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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
 Mean0.328
 SD0.654
 Sharpe ratio (Glass type estimate) 0.502
 Sharpe ratio (Hedges UMVUE)0.501
 df858.000
 t0.793
 p0.214
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.739
 Upperbound of 95% confidence interval for Sharpe Ratio1.742
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.739
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.742
Statistics related to Sortino ratio
 Sortino ratio0.879
 Upside Potential Ratio7.678
 Upside part of mean2.866
 Downside part of mean-2.538
 Upside SD0.537
 Downside SD0.373
 N nonnegative terms371.000
 N negative terms488.000
Statistics related to linear regression on benchmark
 N of observations859.000
 Mean of predictor0.142
 Mean of criterion0.328
 SD of predictor0.121
 SD of criterion0.654
 Covariance0.009
 r0.110
 b (slope, estimate of beta)0.595
 a (intercept, estimate of alpha)0.244
 Mean Square Error0.423
 DF error857.000
 t(b)3.233
 p(b)0.001
 t(a)0.591
 p(a)0.277
 Lowerbound of 95% confidence interval for beta0.234
 Upperbound of 95% confidence interval for beta0.956
 Lowerbound of 95% confidence interval for alpha-0.566
 Upperbound of 95% confidence interval for alpha1.053
 Treynor index (mean / b)0.552
 Jensen alpha (a)0.244
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.135
 SD0.609
 Sharpe ratio (Glass type estimate) 0.222
 Sharpe ratio (Hedges UMVUE)0.222
 df858.000
 t0.351
 p0.363
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.018
 Upperbound of 95% confidence interval for Sharpe Ratio1.463
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.018
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.462
Statistics related to Sortino ratio
 Sortino ratio0.342
 Upside Potential Ratio6.950
 Upside part of mean2.748
 Downside part of mean-2.613
 Upside SD0.463
 Downside SD0.395
 N nonnegative terms371.000
 N negative terms488.000
Statistics related to linear regression on benchmark
 N of observations859.000
 Mean of predictor0.135
 Mean of criterion0.135
 SD of predictor0.121
 SD of criterion0.609
 Covariance0.008
 r0.109
 b (slope, estimate of beta)0.552
 a (intercept, estimate of alpha)0.061
 Mean Square Error0.367
 DF error857.000
 t(b)3.224
 p(b)0.001
 t(a)0.159
 p(a)0.437
 Lowerbound of 95% confidence interval for beta0.216
 Upperbound of 95% confidence interval for beta0.888
 Lowerbound of 95% confidence interval for alpha-0.692
 Upperbound of 95% confidence interval for alpha0.815
 Treynor index (mean / b)0.245
 Jensen alpha (a)0.061
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 VaR0.039
ORDER STATISTICS
Quartiles of return rates
 Number of observations859.000
 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 low75.000
 Percentage of outliers low0.087
 Mean of outliers low0.945
 Number of outliers high68.000
 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)0.453
 VaR(95%) (moments method)0.022
 Expected Shortfall (moments method)0.049
 Extreme Value Index (regression method)0.313
 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)0.226
 Compounded annual return (geometric extrapolation)0.196
 Calmar ratio (compounded annual return / max draw down)0.249
 Compounded annual return / average of 25% largest draw downs0.970
 Compounded annual return / Expected Shortfall lognormal3.021
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.617
 SD1.036
 Sharpe ratio (Glass type estimate) 1.561
 Sharpe ratio (Hedges UMVUE)1.554
 df171.000
 t1.104
 p0.447
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.218
 Upperbound of 95% confidence interval for Sharpe Ratio4.335
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.223
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.331
Statistics related to Sortino ratio
 Sortino ratio6.404
 Upside Potential Ratio10.967
 Upside part of mean2.768
 Downside part of mean-1.152
 Upside SD1.005
 Downside SD0.252
 N nonnegative terms48.000
 N negative terms124.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.135
 Mean of criterion1.617
 SD of predictor0.132
 SD of criterion1.036
 Covariance0.017
 r0.121
 b (slope, estimate of beta)0.947
 a (intercept, estimate of alpha)1.489
 Mean Square Error1.063
 DF error170.000
 t(b)1.589
 p(b)0.440
 t(a)1.020
 p(a)0.461
 Lowerbound of 95% confidence interval for beta-0.229
 Upperbound of 95% confidence interval for beta2.123
 Lowerbound of 95% confidence interval for alpha-1.394
 Upperbound of 95% confidence interval for alpha4.372
 Treynor index (mean / b)1.708
 Jensen alpha (a)1.489
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean1.201
 SD0.856
 Sharpe ratio (Glass type estimate) 1.403
 Sharpe ratio (Hedges UMVUE)1.397
 df171.000
 t0.992
 p0.452
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.374
 Upperbound of 95% confidence interval for Sharpe Ratio4.177
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.379
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.173
Statistics related to Sortino ratio
 Sortino ratio4.562
 Upside Potential Ratio9.064
 Upside part of mean2.387
 Downside part of mean-1.185
 Upside SD0.815
 Downside SD0.263
 N nonnegative terms48.000
 N negative terms124.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.126
 Mean of criterion1.201
 SD of predictor0.133
 SD of criterion0.856
 Covariance0.014
 r0.120
 b (slope, estimate of beta)0.777
 a (intercept, estimate of alpha)1.104
 Mean Square Error0.727
 DF error170.000
 t(b)1.582
 p(b)0.440
 t(a)0.914
 p(a)0.465
 Lowerbound of 95% confidence interval for beta-0.193
 Upperbound of 95% confidence interval for beta1.747
 Lowerbound of 95% confidence interval for alpha-1.279
 Upperbound of 95% confidence interval for alpha3.486
 Treynor index (mean / b)1.546
 Jensen alpha (a)1.104
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.070
 Expected Shortfall on VaR0.088
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.021
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 10.987
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.032
 Inter Quartile Range0.001
 Number outliers low22.000
 Percentage of outliers low0.128
 Mean of outliers low0.975
 Number of outliers high36.000
 Percentage of outliers high0.209
 Mean of outliers high1.038
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.006
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.347
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.031
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations4.000
 Minimum0.026
 Quartile 10.044
 Median0.063
 Quartile 30.118
 Maximum0.242
 Mean of quarter 10.026
 Mean of quarter 20.050
 Mean of quarter 30.076
 Mean of quarter 40.242
 Inter Quartile Range0.074
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.250
 Mean of outliers high0.242
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)1.728
 Compounded annual return (geometric extrapolation)2.474
 Calmar ratio (compounded annual return / max draw down)10.208
 Compounded annual return / average of 25% largest draw downs10.208
 Compounded annual return / Expected Shortfall lognormal28.277