Skewness risk
Encyclopedia
Skewness risk in financial modeling
denotes that observations are not spread symmetrically around an average
value. As a result, the average and the median
can be different. Skewness risk applies to any quantitative model that relies on a symmetric distribution (such as the normal distribution).
Ignoring skewness risk, by assuming that variables are symmetrically distributed when they are not, will cause any model to understate the risk of variables with high skewness.
Skewness risk plays an important role in hypothesis testing. The analysis of variance
, the most common test used in hypothesis testing, assumes that the data is normally distributed. If the variables tested are not normally distributed because they are too skewed, the test cannot be used. Instead, nonparametric tests can be used, such as the Mann–Whitney test for unpaired situation or the sign test
for paired situation.
Skewness risk and kurtosis risk
also have technical implications in calculation of value at risk
. If either are ignored, the Value at Risk calculations will be flawed.
Benoît Mandelbrot
, a French mathematician, extensively researched this issue. He feels that the extensive reliance on the normal distribution for much of the body of modern finance and investment theory is a serious flaw of any related models (including the Black–Scholes model and CAPM). He explained his views and alternative finance theory in a book: The Misbehavior of Markets.
In options markets, the difference in implied volatility at different strike prices represents the market's view of skew, and is called volatility skew. (In pure Black–Scholes, implied volatility is constant with respect to strike and time to maturity.)
Financial modeling
Financial modeling is the task of building an abstract representation of a financial decision making situation. This is a mathematical model designed to represent the performance of a financial asset or a portfolio, of a business, a project, or any other investment...
denotes that observations are not spread symmetrically around an average
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....
value. As a result, the average and the median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
can be different. Skewness risk applies to any quantitative model that relies on a symmetric distribution (such as the normal distribution).
Ignoring skewness risk, by assuming that variables are symmetrically distributed when they are not, will cause any model to understate the risk of variables with high skewness.
Skewness risk plays an important role in hypothesis testing. The analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
, the most common test used in hypothesis testing, assumes that the data is normally distributed. If the variables tested are not normally distributed because they are too skewed, the test cannot be used. Instead, nonparametric tests can be used, such as the Mann–Whitney test for unpaired situation or the sign test
Sign test
In statistics, the sign test can be used to test the hypothesis that there is "no difference in medians" between the continuous distributions of two random variables X and Y, in the situation when we can draw paired samples from X and Y...
for paired situation.
Skewness risk and kurtosis risk
Kurtosis risk
Kurtosis risk in statistics and decision theory denotes the fact that observations are spread in a wider fashion than the normal distribution entails...
also have technical implications in calculation of value at risk
Value at risk
In financial mathematics and financial risk management, Value at Risk is a widely used risk measure of the risk of loss on a specific portfolio of financial assets...
. If either are ignored, the Value at Risk calculations will be flawed.
Benoît Mandelbrot
Benoît Mandelbrot
Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...
, a French mathematician, extensively researched this issue. He feels that the extensive reliance on the normal distribution for much of the body of modern finance and investment theory is a serious flaw of any related models (including the Black–Scholes model and CAPM). He explained his views and alternative finance theory in a book: The Misbehavior of Markets.
In options markets, the difference in implied volatility at different strike prices represents the market's view of skew, and is called volatility skew. (In pure Black–Scholes, implied volatility is constant with respect to strike and time to maturity.)