When market volatility intensifies or stagnates, financial websites, bloggers, social media, newspapers and TV commentators will all mention VIX^{®}The official name of VIX is the CBOE Volatility Index, which is a benchmark index specifically used to track the volatility of the Standard & Poor’s 500 Index. Most investors familiar with VIX usually call it a “fear indicator” because it has become a representative of market volatility.

VIX was created by the Chicago Board Options Exchange (CBOE), which claims to be “the largest US options exchange and creator of listed options.” The Chicago Board Options Exchange operates a for-profit business that sells (among other things) investments to experienced investors. These include hedge funds, professional money managers, and individuals seeking to profit from market volatility. In order to promote and encourage these investments, the Chicago Board Options Exchange developed VIX, which can track market fluctuations in real time.

Although the mathematical principles behind the calculations and accompanying explanations occupy most of the 15-page white paper published by CBOE, we will provide highlights in the overview. The following is the calculation behind VIX, provided by examples and information provided by CBOE.

Key points

- VIX is a benchmark index specifically designed to track the volatility of the Standard & Poor’s 500 Index.
- VIX is calculated using a formula, and the expected volatility is derived from the weighted prices of average out-of-the-money put options and call options.
- Volatility is useful to investors because it provides them with a way to measure the market environment; it also provides investment opportunities.

## For those who are slightly curious, take a look at VIX

The Chicago Board Options Exchange provides the following formula as a general example for calculating VIX:

$$

σ

2

=

2

Ton

∑

A generation

Δ

Potassium

A generation

Potassium

A generation

2

electronic

resistance

Ton

ask

(

Potassium

A generation

)

–

1

Ton

[

F

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−

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2

sigma^2 = frac{2}{T}sum_i frac{Delta K_i}{K_i^2}e^{RT} Q(K_i)-frac{1}{T}left [frac{F}{K_0} – 1right]^2

σ2=Ton2∑A generationPotassiumA generation2ΔPotassiumA generationelectronicresistanceTonask(PotassiumA generation)–Ton1[KF−1]2

For most people who do not make a living from mathematics, the calculations behind each part of the equation are quite complicated. They are also too complicated to be fully explained in a short article, so let’s add some numbers to the formula to make the math easier to understand:

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σ

2

=

2

1

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6

5

2

5

,

6

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.

6

6

4

7

2

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6

1

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9

2

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4

3

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2

6

1

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9

2

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1

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+

σ

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9

2

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,

6

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.

6

3

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1

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5

2

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begin{aligned} sigma^2 =& tfrac{21,600}{525,600} times 0.066472 times left (tfrac{61,920-43,00}{61,920-21,600} right) +\ phantom{ sigma^2 =)& tfrac{61,920}{525,600} times 0.063667 times left (tfrac{43,200-21,600}{61,920-21,600} right) times tfrac{043667 times left sigma ^2 =& 0.0643180321 \ sigma =& 0.253610 \ end{alignment}

σ2=σ2=σ2=σ= 525,621,6×.66472×(61,92–21,661,92–43,2)+ 525,661,92×.63667×(61,92–21,643,2–21,6)×43,2525,6 .64318321 .25361

$$

Volt

A generation

X

=

1

×

σ

=

2

5

.

3

6

VIX = 100 times sigma = 25.36

VoltA generationX=1×σ=25.36

## Delve into the details of the volatility index

VIX is calculated using the formula of deriving the expected volatility from the weighted prices of average out-of-the-money put options and call options. Using options that expire in 16 days and 44 days respectively, we will start from the leftmost side of the formula in the example below. The symbol on the left of “=” means that the number obtained by calculating the square root of the sum is multiplied by 100.

To get the number:

- The first group of numbers to the right of “=” represents time. This number is determined by dividing the expiration time (in minutes) of the most recent term option by 525,600, which represents 365 days in a year. Assuming that the VIX calculation time is 8:30 am, the expiration time of the 16-day option will be the number of minutes between 8:30 am today and 8:30 am on the settlement day. In other words, the expiry time does not include today’s midnight to 8:30 am, nor does it include 8:30 am to midnight on the settlement day (not including the full 24 hours). The number of days we will use is technically 15 (16 days minus 24 hours), so it is 15 days x 24 hours x 60 minutes = 21,600. Use the same method to obtain the expiration time (in minutes) of the 44-day option to obtain 43 days x 24 hours x 60 minutes = 61,920 (step 4).
- The result is multiplied by the volatility of the option, which is represented by 0.066472 in the example.
- Then multiply the result by the number of minutes until the next term option expires (61,920) minus the number of minutes within 30 days (43,200). This result is divided by the number of minutes the next term option expires (61,920) minus the number of minutes the recent option expires (21,600). In case you want to know where 30 days come from, VIX uses a weighted average of options, which have a fixed expiration date of 30 days.
- The result will be added to the total time calculation for the second option, which is 61,920 divided by the number of minutes in 365 days of a year (525,600). As in the first calculation, the result is multiplied by the volatility of the option, which is represented by 0.063667 in the example.
- Next, we repeat the process in step 3, multiplying the result of step 4 by the number of minutes in 30 days (43,200) minus the number of minutes in which the recent option expires (21,600). We divide this result by the number of minutes until the next option expires (61,920) minus the number of minutes until the recent option expires (21,600).
- Then multiply the sum of all previous calculations by the number of minutes in 365 days of the year (525,600) and divide by the number of minutes in 30 days (43,200).
- The square root of this number multiplied by 100 equals VIX.

Obviously, the order of operations is crucial in calculations, and for most of us, calculating VIX is not the way we choose to spend Saturday afternoon. If we do this, the exercise will definitely take up most of the day. Fortunately, you never have to calculate VIX, because CBOE will calculate it for you. Thanks to the Internet, you can go online, enter the stock code VIX and immediately send the number to your screen.

## Investment volatility

Volatility is useful to investors because it provides them with a way to measure the market environment. It also provides investment opportunities. Since volatility is usually related to the negative performance of the stock market, volatility investments can be used to hedge risks. Of course, volatility can also signal a rapidly rising market. Regardless of whether the direction is upward or downward, volatility investment can also be used for hype.

As one might expect, the investment tools used for this purpose can be quite complex. VIX options and futures provide popular tools through which sophisticated traders can hedge or implement their hunches. Professional investors often use these.

Exchange-traded bills (an unsecured, non-subordinated debt securities) can also be used. ETNs that track volatility include iPath S&P 500 VIX short-term futures (VXX) and VelocityShares daily inverse VIX short-term futures (XIV).

Exchange-traded funds provide many investors with a more familiar tool. Volatility ETF options include ProShares Ultra VIX short-term futures (UVXY) and ProShares VIX mid-term futures (VIXM).

Before making an investment decision, you should thoroughly evaluate the pros and cons of each of these investment tools.

## Bottom line

Regardless of the purpose (hedging or speculation) or the specific investment tool chosen, you cannot invest in volatility without spending some time understanding the market, investment tools and the range of possible outcomes. Compared with making mathematical mistakes in VIX calculations, if you do not make proper preparations and adopt prudent investment methods, your personal bottom line will be more adversely affected.

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