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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
 Mean0.339
 SD0.663
 Sharpe ratio (Glass type estimate) 0.511
 Sharpe ratio (Hedges UMVUE)0.510
 df834.000
 t0.796
 p0.213
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.747
 Upperbound of 95% confidence interval for Sharpe Ratio1.769
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.748
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.769
Statistics related to Sortino ratio
 Sortino ratio0.895
 Upside Potential Ratio7.788
 Upside part of mean2.949
 Downside part of mean-2.610
 Upside SD0.545
 Downside SD0.379
 N nonnegative terms371.000
 N negative terms464.000
Statistics related to linear regression on benchmark
 N of observations835.000
 Mean of predictor0.155
 Mean of criterion0.339
 SD of predictor0.118
 SD of criterion0.663
 Covariance0.009
 r0.114
 b (slope, estimate of beta)0.638
 a (intercept, estimate of alpha)0.240
 Mean Square Error0.435
 DF error833.000
 t(b)3.301
 p(b)0.001
 t(a)0.566
 p(a)0.286
 Lowerbound of 95% confidence interval for beta0.259
 Upperbound of 95% confidence interval for beta1.018
 Lowerbound of 95% confidence interval for alpha-0.593
 Upperbound of 95% confidence interval for alpha1.073
 Treynor index (mean / b)0.531
 Jensen alpha (a)0.240
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.141
 SD0.618
 Sharpe ratio (Glass type estimate) 0.227
 Sharpe ratio (Hedges UMVUE)0.227
 df834.000
 t0.354
 p0.362
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.031
 Upperbound of 95% confidence interval for Sharpe Ratio1.486
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.031
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.485
Statistics related to Sortino ratio
 Sortino ratio0.350
 Upside Potential Ratio7.049
 Upside part of mean2.827
 Downside part of mean-2.687
 Upside SD0.469
 Downside SD0.401
 N nonnegative terms371.000
 N negative terms464.000
Statistics related to linear regression on benchmark
 N of observations835.000
 Mean of predictor0.148
 Mean of criterion0.141
 SD of predictor0.118
 SD of criterion0.618
 Covariance0.008
 r0.113
 b (slope, estimate of beta)0.593
 a (intercept, estimate of alpha)0.053
 Mean Square Error0.377
 DF error833.000
 t(b)3.295
 p(b)0.001
 t(a)0.134
 p(a)0.447
 Lowerbound of 95% confidence interval for beta0.240
 Upperbound of 95% confidence interval for beta0.947
 Lowerbound of 95% confidence interval for alpha-0.722
 Upperbound of 95% confidence interval for alpha0.828
 Treynor index (mean / b)0.237
 Jensen alpha (a)0.053
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 observations835.000
 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 high0.072
 Mean of outliers high1.065
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.402
 VaR(95%) (moments method)0.022
 Expected Shortfall (moments method)0.046
 Extreme Value Index (regression method)0.274
 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)0.233
 Compounded annual return (geometric extrapolation)0.203
 Calmar ratio (compounded annual return / max draw down)0.257
 Compounded annual return / average of 25% largest draw downs1.000
 Compounded annual return / Expected Shortfall lognormal3.074
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.284
 SD1.067
 Sharpe ratio (Glass type estimate) 1.203
 Sharpe ratio (Hedges UMVUE)1.198
 df171.000
 t0.851
 p0.459
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.573
 Upperbound of 95% confidence interval for Sharpe Ratio3.976
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.577
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.972
Statistics related to Sortino ratio
 Sortino ratio3.825
 Upside Potential Ratio9.599
 Upside part of mean3.222
 Downside part of mean-1.938
 Upside SD1.012
 Downside SD0.336
 N nonnegative terms58.000
 N negative terms114.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.212
 Mean of criterion1.284
 SD of predictor0.115
 SD of criterion1.067
 Covariance0.018
 r0.145
 b (slope, estimate of beta)1.349
 a (intercept, estimate of alpha)0.998
 Mean Square Error1.122
 DF error170.000
 t(b)1.911
 p(b)0.427
 t(a)0.663
 p(a)0.475
 Lowerbound of 95% confidence interval for beta-0.044
 Upperbound of 95% confidence interval for beta2.741
 Lowerbound of 95% confidence interval for alpha-1.974
 Upperbound of 95% confidence interval for alpha3.969
 Treynor index (mean / b)0.952
 Jensen alpha (a)0.998
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.836
 SD0.896
 Sharpe ratio (Glass type estimate) 0.933
 Sharpe ratio (Hedges UMVUE)0.929
 df171.000
 t0.660
 p0.468
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.842
 Upperbound of 95% confidence interval for Sharpe Ratio3.706
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.844
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.703
Statistics related to Sortino ratio
 Sortino ratio2.391
 Upside Potential Ratio8.103
 Upside part of mean2.834
 Downside part of mean-1.998
 Upside SD0.823
 Downside SD0.350
 N nonnegative terms58.000
 N negative terms114.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.206
 Mean of criterion0.836
 SD of predictor0.115
 SD of criterion0.896
 Covariance0.015
 r0.145
 b (slope, estimate of beta)1.132
 a (intercept, estimate of alpha)0.603
 Mean Square Error0.790
 DF error170.000
 t(b)1.914
 p(b)0.427
 t(a)0.478
 p(a)0.482
 Lowerbound of 95% confidence interval for beta-0.035
 Upperbound of 95% confidence interval for beta2.299
 Lowerbound of 95% confidence interval for alpha-1.890
 Upperbound of 95% confidence interval for alpha3.096
 Treynor index (mean / b)0.739
 Jensen alpha (a)0.603
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 31.002
 Maximum1.591
 Mean of quarter 10.978
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.037
 Inter Quartile Range0.002
 Number outliers low29.000
 Percentage of outliers low0.169
 Mean of outliers low0.967
 Number of outliers high32.000
 Percentage of outliers high0.186
 Mean of outliers high1.049
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.520
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)0.192
 VaR(95%) (regression method)0.022
 Expected Shortfall (regression method)0.043
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.242
 Quartile 10.251
 Median0.260
 Quartile 30.269
 Maximum0.278
 Mean of quarter 10.242
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.278
 Inter Quartile Range0.018
 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)1.105
 Compounded annual return (geometric extrapolation)1.411
 Calmar ratio (compounded annual return / max draw down)5.069
 Compounded annual return / average of 25% largest draw downs5.069
 Compounded annual return / Expected Shortfall lognormal15.259