Standard Deviation And Volatility

Traders typically calculate volatility for an underlying contract by observing price changes at regular intervals. Let’s begin by assuming that we plan to observe price changes at the end of every day. Because there are 365 days in a year, it might seem that prices can change 365 times per year. In this text, though, we are focusing primarily on exchange-traded contracts. Because most exchanges are closed on weekends and holidays, if we observe the price of an underlying contract at the end of every day, prices cannot really change 365 times per year. Depending on the exchange, there are probably somewhere between 250 and 260 trading days in a year.3 Because we need the square root of the number of trading days, for convenience, many traders assume that there are 256 trading days in a year given that the square root of 256 is a whole number, 16. If we make this assumption, then

To approximate a daily standard deviation, we can divide the annual volatility by 16.

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Returning to our contract trading at 100 with a volatility of 20 percent, what is a one standard deviation price change from one day to the next? The answer is 20%/16 = 1¼%, so a one standard deviation daily price change is 1¼% × 100 = 1.25. We expect to see a price change of 1.25 or less approximately two trading days out of every three and a price change of 2.50 or less approximately 19 trading days out of every 20. Only one day in 20 would we expect to see a price change of more than 2.50.

We can do the same type of calculation for a weekly standard deviation. Now we must ask how many times per year prices can change if we look at prices once a week. There are no complete weeks when no trading takes place, so we must make our calculations using all 52 trading weeks in a year. Therefore,

To approximate a weekly standard deviation, we can divide the annual volatility by 7.2. Dividing our annual volatility of 20 percent by the square root of 52, or approximately 7.2, we get 20%/7.2 » 2.78. For our contract trading at 100, we would expect to see a price change of 2.78 or less two weeks out of every three, a price change of 5.56 or less 19 weeks out of every 20, and only one week in 20 would we expect to see a price change of more than 5.56.

If we want to be as accurate as possible, when estimating a daily or weekly standard deviation, we ought to begin by calculating the one-day or one-week forward price. But for short periods of time, the forward price is so close to the current price that most traders assume for convenience that a one-day or one-week distribution is centered around the current price. If we need to play some games at Stargames, then we simply go here at http://stargamesgutscheincode.blogspot.com.

Suppose that a stock is trading at $45 per share and has an annual volatility of 37 percent. What is an approximate one and two standard deviation price range from one day to the next and from one week to the next? For one day, we can divide the annual volatility by 16 (the square root of 256, the number of trading days in a year)