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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
 Mean0.411
 SD0.763
 Sharpe ratio (Glass type estimate) 0.539
 Sharpe ratio (Hedges UMVUE)0.524
 df28.000
 t0.838
 p0.205
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.734
 Upperbound of 95% confidence interval for Sharpe Ratio1.803
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.744
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.793
Statistics related to Sortino ratio
 Sortino ratio0.941
 Upside Potential Ratio2.806
 Upside part of mean1.226
 Downside part of mean-0.814
 Upside SD0.620
 Downside SD0.437
 N nonnegative terms17.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations29.000
 Mean of predictor0.155
 Mean of criterion0.411
 SD of predictor0.110
 SD of criterion0.763
 Covariance0.011
 r0.132
 b (slope, estimate of beta)0.918
 a (intercept, estimate of alpha)0.269
 Mean Square Error0.593
 DF error27.000
 t(b)0.691
 p(b)0.248
 t(a)0.501
 p(a)0.310
 Lowerbound of 95% confidence interval for beta-1.806
 Upperbound of 95% confidence interval for beta3.641
 Lowerbound of 95% confidence interval for alpha-0.831
 Upperbound of 95% confidence interval for alpha1.369
 Treynor index (mean / b)0.448
 Jensen alpha (a)0.269
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.141
 SD0.741
 Sharpe ratio (Glass type estimate) 0.191
 Sharpe ratio (Hedges UMVUE)0.186
 df28.000
 t0.297
 p0.384
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.073
 Upperbound of 95% confidence interval for Sharpe Ratio1.451
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.076
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.447
Statistics related to Sortino ratio
 Sortino ratio0.276
 Upside Potential Ratio2.088
 Upside part of mean1.070
 Downside part of mean-0.929
 Upside SD0.518
 Downside SD0.513
 N nonnegative terms17.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations29.000
 Mean of predictor0.148
 Mean of criterion0.141
 SD of predictor0.108
 SD of criterion0.741
 Covariance0.008
 r0.103
 b (slope, estimate of beta)0.706
 a (intercept, estimate of alpha)0.037
 Mean Square Error0.563
 DF error27.000
 t(b)0.540
 p(b)0.297
 t(a)0.071
 p(a)0.472
 Lowerbound of 95% confidence interval for beta-1.977
 Upperbound of 95% confidence interval for beta3.389
 Lowerbound of 95% confidence interval for alpha-1.030
 Upperbound of 95% confidence interval for alpha1.104
 Treynor index (mean / b)0.200
 Jensen alpha (a)0.037
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.288
 Expected Shortfall on VaR0.347
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 observations29.000
 Minimum0.633
 Quartile 10.848
 Median1.015
 Quartile 31.190
 Maximum1.667
 Mean of quarter 10.786
 Mean of quarter 20.975
 Mean of quarter 31.113
 Mean of quarter 41.313
 Inter Quartile Range0.341
 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)0.258
 Expected Shortfall (moments method)0.414
 Extreme Value Index (regression method)1.149
 VaR(95%) (regression method)0.208
 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)0.234
 Compounded annual return (geometric extrapolation)0.204
 Calmar ratio (compounded annual return / max draw down)0.264
 Compounded annual return / average of 25% largest draw downs0.264
 Compounded annual return / Expected Shortfall lognormal0.587
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.337
 SD0.661
 Sharpe ratio (Glass type estimate) 0.509
 Sharpe ratio (Hedges UMVUE)0.509
 df839.000
 t0.795
 p0.213
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.746
 Upperbound of 95% confidence interval for Sharpe Ratio1.763
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.746
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.763
Statistics related to Sortino ratio
 Sortino ratio0.892
 Upside Potential Ratio7.765
 Upside part of mean2.931
 Downside part of mean-2.595
 Upside SD0.543
 Downside SD0.378
 N nonnegative terms371.000
 N negative terms469.000
Statistics related to linear regression on benchmark
 N of observations840.000
 Mean of predictor0.150
 Mean of criterion0.337
 SD of predictor0.118
 SD of criterion0.661
 Covariance0.009
 r0.114
 b (slope, estimate of beta)0.637
 a (intercept, estimate of alpha)0.241
 Mean Square Error0.432
 DF error838.000
 t(b)3.310
 p(b)0.000
 t(a)0.572
 p(a)0.284
 Lowerbound of 95% confidence interval for beta0.259
 Upperbound of 95% confidence interval for beta1.015
 Lowerbound of 95% confidence interval for alpha-0.587
 Upperbound of 95% confidence interval for alpha1.069
 Treynor index (mean / b)0.528
 Jensen alpha (a)0.241
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.139
 SD0.616
 Sharpe ratio (Glass type estimate) 0.226
 Sharpe ratio (Hedges UMVUE)0.226
 df839.000
 t0.354
 p0.362
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.028
 Upperbound of 95% confidence interval for Sharpe Ratio1.481
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.028
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.480
Statistics related to Sortino ratio
 Sortino ratio0.349
 Upside Potential Ratio7.028
 Upside part of mean2.810
 Downside part of mean-2.671
 Upside SD0.468
 Downside SD0.400
 N nonnegative terms371.000
 N negative terms469.000
Statistics related to linear regression on benchmark
 N of observations840.000
 Mean of predictor0.143
 Mean of criterion0.139
 SD of predictor0.118
 SD of criterion0.616
 Covariance0.008
 r0.113
 b (slope, estimate of beta)0.592
 a (intercept, estimate of alpha)0.055
 Mean Square Error0.375
 DF error838.000
 t(b)3.303
 p(b)0.000
 t(a)0.139
 p(a)0.445
 Lowerbound of 95% confidence interval for beta0.240
 Upperbound of 95% confidence interval for beta0.944
 Lowerbound of 95% confidence interval for alpha-0.716
 Upperbound of 95% confidence interval for alpha0.825
 Treynor index (mean / b)0.235
 Jensen alpha (a)0.055
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.053
 Expected Shortfall on VaR0.066
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 observations840.000
 Minimum0.762
 Quartile 10.994
 Median1.000
 Quartile 31.009
 Maximum1.591
 Mean of quarter 10.971
 Mean of quarter 20.999
 Mean of quarter 31.003
 Mean of quarter 41.031
 Inter Quartile Range0.015
 Number outliers low73.000
 Percentage of outliers low0.087
 Mean of outliers low0.945
 Number of outliers high60.000
 Percentage of outliers high0.071
 Mean of outliers high1.065
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.416
 VaR(95%) (moments method)0.023
 Expected Shortfall (moments method)0.047
 Extreme Value Index (regression method)0.278
 VaR(95%) (regression method)0.026
 Expected Shortfall (regression method)0.048
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)0.231
 Compounded annual return (geometric extrapolation)0.201
 Calmar ratio (compounded annual return / max draw down)0.256
 Compounded annual return / average of 25% largest draw downs0.994
 Compounded annual return / Expected Shortfall lognormal3.062
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.169
 SD1.064
 Sharpe ratio (Glass type estimate) 1.099
 Sharpe ratio (Hedges UMVUE)1.094
 df171.000
 t0.777
 p0.462
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.677
 Upperbound of 95% confidence interval for Sharpe Ratio3.872
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.680
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.868
Statistics related to Sortino ratio
 Sortino ratio3.496
 Upside Potential Ratio9.131
 Upside part of mean3.054
 Downside part of mean-1.884
 Upside SD1.009
 Downside SD0.334
 N nonnegative terms55.000
 N negative terms117.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.161
 Mean of criterion1.169
 SD of predictor0.115
 SD of criterion1.064
 Covariance0.017
 r0.141
 b (slope, estimate of beta)1.308
 a (intercept, estimate of alpha)0.958
 Mean Square Error1.116
 DF error170.000
 t(b)1.856
 p(b)0.430
 t(a)0.639
 p(a)0.476
 Lowerbound of 95% confidence interval for beta-0.083
 Upperbound of 95% confidence interval for beta2.699
 Lowerbound of 95% confidence interval for alpha-2.000
 Upperbound of 95% confidence interval for alpha3.916
 Treynor index (mean / b)0.894
 Jensen alpha (a)0.958
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.725
 SD0.892
 Sharpe ratio (Glass type estimate) 0.813
 Sharpe ratio (Hedges UMVUE)0.809
 df171.000
 t0.575
 p0.472
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.961
 Upperbound of 95% confidence interval for Sharpe Ratio3.585
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.964
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.582
Statistics related to Sortino ratio
 Sortino ratio2.081
 Upside Potential Ratio7.657
 Upside part of mean2.668
 Downside part of mean-1.943
 Upside SD0.819
 Downside SD0.348
 N nonnegative terms55.000
 N negative terms117.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.155
 Mean of criterion0.725
 SD of predictor0.115
 SD of criterion0.892
 Covariance0.014
 r0.140
 b (slope, estimate of beta)1.087
 a (intercept, estimate of alpha)0.557
 Mean Square Error0.785
 DF error170.000
 t(b)1.844
 p(b)0.430
 t(a)0.443
 p(a)0.483
 Lowerbound of 95% confidence interval for beta-0.077
 Upperbound of 95% confidence interval for beta2.252
 Lowerbound of 95% confidence interval for alpha-1.923
 Upperbound of 95% confidence interval for alpha3.036
 Treynor index (mean / b)0.667
 Jensen alpha (a)0.557
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.074
 Expected Shortfall on VaR0.092
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.015
 Expected Shortfall on VaR0.033
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 10.978
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.035
 Inter Quartile Range0.001
 Number outliers low29.000
 Percentage of outliers low0.169
 Mean of outliers low0.968
 Number of outliers high31.000
 Percentage of outliers high0.180
 Mean of outliers high1.048
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.260
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)0.224
 VaR(95%) (regression method)0.020
 Expected Shortfall (regression method)0.042
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.242
 Quartile 10.250
 Median0.257
 Quartile 30.265
 Maximum0.272
 Mean of quarter 10.242
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.272
 Inter Quartile Range0.015
 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)0.938
 Compounded annual return (geometric extrapolation)1.158
 Calmar ratio (compounded annual return / max draw down)4.254
 Compounded annual return / average of 25% largest draw downs4.254
 Compounded annual return / Expected Shortfall lognormal12.533