Calculate Tracking Error of returns against a benchmark

Source: R/TrackingError.R

A measure of the unexplained portion of performance relative to a benchmark.

TrackingError(Ra, Rb, scale = NA)

Arguments

Ra

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

Rb

return vector of the benchmark asset

scale

number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4)

Details

Tracking error is calculated by taking the square root of the average of the squared deviations between the investment's returns and the benchmark's returns, then multiplying the result by the square root of the scale of the returns.

$$ TrackingError = \sqrt{\sum\frac{(R_{a}-R_{b})^{2}}{len(R_{a})\sqrt{scale}}} $$

References

Sharpe, W.F. The Sharpe Ratio,Journal of Portfolio Management,Fall 1994, 49-58.

See also

InformationRatio TrackingError

Author

Peter Carl

Examples


data(managers)
TrackingError(managers[,1,drop=FALSE], managers[,8,drop=FALSE]) 
#> [1] 0.1131667
TrackingError(managers[,1:6], managers[,8,drop=FALSE]) 
#>                               HAM1      HAM2      HAM3      HAM4      HAM5
#> Tracking Error: SP500 TR 0.1131667 0.1533647 0.1158673 0.1596656 0.1800291
#>                              HAM6
#> Tracking Error: SP500 TR 0.112839
TrackingError(managers[,1:6], managers[,8:7,drop=FALSE])
#>                                   HAM1       HAM2       HAM3      HAM4
#> Tracking Error: SP500 TR    0.11316666 0.15336472 0.11586735 0.1596656
#> Tracking Error: EDHEC LS EQ 0.07577263 0.09071824 0.08156934 0.1569067
#>                                  HAM5       HAM6
#> Tracking Error: SP500 TR    0.1800291 0.11283904
#> Tracking Error: EDHEC LS EQ 0.1421533 0.05651657