Try Hack Me Volatility

[Tijuana Strauhal]

AdamHayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Volatility is a statistical measure of the dispersion of data around its mean over a certain period of time. It is calculated as the standard deviation multiplied by the square root of the number of time periods, T. In finance, it represents this dispersion of market prices, on an annualized basis.

Volatility is often used to describe risk, but this is not necessarily always the case. Risk involves the chances of experiencing a loss, while volatility describes how much and quickly prices move. If increased price movements also increase the chance of losses, then risk is likewise increased.

Whether volatility is good or bad depends on what kind of trader you are and what your risk appetite is. For long-term investors, volatility can spell trouble, but for day traders and options traders, volatility often equals trading opportunities.

Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option).

For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the width of the distribution increases as time increases. This is because there is an increasing probability that the instrument's price will be farther away from the initial price as time increases. However, rather than increase linearly, the volatility increases with the square-root of time as time increases, because some fluctuations are expected to cancel each other out, so the most likely deviation after twice the time will not be twice the distance from zero.

Since observed price changes do not follow Gaussian distributions, others such as the Lvy distribution are often used.[1] These can capture attributes such as "fat tails".Volatility is a statistical measure of dispersion around the average of any random variable such as market parameters etc.

For any fund that evolves randomly with time, volatility is defined as the standard deviation of a sequence of random variables, each of which is the return of the fund over some corresponding sequence of (equally sized) times.

The formulas used above to convert returns or volatility measures from one time period to another assume a particular underlying model or process. These formulas are accurate extrapolations of a random walk, or Wiener process, whose steps have finite variance. However, more generally, for natural stochastic processes, the precise relationship between volatility measures for different time periods is more complicated. Some use the Lvy stability exponent α to extrapolate natural processes:

Roll (1984) shows that volatility is affected by market microstructure.[3] Glosten and Milgrom (1985) shows that at least one source of volatility can be explained by the liquidity provision process. When market makers infer the possibility of adverse selection, they adjust their trading ranges, which in turn increases the band of price oscillation.[4]

Volatility does not measure the direction of price changes, merely their dispersion. This is because when calculating standard deviation (or variance), all differences are squared, so that negative and positive differences are combined into one quantity. Two instruments with different volatilities may have the same expected return, but the instrument with higher volatility will have larger swings in values over a given period of time.

Although the Black-Scholes equation assumes predictable constant volatility, this is not observed in real markets. Amongst more realistic models are Emanuel Derman and Iraj Kani's[5] and Bruno Dupire's local volatility, Poisson process where volatility jumps to new levels with a predictable frequency, and the increasingly popular Heston model of stochastic volatility.[6][link broken]

It is common knowledge that many types of assets experience periods of high and low volatility. That is, during some periods, prices go up and down quickly, while during other times they barely move at all.[7] In foreign exchange market, price changes are seasonally heteroskedastic with periods of one day and one week.[8][9]

Periods when prices fall quickly (a crash) are often followed by prices going down even more, or going up by an unusual amount. Also, a time when prices rise quickly (a possible bubble) may often be followed by prices going up even more, or going down by an unusual amount.

Measures of volatility depend not only on the period over which it is measured, but also on the selected time resolution, as the information flow between short-term and long-term traders is asymmetric.[clarification needed] As a result, volatility measured with high resolution contains information that is not covered by low resolution volatility and vice versa.[10]

The risk parity weighted volatility of the three assets Gold, Treasury bonds and Nasdaq acting as proxy for the Marketportfolio[clarification needed] seems to have a low point at 4% after turning upwards for the 8th time since 1974 at this reading in the summer of 2014.[clarification needed][citation needed]

Some authors point out that realized volatility and implied volatility are backward and forward looking measures, and do not reflect current volatility. To address that issue an alternative, ensemble measures of volatility were suggested. One of the measures is defined as the standard deviation of ensemble returns instead of time series of returns.[11] Another considers the regular sequence of directional-changes as the proxy for the instantaneous volatility.[12]

One method of measuring Volatility, often used by quant option trading firms, divides up volatility into two components. Clean volatility - the amount of volatility caused standard events like daily transactions and general noise - and dirty vol, the amount caused by specific events like earnings or policy announcements.[13] For instance, a company like Microsoft would have clean volatility caused by people buying and selling on a daily basis but dirty (or event vol) events like quarterly earnings or a possibly anti-trust announcement.

Breaking down volatility into two components is useful in order to accurately price how much an option is worth, especially when identifying what events may contribute to a swing. The job of fundamental analysts at market makers and option trading boutique firms typically entails trying to assign numeric values to these numbers.

Using a simplification of the above formula it is possible to estimate annualized volatility based solely on approximate observations. Suppose you notice that a market price index, which has a current value near 10,000, has moved about 100 points a day, on average, for many days. This would constitute a 1% daily movement, up or down.

Volatility thus mathematically represents a drag on the CAGR (formalized as the "volatility tax"). Realistically, most financial assets have negative skewness and leptokurtosis, so this formula tends to be over-optimistic. Some people use the formula:

Previous research by Pew that studied longer-term, two-year income shifts showed that many families face significant changes in income: As of 2011, 43 percent of families endured swings of more than 25 percent.4 Such fluctuations, also called income volatility, make it difficult for families to plan, pay regular expenses, save, or pay down debt.5 But little research has investigated and compared the impact of changes in year-to-year income on American families, including those of different incomes, races, education levels, and ages. Moreover, data dividing volatility into gains and losses are scarce, making it difficult to examine how families adapt to these different experiences; the research that does exist has focused largely on income loss because it is so detrimental to family financial health.

This analysis aims to fill that gap by exploring what, if any, differences exist between families that experienced income volatility and those that did not, as well as between those that had income gains and those that had losses, and by examining the relationship between income volatility and overall family financial security.

* Age cohorts are defined using thresholds from the Pew Research Center. At the time of the 2014 survey, millennials were ages 18 to 33, Gen Xers were 34 to 49, baby boomers were 50 to 68, and members of the silent generation were 69 to 86.

Although income volatility is more prevalent among certain households, these findings show that changes in annual income can affect all types and that despite improving macroeconomic indicators, many Americans still feel financially precarious. Understanding the factors that have an impact on family balance sheets can help policymakers develop better programs and policies to improve short-term economic stability and, in turn, improve household financial security.

For many families, household income is not steady.6 Fluctuations typically occur during changes in household composition, such as marriage or childbirth, or transitions such as retirement, and these changes can be anticipated and planned for. However, some income shifts are not entirely expected. For example, a breadwinner may face diminished work hours or become ill. Alternately, a family member may receive a promotion or a bonus.7 In addition, the size of these income dips and spikes or whether they will be one-time, repeated, or ongoing occurrences may not be known in advance. Among many factors that inhibit household financial stability, large income swings may make it challenging to plan and budget and may leave families feeling less financially stable.

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