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Advanced Statistics: Green Dog

Advanced Statistics module contributed by Jules Ellis, C2 Member.

Jules has written a very helpful guide for these statistics.

MonthlyDaily (all)Daily (last 6 mo.)
ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.396
 SD0.750
 Sharpe ratio (Glass type estimate) 0.528
 Sharpe ratio (Hedges UMVUE)0.514
 df29.000
 t0.835
 p0.205
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.723
 Upperbound of 95% confidence interval for Sharpe Ratio1.771
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.732
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.761
Statistics related to Sortino ratio
 Sortino ratio0.922
 Upside Potential Ratio2.758
 Upside part of mean1.185
 Downside part of mean-0.789
 Upside SD0.610
 Downside SD0.429
 N nonnegative terms17.000
 N negative terms13.000
Statistics related to linear regression on benchmark
 N of observations30.000
 Mean of predictor0.145
 Mean of criterion0.396
 SD of predictor0.109
 SD of criterion0.750
 Covariance0.011
 r0.135
 b (slope, estimate of beta)0.930
 a (intercept, estimate of alpha)0.261
 Mean Square Error0.572
 DF error28.000
 t(b)0.721
 p(b)0.239
 t(a)0.507
 p(a)0.308
 Lowerbound of 95% confidence interval for beta-1.714
 Upperbound of 95% confidence interval for beta3.575
 Lowerbound of 95% confidence interval for alpha-0.792
 Upperbound of 95% confidence interval for alpha1.313
 Treynor index (mean / b)0.426
 Jensen alpha (a)0.261
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.135
 SD0.728
 Sharpe ratio (Glass type estimate) 0.186
 Sharpe ratio (Hedges UMVUE)0.181
 df29.000
 t0.294
 p0.386
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.056
 Upperbound of 95% confidence interval for Sharpe Ratio1.425
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.060
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.421
Statistics related to Sortino ratio
 Sortino ratio0.268
 Upside Potential Ratio2.053
 Upside part of mean1.035
 Downside part of mean-0.900
 Upside SD0.510
 Downside SD0.504
 N nonnegative terms17.000
 N negative terms13.000
Statistics related to linear regression on benchmark
 N of observations30.000
 Mean of predictor0.138
 Mean of criterion0.135
 SD of predictor0.108
 SD of criterion0.728
 Covariance0.008
 r0.104
 b (slope, estimate of beta)0.705
 a (intercept, estimate of alpha)0.038
 Mean Square Error0.543
 DF error28.000
 t(b)0.555
 p(b)0.292
 t(a)0.075
 p(a)0.470
 Lowerbound of 95% confidence interval for beta-1.900
 Upperbound of 95% confidence interval for beta3.310
 Lowerbound of 95% confidence interval for alpha-0.983
 Upperbound of 95% confidence interval for alpha1.058
 Treynor index (mean / b)0.192
 Jensen alpha (a)0.038
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.284
 Expected Shortfall on VaR0.342
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.140
 Expected Shortfall on VaR0.267
ORDER STATISTICS
Quartiles of return rates
 Number of observations30.000
 Minimum0.633
 Quartile 10.849
 Median1.015
 Quartile 31.180
 Maximum1.667
 Mean of quarter 10.786
 Mean of quarter 20.973
 Mean of quarter 31.088
 Mean of quarter 41.298
 Inter Quartile Range0.332
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.414
 VaR(95%) (moments method)0.255
 Expected Shortfall (moments method)0.409
 Extreme Value Index (regression method)1.149
 VaR(95%) (regression method)0.206
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.006
 Quartile 10.143
 Median0.279
 Quartile 30.525
 Maximum0.771
 Mean of quarter 10.006
 Mean of quarter 20.279
 Mean of quarter 3NA
 Mean of quarter 40.771
 Inter Quartile Range0.382
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.226
 Compounded annual return (geometric extrapolation)0.196
 Calmar ratio (compounded annual return / max draw down)0.255
 Compounded annual return / average of 25% largest draw downs0.255
 Compounded annual return / Expected Shortfall lognormal0.573
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.327
 SD0.653
 Sharpe ratio (Glass type estimate) 0.501
 Sharpe ratio (Hedges UMVUE)0.501
 df860.000
 t0.793
 p0.214
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.738
 Upperbound of 95% confidence interval for Sharpe Ratio1.740
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.738
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.740
Statistics related to Sortino ratio
 Sortino ratio0.878
 Upside Potential Ratio7.669
 Upside part of mean2.860
 Downside part of mean-2.532
 Upside SD0.536
 Downside SD0.373
 N nonnegative terms371.000
 N negative terms490.000
Statistics related to linear regression on benchmark
 N of observations861.000
 Mean of predictor0.152
 Mean of criterion0.327
 SD of predictor0.121
 SD of criterion0.653
 Covariance0.009
 r0.109
 b (slope, estimate of beta)0.588
 a (intercept, estimate of alpha)0.238
 Mean Square Error0.422
 DF error859.000
 t(b)3.217
 p(b)0.001
 t(a)0.578
 p(a)0.282
 Lowerbound of 95% confidence interval for beta0.229
 Upperbound of 95% confidence interval for beta0.947
 Lowerbound of 95% confidence interval for alpha-0.570
 Upperbound of 95% confidence interval for alpha1.046
 Treynor index (mean / b)0.557
 Jensen alpha (a)0.238
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.135
 SD0.608
 Sharpe ratio (Glass type estimate) 0.222
 Sharpe ratio (Hedges UMVUE)0.222
 df860.000
 t0.351
 p0.363
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.017
 Upperbound of 95% confidence interval for Sharpe Ratio1.461
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.017
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.461
Statistics related to Sortino ratio
 Sortino ratio0.342
 Upside Potential Ratio6.942
 Upside part of mean2.742
 Downside part of mean-2.607
 Upside SD0.462
 Downside SD0.395
 N nonnegative terms371.000
 N negative terms490.000
Statistics related to linear regression on benchmark
 N of observations861.000
 Mean of predictor0.145
 Mean of criterion0.135
 SD of predictor0.121
 SD of criterion0.608
 Covariance0.008
 r0.109
 b (slope, estimate of beta)0.546
 a (intercept, estimate of alpha)0.056
 Mean Square Error0.366
 DF error859.000
 t(b)3.210
 p(b)0.001
 t(a)0.146
 p(a)0.442
 Lowerbound of 95% confidence interval for beta0.212
 Upperbound of 95% confidence interval for beta0.880
 Lowerbound of 95% confidence interval for alpha-0.696
 Upperbound of 95% confidence interval for alpha0.808
 Treynor index (mean / b)0.247
 Jensen alpha (a)0.056
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.052
 Expected Shortfall on VaR0.065
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.039
ORDER STATISTICS
Quartiles of return rates
 Number of observations861.000
 Minimum0.762
 Quartile 10.995
 Median1.000
 Quartile 31.009
 Maximum1.591
 Mean of quarter 10.972
 Mean of quarter 20.999
 Mean of quarter 31.003
 Mean of quarter 41.031
 Inter Quartile Range0.014
 Number outliers low75.000
 Percentage of outliers low0.087
 Mean of outliers low0.945
 Number of outliers high68.000
 Percentage of outliers high0.079
 Mean of outliers high1.061
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.462
 VaR(95%) (moments method)0.022
 Expected Shortfall (moments method)0.050
 Extreme Value Index (regression method)0.313
 VaR(95%) (regression method)0.025
 Expected Shortfall (regression method)0.047
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations32.000
 Minimum0.000
 Quartile 10.007
 Median0.026
 Quartile 30.049
 Maximum0.788
 Mean of quarter 10.002
 Mean of quarter 20.018
 Mean of quarter 30.035
 Mean of quarter 40.203
 Inter Quartile Range0.042
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.094
 Mean of outliers high0.427
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.868
 VaR(95%) (moments method)0.204
 Expected Shortfall (moments method)1.609
 Extreme Value Index (regression method)1.426
 VaR(95%) (regression method)0.192
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.226
 Compounded annual return (geometric extrapolation)0.196
 Calmar ratio (compounded annual return / max draw down)0.249
 Compounded annual return / average of 25% largest draw downs0.967
 Compounded annual return / Expected Shortfall lognormal3.016
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.641
 SD1.035
 Sharpe ratio (Glass type estimate) 1.585
 Sharpe ratio (Hedges UMVUE)1.578
 df171.000
 t1.121
 p0.446
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.194
 Upperbound of 95% confidence interval for Sharpe Ratio4.360
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.199
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.355
Statistics related to Sortino ratio
 Sortino ratio6.518
 Upside Potential Ratio10.994
 Upside part of mean2.768
 Downside part of mean-1.127
 Upside SD1.005
 Downside SD0.252
 N nonnegative terms48.000
 N negative terms124.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.188
 Mean of criterion1.641
 SD of predictor0.135
 SD of criterion1.035
 Covariance0.016
 r0.117
 b (slope, estimate of beta)0.895
 a (intercept, estimate of alpha)1.473
 Mean Square Error1.064
 DF error170.000
 t(b)1.532
 p(b)0.442
 t(a)1.007
 p(a)0.461
 Lowerbound of 95% confidence interval for beta-0.258
 Upperbound of 95% confidence interval for beta2.049
 Lowerbound of 95% confidence interval for alpha-1.414
 Upperbound of 95% confidence interval for alpha4.360
 Treynor index (mean / b)1.834
 Jensen alpha (a)1.473
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean1.226
 SD0.856
 Sharpe ratio (Glass type estimate) 1.433
 Sharpe ratio (Hedges UMVUE)1.427
 df171.000
 t1.013
 p0.451
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.345
 Upperbound of 95% confidence interval for Sharpe Ratio4.207
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.349
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.203
Statistics related to Sortino ratio
 Sortino ratio4.668
 Upside Potential Ratio9.085
 Upside part of mean2.387
 Downside part of mean-1.161
 Upside SD0.815
 Downside SD0.263
 N nonnegative terms48.000
 N negative terms124.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.179
 Mean of criterion1.226
 SD of predictor0.135
 SD of criterion0.856
 Covariance0.013
 r0.116
 b (slope, estimate of beta)0.736
 a (intercept, estimate of alpha)1.095
 Mean Square Error0.727
 DF error170.000
 t(b)1.527
 p(b)0.442
 t(a)0.906
 p(a)0.465
 Lowerbound of 95% confidence interval for beta-0.215
 Upperbound of 95% confidence interval for beta1.688
 Lowerbound of 95% confidence interval for alpha-1.292
 Upperbound of 95% confidence interval for alpha3.481
 Treynor index (mean / b)1.666
 Jensen alpha (a)1.095
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.070
 Expected Shortfall on VaR0.087
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.021
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.001
 Maximum1.591
 Mean of quarter 10.987
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.032
 Inter Quartile Range0.001
 Number outliers low21.000
 Percentage of outliers low0.122
 Mean of outliers low0.974
 Number of outliers high36.000
 Percentage of outliers high0.209
 Mean of outliers high1.038
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.188
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)0.385
 VaR(95%) (regression method)0.010
 Expected Shortfall (regression method)0.030
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations4.000
 Minimum0.026
 Quartile 10.044
 Median0.057
 Quartile 30.109
 Maximum0.242
 Mean of quarter 10.026
 Mean of quarter 20.050
 Mean of quarter 30.065
 Mean of quarter 40.242
 Inter Quartile Range0.066
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.250
 Mean of outliers high0.242
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)1.775
 Compounded annual return (geometric extrapolation)2.562
 Calmar ratio (compounded annual return / max draw down)10.570
 Compounded annual return / average of 25% largest draw downs10.570
 Compounded annual return / Expected Shortfall lognormal29.311