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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
 Mean0.322
 SD0.649
 Sharpe ratio (Glass type estimate) 0.497
 Sharpe ratio (Hedges UMVUE)0.496
 df872.000
 t0.791
 p0.214
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.734
 Upperbound of 95% confidence interval for Sharpe Ratio1.727
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.734
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.727
Statistics related to Sortino ratio
 Sortino ratio0.870
 Upside Potential Ratio7.616
 Upside part of mean2.820
 Downside part of mean-2.498
 Upside SD0.533
 Downside SD0.370
 N nonnegative terms371.000
 N negative terms502.000
Statistics related to linear regression on benchmark
 N of observations873.000
 Mean of predictor0.159
 Mean of criterion0.322
 SD of predictor0.120
 SD of criterion0.649
 Covariance0.009
 r0.109
 b (slope, estimate of beta)0.586
 a (intercept, estimate of alpha)0.229
 Mean Square Error0.416
 DF error871.000
 t(b)3.233
 p(b)0.001
 t(a)0.564
 p(a)0.286
 Lowerbound of 95% confidence interval for beta0.230
 Upperbound of 95% confidence interval for beta0.942
 Lowerbound of 95% confidence interval for alpha-0.568
 Upperbound of 95% confidence interval for alpha1.026
 Treynor index (mean / b)0.550
 Jensen alpha (a)0.229
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.132
 SD0.604
 Sharpe ratio (Glass type estimate) 0.219
 Sharpe ratio (Hedges UMVUE)0.219
 df872.000
 t0.349
 p0.363
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.011
 Upperbound of 95% confidence interval for Sharpe Ratio1.450
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.011
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.449
Statistics related to Sortino ratio
 Sortino ratio0.338
 Upside Potential Ratio6.894
 Upside part of mean2.704
 Downside part of mean-2.572
 Upside SD0.459
 Downside SD0.392
 N nonnegative terms371.000
 N negative terms502.000
Statistics related to linear regression on benchmark
 N of observations873.000
 Mean of predictor0.152
 Mean of criterion0.132
 SD of predictor0.121
 SD of criterion0.604
 Covariance0.008
 r0.109
 b (slope, estimate of beta)0.545
 a (intercept, estimate of alpha)0.050
 Mean Square Error0.361
 DF error871.000
 t(b)3.227
 p(b)0.001
 t(a)0.132
 p(a)0.448
 Lowerbound of 95% confidence interval for beta0.213
 Upperbound of 95% confidence interval for beta0.876
 Lowerbound of 95% confidence interval for alpha-0.692
 Upperbound of 95% confidence interval for alpha0.792
 Treynor index (mean / b)0.243
 Jensen alpha (a)0.050
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 VaR0.038
ORDER STATISTICS
Quartiles of return rates
 Number of observations873.000
 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 low84.000
 Percentage of outliers low0.096
 Mean of outliers low0.948
 Number of outliers high69.000
 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)0.433
 VaR(95%) (moments method)0.021
 Expected Shortfall (moments method)0.045
 Extreme Value Index (regression method)0.301
 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)0.223
 Compounded annual return (geometric extrapolation)0.193
 Calmar ratio (compounded annual return / max draw down)0.245
 Compounded annual return / average of 25% largest draw downs0.953
 Compounded annual return / Expected Shortfall lognormal2.991
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.245
 SD0.579
 Sharpe ratio (Glass type estimate) 0.423
 Sharpe ratio (Hedges UMVUE)0.421
 df171.000
 t0.299
 p0.485
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.350
 Upperbound of 95% confidence interval for Sharpe Ratio3.195
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.351
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.193
Statistics related to Sortino ratio
 Sortino ratio1.068
 Upside Potential Ratio4.756
 Upside part of mean1.092
 Downside part of mean-0.847
 Upside SD0.530
 Downside SD0.230
 N nonnegative terms41.000
 N negative terms131.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.205
 Mean of criterion0.245
 SD of predictor0.131
 SD of criterion0.579
 Covariance0.008
 r0.111
 b (slope, estimate of beta)0.492
 a (intercept, estimate of alpha)0.144
 Mean Square Error0.333
 DF error170.000
 t(b)1.462
 p(b)0.444
 t(a)0.176
 p(a)0.493
 Lowerbound of 95% confidence interval for beta-0.172
 Upperbound of 95% confidence interval for beta1.156
 Lowerbound of 95% confidence interval for alpha-1.473
 Upperbound of 95% confidence interval for alpha1.762
 Treynor index (mean / b)0.498
 Jensen alpha (a)0.144
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.104
 SD0.513
 Sharpe ratio (Glass type estimate) 0.202
 Sharpe ratio (Hedges UMVUE)0.201
 df171.000
 t0.143
 p0.493
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.570
 Upperbound of 95% confidence interval for Sharpe Ratio2.974
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.571
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.973
Statistics related to Sortino ratio
 Sortino ratio0.431
 Upside Potential Ratio4.066
 Upside part of mean0.978
 Downside part of mean-0.874
 Upside SD0.452
 Downside SD0.241
 N nonnegative terms41.000
 N negative terms131.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.196
 Mean of criterion0.104
 SD of predictor0.132
 SD of criterion0.513
 Covariance0.008
 r0.115
 b (slope, estimate of beta)0.448
 a (intercept, estimate of alpha)0.016
 Mean Square Error0.261
 DF error170.000
 t(b)1.509
 p(b)0.443
 t(a)0.021
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.138
 Upperbound of 95% confidence interval for beta1.035
 Lowerbound of 95% confidence interval for alpha-1.416
 Upperbound of 95% confidence interval for alpha1.447
 Treynor index (mean / b)0.231
 Jensen alpha (a)0.016
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.044
 Expected Shortfall on VaR0.055
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.373
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.013
 Inter Quartile Range0.000
 Number outliers low19.000
 Percentage of outliers low0.110
 Mean of outliers low0.979
 Number of outliers high42.000
 Percentage of outliers high0.244
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.681
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.006
 Extreme Value Index (regression method)0.794
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.052
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.242
 Quartile 10.242
 Median0.242
 Quartile 30.242
 Maximum0.242
 Mean of quarter 1NA
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 4NA
 Inter Quartile Range0.000
 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)0.153
 Compounded annual return (geometric extrapolation)0.159
 Calmar ratio (compounded annual return / max draw down)0.656
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal2.885