Market Volatility

There are many ways to measure volatility but there is no definitive calculation which applies for all situations. Though volatility is an idea we are somewhat familiar with and have experienced, it is not always an easy concept to mathematically measure. Much work has been done on measuring and attempting to predict the volatility of the market.

The first, and simplest way, is to look at the absolute change in price. This is a way many people look at volatility. A market trading at 100 moves to 105. The absolute change is 5.

The second way is to look at the percentage change in price. In the previous example, the move from 100 to 105 would be a 5% change.

The next way is one of the most common methods used to determine volatility for option valuation. Volatility for option evaluation is the standard deviation of price changes. The standard deviation is normally calculated using the closing prices.

To get an annualized volatility when daily prices are used, the standard deviation must be multiplied by the square root of the number of trading days. Since there are approximately 250 trading days in a year the square root of 250 is approximately 16. If weekly prices are used, the square root of 52 is used. Closing prices are normally used in the calculation but highs, lows and opens are equally acceptable.

Since daily prices are used, the annualized volatility is obtained by multiplying the three-day volatility by 16. Therefore, the annualized volatility is equal to 5. 16 = 80%.

Volatility numbers should not be intimidating, and, in fact are quite easy to use. Since they are based on percentages they are similar to measuring market change on a percentage basis. For example, if the market is currently at 100 and the annualized volatility is 25%, the market can be expected to trade up to 125 or down to 75 about 68% of the time during the year. This is obtained by:

1. Dollar move   = 100 x 0.25

                        = 25

2. Potential upside move   = 100 + 25

                                       = 125

3. Potential downside move   = 100 - 25

                                           = 75

When did the 68% come from in the previous example? In statistics the standard deviation is a range about the mean which can be estimated by certain percentages:

 

1. A 1-standard deviation move includes approximately 68% of all possible moves.

2. A 2-standard deviation move includes approximately 95% of all possible moves.

3. A 3-standard deviation move includes almost 100% of all possible moves.

 

In this example 1-standard deviation is equal to 25. A 2-standard deviation or 50 point move would account for almost 95% of all occurrences.

Volatility calculations are integral in evaluating the theoretical value of options. The Black Scholes model, discussed, was a pioneering breakthrough in determining option prices and employed volatility calculations like these.