# Variance

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```					Variance

In mathematics - probability theory and statistics, we learnt that variance is a description of how far
values in a data sample lies from the mean, and that variance is one of the moments of a distribution

The standard deviation of a data set is the square root of its variance

Source: ngureco

Standard Deviation

We also learnt that Standard deviation is a measure of variability or diversity that shows how much
variation there is from the mean. The standard deviation of a data set is the square root of its variance.

To the right is the formula for standard deviation.

Risk in an Investment

In finance, standard deviation is used in determining risk in an investment – that is, standard deviation
provides investors with a mathematical basis for their investment decisions. If you would want to trade
stocks, bonds, stock options, property, mutual funds, index mutual funds, and ETFs, when you get in to
the market you will definitely be hearing much about standard deviation. Standard deviation in finance
is known as volatility.

Volatility

In the stock market and financial markets, volatility refers to the standard deviation of a financial
instrument within a given time frame. Volatility is thus used to quantify the risk of the financial
instrument over the given time period. In finance, volatility is calculated over a given time period and
then expressed in annualized terms as a percentage.

In mathematics we know that
volatility refers to the standard deviation of a financial instrument

log(10) = 1

And that log(10) = 1, we then break that formula a little bit more (outside the scope of this article) to get
volatility as follows:

Let P = LN{(high price)/(low price)}²

where LN is log normal.

Volatility =√(P) * √(252) * 100

We use 252 to annualize because there are 252 trading days in a year and we multiply by 100 to have
volatility as a percentage.

If we use the high and low prices for a stock in intraday trading, we get a different annualized volatility
value than from when we use high and low prices for weekly or monthly data. So, when you calculate
less volatile on end of day to end of day trading, and so on and so forth.

Excel Formula for Volatility

In MS excel, we can easily compute the volatility of a security or a stock as follows: in this case, we take
daily volatility and average for say, the last ten trading days, before annualizing the same

In column A1, B1, and C1, input the high, low and closing prices of a stock. The data can be obtained free
from Yahoo Finance, or anywhere else from internet. Input data for several days; say for the last 100
Calculate P in column D1 by inputting the formula “={LN((A1)/(B1))}^2”

Calculate Volatility in column E1 by inputting the formula “=SQRT(SUM(D1:D10)/10)*SQRT(252)*100”

Notice we did not use C1 which is the closing price.

The above therefore is the Excel Formula for Volatility (which is also the excel formula for standard
deviation).

A stock with a higher volatility has a higher return and a higher risk. The opposite is also true.

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Implied Volatility

In stocks, we have stock options. You can read the options basics elsewhere. Ideally, a stock option
should have volatility equal to that of the underlying stock. When the price of a stock option is
calculated using the volatility of the underlying stock, we get the theoretical price of the option. But
hardly do options have volatility equal to that of the stock. The volatility implied by stock options can be
higher or lower depending on how the market views the options. The options volatility is therefore
called implied volatility. When implied volatility of options is high we say options’ premium is high. The
opposite is also true.

As much as 90% of options traders do not consider implied volatility when trading options and if they do
they do not know how to trade it. Implied volatility is the single most important variable in the pricing of
an option. Let’s consider the QQQQ trading at \$50 in November 22. Lets then consider the call option
with a strike price of 51 for the same QQQQ that will expire in January next year and compare prices at
different implied volatility. Everything else will be retained the same:

At implied volatility equals 20, the price of the option is \$1.31

At implied volatility equals 21, the price of the option is \$1.40

At implied volatility equals 25, the price of the option is \$1.72

At implied volatility equals 50, the price of the option is \$3.77

At implied volatility equals 75, the price of the option is \$5.82

At implied volatility equals 100, the price of the option is \$7.85

Its quit normal for implied volatility to change from 20% to 21% and it happens almost everyday. If you
had invested \$131,000 in such options you will find your investment is now worth \$140,000. The
opposite is also true. If the implied volatility was to increase from 20% to 50%, your \$131,000 will
become \$377,000. And that can happen in a day. The opposite is also true.

To try to trade uncovered options is very risky and is not advised for beginning traders. Keep off! This is
as good as having a flame next to petrol and before you realize there is fire you are already burnt.

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The best trading strategies for beginning traders in options are those that use a combination of long
options and short options such that when the long option loses, the short option gains. A good example
is the option strategy known as calendar spread or horizontal spread. A calendar spread is an option
trading strategy where a trader simultaneously purchases options expiring in a particular month and sell
equal number of options of the same stock expiring in another month. The difference between the legs
of the spread is only the expiration month; the options are based on the same underlying market and
strike price. Options strategies involving combination of long and short legs are safer and more traders
should trade them than they are currently doing.

way to help would be to link back to this webpage from your web page, blog, or discussion forums.

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