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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
 Mean0.334
 SD0.659
 Sharpe ratio (Glass type estimate) 0.506
 Sharpe ratio (Hedges UMVUE)0.506
 df846.000
 t0.795
 p0.214
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.743
 Upperbound of 95% confidence interval for Sharpe Ratio1.756
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.743
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.755
Statistics related to Sortino ratio
 Sortino ratio0.887
 Upside Potential Ratio7.732
 Upside part of mean2.907
 Downside part of mean-2.573
 Upside SD0.541
 Downside SD0.376
 N nonnegative terms371.000
 N negative terms476.000
Statistics related to linear regression on benchmark
 N of observations847.000
 Mean of predictor0.148
 Mean of criterion0.334
 SD of predictor0.118
 SD of criterion0.659
 Covariance0.009
 r0.113
 b (slope, estimate of beta)0.634
 a (intercept, estimate of alpha)0.240
 Mean Square Error0.429
 DF error845.000
 t(b)3.314
 p(b)0.000
 t(a)0.574
 p(a)0.283
 Lowerbound of 95% confidence interval for beta0.258
 Upperbound of 95% confidence interval for beta1.009
 Lowerbound of 95% confidence interval for alpha-0.581
 Upperbound of 95% confidence interval for alpha1.061
 Treynor index (mean / b)0.526
 Jensen alpha (a)0.240
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.138
 SD0.613
 Sharpe ratio (Glass type estimate) 0.225
 Sharpe ratio (Hedges UMVUE)0.225
 df846.000
 t0.353
 p0.362
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.024
 Upperbound of 95% confidence interval for Sharpe Ratio1.474
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.024
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.474
Statistics related to Sortino ratio
 Sortino ratio0.346
 Upside Potential Ratio6.999
 Upside part of mean2.787
 Downside part of mean-2.649
 Upside SD0.466
 Downside SD0.398
 N nonnegative terms371.000
 N negative terms476.000
Statistics related to linear regression on benchmark
 N of observations847.000
 Mean of predictor0.141
 Mean of criterion0.138
 SD of predictor0.118
 SD of criterion0.613
 Covariance0.008
 r0.113
 b (slope, estimate of beta)0.589
 a (intercept, estimate of alpha)0.055
 Mean Square Error0.372
 DF error845.000
 t(b)3.307
 p(b)0.000
 t(a)0.141
 p(a)0.444
 Lowerbound of 95% confidence interval for beta0.239
 Upperbound of 95% confidence interval for beta0.938
 Lowerbound of 95% confidence interval for alpha-0.709
 Upperbound of 95% confidence interval for alpha0.819
 Treynor index (mean / b)0.234
 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 VaR0.065
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 observations847.000
 Minimum0.762
 Quartile 10.994
 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 Range0.015
 Number outliers low74.000
 Percentage of outliers low0.087
 Mean of outliers low0.945
 Number of outliers high64.000
 Percentage of outliers high0.076
 Mean of outliers high1.063
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.447
 VaR(95%) (moments method)0.023
 Expected Shortfall (moments method)0.050
 Extreme Value Index (regression method)0.291
 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)0.229
 Compounded annual return (geometric extrapolation)0.199
 Calmar ratio (compounded annual return / max draw down)0.253
 Compounded annual return / average of 25% largest draw downs0.985
 Compounded annual return / Expected Shortfall lognormal3.047
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.337
 SD1.051
 Sharpe ratio (Glass type estimate) 1.272
 Sharpe ratio (Hedges UMVUE)1.266
 df171.000
 t0.899
 p0.456
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.505
 Upperbound of 95% confidence interval for Sharpe Ratio4.045
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.509
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.041
Statistics related to Sortino ratio
 Sortino ratio4.439
 Upside Potential Ratio9.677
 Upside part of mean2.914
 Downside part of mean-1.577
 Upside SD1.006
 Downside SD0.301
 N nonnegative terms53.000
 N negative terms119.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.151
 Mean of criterion1.337
 SD of predictor0.115
 SD of criterion1.051
 Covariance0.016
 r0.133
 b (slope, estimate of beta)1.209
 a (intercept, estimate of alpha)1.154
 Mean Square Error1.092
 DF error170.000
 t(b)1.746
 p(b)0.434
 t(a)0.779
 p(a)0.470
 Lowerbound of 95% confidence interval for beta-0.158
 Upperbound of 95% confidence interval for beta2.576
 Lowerbound of 95% confidence interval for alpha-1.770
 Upperbound of 95% confidence interval for alpha4.079
 Treynor index (mean / b)1.106
 Jensen alpha (a)1.154
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.906
 SD0.876
 Sharpe ratio (Glass type estimate) 1.035
 Sharpe ratio (Hedges UMVUE)1.030
 df171.000
 t0.732
 p0.464
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.741
 Upperbound of 95% confidence interval for Sharpe Ratio3.807
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.744
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.804
Statistics related to Sortino ratio
 Sortino ratio2.889
 Upside Potential Ratio8.070
 Upside part of mean2.531
 Downside part of mean-1.625
 Upside SD0.816
 Downside SD0.314
 N nonnegative terms53.000
 N negative terms119.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.144
 Mean of criterion0.906
 SD of predictor0.116
 SD of criterion0.876
 Covariance0.013
 r0.130
 b (slope, estimate of beta)0.988
 a (intercept, estimate of alpha)0.764
 Mean Square Error0.758
 DF error170.000
 t(b)1.716
 p(b)0.435
 t(a)0.619
 p(a)0.476
 Lowerbound of 95% confidence interval for beta-0.149
 Upperbound of 95% confidence interval for beta2.125
 Lowerbound of 95% confidence interval for alpha-1.672
 Upperbound of 95% confidence interval for alpha3.200
 Treynor index (mean / b)0.917
 Jensen alpha (a)0.764
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.072
 Expected Shortfall on VaR0.090
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.013
 Expected Shortfall on VaR0.028
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 10.982
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.034
 Inter Quartile Range0.001
 Number outliers low26.000
 Percentage of outliers low0.151
 Mean of outliers low0.970
 Number of outliers high35.000
 Percentage of outliers high0.203
 Mean of outliers high1.041
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.099
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)0.405
 VaR(95%) (regression method)0.016
 Expected Shortfall (regression method)0.044
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.242
 Quartile 10.245
 Median0.248
 Quartile 30.251
 Maximum0.254
 Mean of quarter 10.242
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.254
 Inter Quartile Range0.006
 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)1.216
 Compounded annual return (geometric extrapolation)1.586
 Calmar ratio (compounded annual return / max draw down)6.256
 Compounded annual return / average of 25% largest draw downs6.256
 Compounded annual return / Expected Shortfall lognormal17.572