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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
 Mean0.324
 SD0.650
 Sharpe ratio (Glass type estimate) 0.498
 Sharpe ratio (Hedges UMVUE)0.497
 df869.000
 t0.792
 p0.214
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.735
 Upperbound of 95% confidence interval for Sharpe Ratio1.730
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.735
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.730
Statistics related to Sortino ratio
 Sortino ratio0.872
 Upside Potential Ratio7.630
 Upside part of mean2.830
 Downside part of mean-2.507
 Upside SD0.533
 Downside SD0.371
 N nonnegative terms371.000
 N negative terms499.000
Statistics related to linear regression on benchmark
 N of observations870.000
 Mean of predictor0.156
 Mean of criterion0.324
 SD of predictor0.121
 SD of criterion0.650
 Covariance0.009
 r0.109
 b (slope, estimate of beta)0.587
 a (intercept, estimate of alpha)0.232
 Mean Square Error0.418
 DF error868.000
 t(b)3.230
 p(b)0.001
 t(a)0.569
 p(a)0.285
 Lowerbound of 95% confidence interval for beta0.230
 Upperbound of 95% confidence interval for beta0.944
 Lowerbound of 95% confidence interval for alpha-0.568
 Upperbound of 95% confidence interval for alpha1.032
 Treynor index (mean / b)0.551
 Jensen alpha (a)0.232
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.133
 SD0.605
 Sharpe ratio (Glass type estimate) 0.220
 Sharpe ratio (Hedges UMVUE)0.220
 df869.000
 t0.350
 p0.363
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.013
 Upperbound of 95% confidence interval for Sharpe Ratio1.452
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.013
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.452
Statistics related to Sortino ratio
 Sortino ratio0.339
 Upside Potential Ratio6.906
 Upside part of mean2.714
 Downside part of mean-2.580
 Upside SD0.460
 Downside SD0.393
 N nonnegative terms371.000
 N negative terms499.000
Statistics related to linear regression on benchmark
 N of observations870.000
 Mean of predictor0.149
 Mean of criterion0.133
 SD of predictor0.121
 SD of criterion0.605
 Covariance0.008
 r0.109
 b (slope, estimate of beta)0.546
 a (intercept, estimate of alpha)0.052
 Mean Square Error0.362
 DF error868.000
 t(b)3.224
 p(b)0.001
 t(a)0.137
 p(a)0.446
 Lowerbound of 95% confidence interval for beta0.213
 Upperbound of 95% confidence interval for beta0.878
 Lowerbound of 95% confidence interval for alpha-0.693
 Upperbound of 95% confidence interval for alpha0.796
 Treynor index (mean / b)0.244
 Jensen alpha (a)0.052
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 observations870.000
 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 low78.000
 Percentage of outliers low0.090
 Mean of outliers low0.946
 Number of outliers high68.000
 Percentage of outliers high0.078
 Mean of outliers high1.061
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.471
 VaR(95%) (moments method)0.022
 Expected Shortfall (moments method)0.050
 Extreme Value Index (regression method)0.310
 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)0.194
 Calmar ratio (compounded annual return / max draw down)0.246
 Compounded annual return / average of 25% largest draw downs0.957
 Compounded annual return / Expected Shortfall lognormal2.997
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.446
 SD1.018
 Sharpe ratio (Glass type estimate) 1.421
 Sharpe ratio (Hedges UMVUE)1.415
 df171.000
 t1.005
 p0.451
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.356
 Upperbound of 95% confidence interval for Sharpe Ratio4.195
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.361
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.191
Statistics related to Sortino ratio
 Sortino ratio6.223
 Upside Potential Ratio10.085
 Upside part of mean2.344
 Downside part of mean-0.897
 Upside SD0.991
 Downside SD0.232
 N nonnegative terms43.000
 N negative terms129.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.245
 Mean of criterion1.446
 SD of predictor0.133
 SD of criterion1.018
 Covariance0.018
 r0.132
 b (slope, estimate of beta)1.005
 a (intercept, estimate of alpha)1.200
 Mean Square Error1.023
 DF error170.000
 t(b)1.734
 p(b)0.434
 t(a)0.834
 p(a)0.468
 Lowerbound of 95% confidence interval for beta-0.139
 Upperbound of 95% confidence interval for beta2.150
 Lowerbound of 95% confidence interval for alpha-1.638
 Upperbound of 95% confidence interval for alpha4.038
 Treynor index (mean / b)1.439
 Jensen alpha (a)1.200
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean1.050
 SD0.835
 Sharpe ratio (Glass type estimate) 1.257
 Sharpe ratio (Hedges UMVUE)1.252
 df171.000
 t0.889
 p0.457
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.520
 Upperbound of 95% confidence interval for Sharpe Ratio4.030
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.523
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.027
Statistics related to Sortino ratio
 Sortino ratio4.314
 Upside Potential Ratio8.119
 Upside part of mean1.976
 Downside part of mean-0.926
 Upside SD0.798
 Downside SD0.243
 N nonnegative terms43.000
 N negative terms129.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.236
 Mean of criterion1.050
 SD of predictor0.134
 SD of criterion0.835
 Covariance0.015
 r0.134
 b (slope, estimate of beta)0.839
 a (intercept, estimate of alpha)0.851
 Mean Square Error0.689
 DF error170.000
 t(b)1.769
 p(b)0.433
 t(a)0.722
 p(a)0.472
 Lowerbound of 95% confidence interval for beta-0.097
 Upperbound of 95% confidence interval for beta1.776
 Lowerbound of 95% confidence interval for alpha-1.476
 Upperbound of 95% confidence interval for alpha3.179
 Treynor index (mean / b)1.251
 Jensen alpha (a)0.851
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.069
 Expected Shortfall on VaR0.086
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.008
 Expected Shortfall on VaR0.017
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.591
 Mean of quarter 10.990
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.027
 Inter Quartile Range0.000
 Number outliers low20.000
 Percentage of outliers low0.116
 Mean of outliers low0.978
 Number of outliers high43.000
 Percentage of outliers high0.250
 Mean of outliers high1.027
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.518
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.004
 Extreme Value Index (regression method)0.599
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.030
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.026
 Quartile 10.080
 Median0.134
 Quartile 30.188
 Maximum0.242
 Mean of quarter 10.026
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.242
 Inter Quartile Range0.108
 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)1.456
 Compounded annual return (geometric extrapolation)1.986
 Calmar ratio (compounded annual return / max draw down)8.192
 Compounded annual return / average of 25% largest draw downs8.192
 Compounded annual return / Expected Shortfall lognormal23.152