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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
 Mean0.317
 SD0.644
 Sharpe ratio (Glass type estimate) 0.492
 Sharpe ratio (Hedges UMVUE)0.492
 df884.000
 t0.790
 p0.215
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.730
 Upperbound of 95% confidence interval for Sharpe Ratio1.715
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.730
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.714
Statistics related to Sortino ratio
 Sortino ratio0.863
 Upside Potential Ratio7.565
 Upside part of mean2.782
 Downside part of mean-2.465
 Upside SD0.529
 Downside SD0.368
 N nonnegative terms371.000
 N negative terms514.000
Statistics related to linear regression on benchmark
 N of observations885.000
 Mean of predictor0.158
 Mean of criterion0.317
 SD of predictor0.125
 SD of criterion0.644
 Covariance0.008
 r0.104
 b (slope, estimate of beta)0.539
 a (intercept, estimate of alpha)0.232
 Mean Square Error0.411
 DF error883.000
 t(b)3.118
 p(b)0.001
 t(a)0.580
 p(a)0.281
 Lowerbound of 95% confidence interval for beta0.200
 Upperbound of 95% confidence interval for beta0.877
 Lowerbound of 95% confidence interval for alpha-0.554
 Upperbound of 95% confidence interval for alpha1.019
 Treynor index (mean / b)0.589
 Jensen alpha (a)0.232
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.130
 SD0.600
 Sharpe ratio (Glass type estimate) 0.217
 Sharpe ratio (Hedges UMVUE)0.217
 df884.000
 t0.348
 p0.364
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.005
 Upperbound of 95% confidence interval for Sharpe Ratio1.439
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.005
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.439
Statistics related to Sortino ratio
 Sortino ratio0.334
 Upside Potential Ratio6.847
 Upside part of mean2.668
 Downside part of mean-2.538
 Upside SD0.456
 Downside SD0.390
 N nonnegative terms371.000
 N negative terms514.000
Statistics related to linear regression on benchmark
 N of observations885.000
 Mean of predictor0.150
 Mean of criterion0.130
 SD of predictor0.125
 SD of criterion0.600
 Covariance0.008
 r0.104
 b (slope, estimate of beta)0.502
 a (intercept, estimate of alpha)0.055
 Mean Square Error0.356
 DF error883.000
 t(b)3.117
 p(b)0.001
 t(a)0.147
 p(a)0.441
 Lowerbound of 95% confidence interval for beta0.186
 Upperbound of 95% confidence interval for beta0.818
 Lowerbound of 95% confidence interval for alpha-0.677
 Upperbound of 95% confidence interval for alpha0.787
 Treynor index (mean / b)0.259
 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%)0.051
 Expected Shortfall on VaR0.064
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 observations885.000
 Minimum0.762
 Quartile 10.995
 Median1.000
 Quartile 31.009
 Maximum1.591
 Mean of quarter 10.973
 Mean of quarter 20.999
 Mean of quarter 31.002
 Mean of quarter 41.030
 Inter Quartile Range0.013
 Number outliers low88.000
 Percentage of outliers low0.099
 Mean of outliers low0.950
 Number of outliers high70.000
 Percentage of outliers high0.079
 Mean of outliers high1.060
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.459
 VaR(95%) (moments method)0.021
 Expected Shortfall (moments method)0.047
 Extreme Value Index (regression method)0.303
 VaR(95%) (regression method)0.024
 Expected Shortfall (regression method)0.046
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)0.220
 Compounded annual return (geometric extrapolation)0.190
 Calmar ratio (compounded annual return / max draw down)0.241
 Compounded annual return / average of 25% largest draw downs0.939
 Compounded annual return / Expected Shortfall lognormal2.966
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.377
 SD0.562
 Sharpe ratio (Glass type estimate) 0.670
 Sharpe ratio (Hedges UMVUE)0.667
 df171.000
 t0.474
 p0.477
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.104
 Upperbound of 95% confidence interval for Sharpe Ratio3.442
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.106
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.440
Statistics related to Sortino ratio
 Sortino ratio2.016
 Upside Potential Ratio5.322
 Upside part of mean0.995
 Downside part of mean-0.618
 Upside SD0.529
 Downside SD0.187
 N nonnegative terms33.000
 N negative terms139.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.214
 Mean of criterion0.377
 SD of predictor0.154
 SD of criterion0.562
 Covariance0.009
 r0.108
 b (slope, estimate of beta)0.395
 a (intercept, estimate of alpha)0.292
 Mean Square Error0.314
 DF error170.000
 t(b)1.415
 p(b)0.446
 t(a)0.367
 p(a)0.486
 Lowerbound of 95% confidence interval for beta-0.156
 Upperbound of 95% confidence interval for beta0.946
 Lowerbound of 95% confidence interval for alpha-1.277
 Upperbound of 95% confidence interval for alpha1.862
 Treynor index (mean / b)0.953
 Jensen alpha (a)0.292
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.245
 SD0.492
 Sharpe ratio (Glass type estimate) 0.498
 Sharpe ratio (Hedges UMVUE)0.496
 df171.000
 t0.352
 p0.483
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.275
 Upperbound of 95% confidence interval for Sharpe Ratio3.270
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.276
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.269
Statistics related to Sortino ratio
 Sortino ratio1.251
 Upside Potential Ratio4.497
 Upside part of mean0.882
 Downside part of mean-0.636
 Upside SD0.450
 Downside SD0.196
 N nonnegative terms33.000
 N negative terms139.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.202
 Mean of criterion0.245
 SD of predictor0.153
 SD of criterion0.492
 Covariance0.009
 r0.115
 b (slope, estimate of beta)0.369
 a (intercept, estimate of alpha)0.171
 Mean Square Error0.241
 DF error170.000
 t(b)1.506
 p(b)0.443
 t(a)0.245
 p(a)0.491
 Lowerbound of 95% confidence interval for beta-0.115
 Upperbound of 95% confidence interval for beta0.852
 Lowerbound of 95% confidence interval for alpha-1.202
 Upperbound of 95% confidence interval for alpha1.543
 Treynor index (mean / b)0.665
 Jensen alpha (a)0.171
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.042
 Expected Shortfall on VaR0.053
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.012
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.373
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.012
 Inter Quartile Range0.000
 Number outliers low17.000
 Percentage of outliers low0.099
 Mean of outliers low0.983
 Number of outliers high34.000
 Percentage of outliers high0.198
 Mean of outliers high1.015
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.580
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.004
 Extreme Value Index (regression method)0.983
 VaR(95%) (regression method)0.003
 Expected Shortfall (regression method)0.405
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.000
 Quartile 10.002
 Median0.005
 Quartile 30.019
 Maximum0.219
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.019
 Mean of quarter 40.219
 Inter Quartile Range0.017
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.200
 Mean of outliers high0.219
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)0.311
 Compounded annual return (geometric extrapolation)0.336
 Calmar ratio (compounded annual return / max draw down)1.534
 Compounded annual return / average of 25% largest draw downs1.534
 Compounded annual return / Expected Shortfall lognormal6.385