorting a stock is method by which one can make the most money if the stock goes DOWN. We have all heard the phrase “buy low, sell high.” This is the same idea in reverse, so our goal in shorting is to “sell high, buy low.” In order to do this, we would:

Borrow shares of a stock (typically from a broker).
Sell the shares on the open market.
Wait for the stock price to decrease.
Once the stock price has decreased, buy the same number of shares from the open market.
Repay those shares to our lender to close the trade.

Shorting diagram

For example, Jason, a value investor, believes that QRS stock, currently trading at $70, is heavily overvalued. To short the QRS stock, he first borrows 100 shares from his broker. He then sells his borrowed shares of QRS on the open market for $70 * 100 = $7,000. Eventually, he must buy back the shares from the market to repay his broker. Three months later, when the price of QRS falls to $55 a share, Jason buys 100 shares from the open market for $55 * 100 = $5,500. Finally, he gives his broker the shares he just bought to close the trade. Through shorting, Jason has realized (or made) a profit of $7000 – $5500 = $1500. Of course, there are commissions.

In order to short a stock on our stock simulator:

Go to www.wallstreetsurvivor.com and log in.
Scroll down to the section that says Make a Trade and click on the title.
Type in the stock to be shorted in the search bar.
When it asks if you want to buy or sell, expand the bar and click Short.
Decide the type of order you want and how many shares you want to short.
Make the trade.

To close the trade:

When it asks if you want to buy or sell, expand the bar and click Cover.
Enter in the same number of shares you previously shorted.
Decide the type of order you want (ex. limit, market, etc.)
Click the Trade button to close the trade.

– Ken Croker, VP.