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**PerformanceAnalytics**: Econometric tools for performance and risk analysis**skewness**: Skewness

# Skewness

### Description

compute skewness of a univariate distribution.

### Usage

1 |

### Arguments

`x` |
a numeric vector or object. |

`na.rm` |
a logical. Should missing values be removed? |

`method` |
a character string which specifies the method of computation.
These are either |

`...` |
arguments to be passed. |

### Details

This function was ported from the RMetrics package fUtilities to eliminate a
dependency on fUtiltiies being loaded every time. The function is identical
except for the addition of `checkData and column support.`

*Skewness(moment) = sum((x-mean(x))^3/var(x)^(3/2))/length(x)*

*skewness(sample) = sum(((x-mean(x))/var(x))^3)*n/((n-1)*(n-2))*

*Skewness(fisher)((sqrt(n*(n-1))/(n-2))*(sum(x^3)/n))/((sum(x^2)/n)^(3/2))*

where *n* is the number of return, *\overline{r}* is the mean of the return
distribution, *σ_P* is its standard deviation and *σ_{S_P}* is its
sample standard deviation

### Author(s)

Diethelm Wuertz, Matthieu Lestel

### References

Carl Bacon, *Practical portfolio performance measurement
and attribution*, second edition 2008 p.83-84

### See Also

`kurtosis`

### Examples

1 2 3 4 5 6 7 8 9 10 11 |

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- ActivePremium: Active Premium or Active Return
- AdjustedSharpeRatio: Adjusted Sharpe ratio of the return distribution
- apply.fromstart: calculate a function over an expanding window always starting...
- apply.rolling: calculate a function over a rolling window
- AppraisalRatio: Appraisal ratio of the return distribution
- AverageDrawdown: Calculates the average depth of the observed drawdowns.
- AverageLength: Calculates the average length (in periods) of the observed...
- AverageRecovery: Calculates the average length (in periods) of the observed...
- BernardoLedoitRatio: Bernardo and Ledoit ratio of the return distribution
- BetaCoMoments: Functions to calculate systematic or beta co-moments of...
- BurkeRatio: Burke ratio of the return distribution
- CalmarRatio: calculate a Calmar or Sterling reward/risk ratio
- CAPM.alpha: calculate single factor model (CAPM) alpha
- CAPM.beta: calculate single factor model (CAPM) beta
- CAPM.dynamic: Time-varying conditional single factor model beta
- CAPM.epsilon: Regression epsilon of the return distribution
- CAPM.jensenAlpha: Jensen's alpha of the return distribution
- CAPM.RiskPremium: utility functions for single factor (CAPM) CML, SML, and...
- CDD: Calculate Uryasev's proposed Conditional Drawdown at Risk...
- centeredmoments: calculate centered Returns
- chart.ACF: Create ACF chart or ACF with PACF two-panel chart
- chart.Bar: wrapper for barchart of returns
- chart.BarVaR: Periodic returns in a bar chart with risk metric overlay
- chart.Boxplot: box whiskers plot wrapper
- chart.CaptureRatios: Chart of Capture Ratios against a benchmark
- chart.Correlation: correlation matrix chart
- chart.CumReturns: Cumulates and graphs a set of periodic returns
- chart.Drawdown: Time series chart of drawdowns through time
- chart.ECDF: Create an ECDF overlaid with a Normal CDF
- chart.Events: Plots a time series with event dates aligned
- chart.Histogram: histogram of returns
- chart.QQPlot: Plot a QQ chart
- chart.Regression: Takes a set of returns and relates them to a market benchmark...
- chart.RelativePerformance: relative performance chart between multiple return series
- chart.RiskReturnScatter: scatter chart of returns vs risk for comparing multiple...
- chart.RollingCorrelation: chart rolling correlation fo multiple assets
- chart.RollingMean: chart the rolling mean return
- chart.RollingPerformance: wrapper to create a chart of rolling performance metrics in a...
- chart.RollingRegression: A wrapper to create charts of relative regression performance...
- chart.Scatter: wrapper to draw scatter plot with sensible defaults
- chart.SnailTrail: chart risk versus return over rolling time periods
- charts.PerformanceSummary: Create combined wealth index, period performance, and...
- charts.RollingPerformance: rolling performance chart
- chart.StackedBar: create a stacked bar plot
- chart.TimeSeries: Creates a time series chart with some extensions.
- chart.VaRSensitivity: show the sensitivity of Value-at-Risk or Expected Shortfall...
- checkData: check input data type and format and coerce to the desired...
- clean.boudt: clean extreme observations in a time series to to provide...
- CoMoments: Functions for calculating comoments of financial time series
- DownsideDeviation: downside risk (deviation, variance) of the return...
- DownsideFrequency: downside frequency of the return distribution
- DRatio: d ratio of the return distribution
- DrawdownDeviation: Calculates a standard deviation-type statistic using...
- DrawdownPeak: Drawdawn peak of the return distribution
- edhec: EDHEC-Risk Hedge Fund Style Indices
- ES: calculates Expected Shortfall(ES) (or Conditional...
- FamaBeta: Fama beta of the return distribution
- findDrawdowns: Find the drawdowns and drawdown levels in a timeseries.
- Frequency: Frequency of the return distribution
- HurstIndex: calculate the Hurst Index The Hurst index can be used to...
- InformationRatio: InformationRatio = ActivePremium/TrackingError
- Kappa: Kappa of the return distribution
- KellyRatio: calculate Kelly criterion ratio (leverage or bet size) for a...
- kurtosis: Kurtosis
- legend: internal functions for setting useful defaults for graphs
- lpm: calculate a lower partial moment for a time series
- M2Sortino: M squared for Sortino of the return distribution
- managers: Hypothetical Alternative Asset Manager and Benchmark Data
- MarketTiming: Market timing models
- MartinRatio: Martin ratio of the return distribution
- maxDrawdown: caclulate the maximum drawdown from peak equity
- MeanAbsoluteDeviation: Mean absolute deviation of the return distribution
- mean.geometric: calculate attributes relative to the mean of the observation...
- Modigliani: Modigliani-Modigliani measure
- MSquared: M squared of the return distribution
- MSquaredExcess: M squared excess of the return distribution
- NetSelectivity: Net selectivity of the return distribution
- Omega: calculate Omega for a return series
- OmegaExcessReturn: Omega excess return of the return distribution
- OmegaSharpeRatio: Omega-Sharpe ratio of the return distribution
- PainIndex: Pain index of the return distribution
- PainRatio: Pain ratio of the return distribution
- PerformanceAnalytics-package: Econometric tools for performance and risk analysis.
- portfolio_bacon: Bacon(2008) Data
- prices: Selected Price Series Example Data
- ProspectRatio: Prospect ratio of the return distribution
- Return.annualized: calculate an annualized return for comparing instruments with...
- Return.annualized.excess: calculates an annualized excess return for comparing...
- Return.calculate: calculate simple or compound returns from prices
- Return.clean: clean returns in a time series to to provide more robust risk...
- Return.cumulative: calculate a compounded (geometric) cumulative return
- Return.excess: Calculates the returns of an asset in excess of the given...
- Return.Geltner: calculate Geltner liquidity-adjusted return series
- Return.portfolio: Calculate weighted returns for a portfolio of assets
- Return.read: Read returns data with different date formats
- Return.relative: calculate the relative return of one asset to another
- Selectivity: Selectivity of the return distribution
- SharpeRatio: calculate a traditional or modified Sharpe Ratio of Return...
- SharpeRatio.annualized: calculate annualized Sharpe Ratio
- skewness: Skewness
- SkewnessKurtosisRatio: Skewness-Kurtosis ratio of the return distribution
- SmoothingIndex: calculate Normalized Getmansky Smoothing Index
- sortDrawdowns: order list of drawdowns from worst to best
- SortinoRatio: calculate Sortino Ratio of performance over downside risk
- SpecificRisk: Specific risk of the return distribution
- StdDev: calculates Standard Deviation for univariate and multivariate...
- StdDev.annualized: calculate a multiperiod or annualized Standard Deviation
- SystematicRisk: Systematic risk of the return distribution
- table.AnnualizedReturns: Annualized Returns Summary: Statistics and Stylized Facts
- table.Arbitrary: wrapper function for combining arbitrary function list into a...
- table.Autocorrelation: table for calculating the first six autocorrelation...
- table.CalendarReturns: Monthly and Calendar year Return table
- table.CAPM: Single Factor Asset-Pricing Model Summary: Statistics and...
- table.CaptureRatios: Calculate and display a table of capture ratio and related...
- table.Correlation: calculate correlalations of multicolumn data
- table.Distributions: Distributions Summary: Statistics and Stylized Facts
- table.DownsideRisk: Downside Risk Summary: Statistics and Stylized Facts
- table.DownsideRiskRatio: Downside Summary: Statistics and ratios
- table.Drawdowns: Worst Drawdowns Summary: Statistics and Stylized Facts
- table.DrawdownsRatio: Drawdowns Summary: Statistics and ratios
- table.HigherMoments: Higher Moments Summary: Statistics and Stylized Facts
- table.InformationRatio: Information ratio Summary: Statistics and Stylized Facts
- table.MonthlyReturns: Returns Summary: Statistics and Stylized Facts
- table.ProbOutPerformance: Outperformance Report of Asset vs Benchmark
- table.RollingPeriods: Rolling Periods Summary: Statistics and Stylized Facts
- table.SpecificRisk: Specific risk Summary: Statistics and Stylized Facts
- table.Variability: Variability Summary: Statistics and Stylized Facts
- textplot: Display text information in a graphics plot.
- TotalRisk: Total risk of the return distribution
- TrackingError: Calculate Tracking Error of returns against a benchmark
- TreynorRatio: calculate Treynor Ratio or modified Treynor Ratio of excess...
- UlcerIndex: calculate the Ulcer Index
- UpDownRatios: calculate metrics on up and down markets for the benchmark...
- UpsideFrequency: upside frequency of the return distribution
- UpsidePotentialRatio: calculate Upside Potential Ratio of upside performance over...
- UpsideRisk: upside risk, variance and potential of the return...
- VaR: calculate various Value at Risk (VaR) measures
- VolatilitySkewness: Volatility and variability of the return distribution
- weights: Selected Portfolio Weights Data
- zerofill: zerofill