Mean absolute deviation of the return distribution

To calculate Mean absolute deviation we take the sum of the absolute value of the difference between the returns and the mean of the returns and we divide it by the number of returns.

MeanAbsoluteDeviation(R, ...)

Arguments

R

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
…

any other passthru parameters

Details

$$MeanAbsoluteDeviation = \frac{\sum^{n}_{i=1}\mid r_i - \overline{r}\mid}{n}$$

where \(n\) is the number of observations of the entire series, \(r_i\) is the return in month i and \(\overline{r}\) is the mean return

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.62

Examples

data(portfolio_bacon)
print(MeanAbsoluteDeviation(portfolio_bacon[,1])) #expected 0.0310
#> [1] 0.03108333

data(managers)
print(MeanAbsoluteDeviation(managers['1996']))
#>                              HAM1     HAM2       HAM3       HAM4 HAM5 HAM6
#> Mean absolute deviation 0.0125375 0.031576 0.02229444 0.02540972  NaN  NaN
#>                         EDHEC LS EQ SP500 TR  US 10Y TR US 3m TR
#> Mean absolute deviation         NaN  0.02225 0.01611653  0.00021
print(MeanAbsoluteDeviation(managers['1996',1]))
#> [1] 0.0125375