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Advanced Statistics: Seven Sentinels ES Pro

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
 Mean1.175
 SD0.892
 Sharpe ratio (Glass type estimate) 1.317
 Sharpe ratio (Hedges UMVUE)1.277
 df25.000
 t1.939
 p0.032
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.075
 Upperbound of 95% confidence interval for Sharpe Ratio2.685
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.101
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.655
Statistics related to Sortino ratio
 Sortino ratio2.585
 Upside Potential Ratio4.053
 Upside part of mean1.843
 Downside part of mean-0.668
 Upside SD0.821
 Downside SD0.455
 N nonnegative terms17.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations26.000
 Mean of predictor0.085
 Mean of criterion1.175
 SD of predictor0.127
 SD of criterion0.892
 Covariance-0.043
 r-0.378
 b (slope, estimate of beta)-2.660
 a (intercept, estimate of alpha)1.403
 Mean Square Error0.711
 DF error24.000
 t(b)-2.001
 p(b)0.972
 t(a)2.402
 p(a)0.012
 Lowerbound of 95% confidence interval for beta-5.403
 Upperbound of 95% confidence interval for beta0.084
 Lowerbound of 95% confidence interval for alpha0.197
 Upperbound of 95% confidence interval for alpha2.608
 Treynor index (mean / b)-0.442
 Jensen alpha (a)1.403
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.772
 SD0.872
 Sharpe ratio (Glass type estimate) 0.886
 Sharpe ratio (Hedges UMVUE)0.859
 df25.000
 t1.304
 p0.102
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.476
 Upperbound of 95% confidence interval for Sharpe Ratio2.231
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.494
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.212
Statistics related to Sortino ratio
 Sortino ratio1.374
 Upside Potential Ratio2.801
 Upside part of mean1.574
 Downside part of mean-0.802
 Upside SD0.682
 Downside SD0.562
 N nonnegative terms17.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations26.000
 Mean of predictor0.077
 Mean of criterion0.772
 SD of predictor0.127
 SD of criterion0.872
 Covariance-0.042
 r-0.383
 b (slope, estimate of beta)-2.636
 a (intercept, estimate of alpha)0.976
 Mean Square Error0.676
 DF error24.000
 t(b)-2.032
 p(b)0.973
 t(a)1.720
 p(a)0.049
 Lowerbound of 95% confidence interval for beta-5.314
 Upperbound of 95% confidence interval for beta0.042
 Lowerbound of 95% confidence interval for alpha-0.195
 Upperbound of 95% confidence interval for alpha2.147
 Treynor index (mean / b)-0.293
 Jensen alpha (a)0.976
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.295
 Expected Shortfall on VaR0.363
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.098
 Expected Shortfall on VaR0.216
ORDER STATISTICS
Quartiles of return rates
 Number of observations26.000
 Minimum0.565
 Quartile 10.986
 Median1.068
 Quartile 31.256
 Maximum1.622
 Mean of quarter 10.798
 Mean of quarter 21.026
 Mean of quarter 31.173
 Mean of quarter 41.409
 Inter Quartile Range0.270
 Number outliers low1.000
 Percentage of outliers low0.038
 Mean of outliers low0.565
 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)0.038
 VaR(95%) (moments method)0.085
 Expected Shortfall (moments method)0.131
 Extreme Value Index (regression method)-0.196
 VaR(95%) (regression method)0.278
 Expected Shortfall (regression method)0.390
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations6.000
 Minimum0.044
 Quartile 10.138
 Median0.241
 Quartile 30.324
 Maximum0.435
 Mean of quarter 10.081
 Mean of quarter 20.197
 Mean of quarter 30.285
 Mean of quarter 40.386
 Inter Quartile Range0.187
 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)2.245
 Compounded annual return (geometric extrapolation)1.262
 Calmar ratio (compounded annual return / max draw down)2.904
 Compounded annual return / average of 25% largest draw downs3.270
 Compounded annual return / Expected Shortfall lognormal3.480
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.429
 SD1.265
 Sharpe ratio (Glass type estimate) 1.129
 Sharpe ratio (Hedges UMVUE)1.128
 df745.000
 t1.663
 p0.048
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.203
 Upperbound of 95% confidence interval for Sharpe Ratio2.461
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.204
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.460
Statistics related to Sortino ratio
 Sortino ratio2.352
 Upside Potential Ratio8.783
 Upside part of mean5.337
 Downside part of mean-3.908
 Upside SD1.112
 Downside SD0.608
 N nonnegative terms332.000
 N negative terms414.000
Statistics related to linear regression on benchmark
 N of observations746.000
 Mean of predictor0.093
 Mean of criterion1.429
 SD of predictor0.182
 SD of criterion1.265
 Covariance-0.020
 r-0.086
 b (slope, estimate of beta)-0.596
 a (intercept, estimate of alpha)1.485
 Mean Square Error1.591
 DF error744.000
 t(b)-2.351
 p(b)0.991
 t(a)1.733
 p(a)0.042
 Lowerbound of 95% confidence interval for beta-1.094
 Upperbound of 95% confidence interval for beta-0.098
 Lowerbound of 95% confidence interval for alpha-0.198
 Upperbound of 95% confidence interval for alpha3.167
 Treynor index (mean / b)-2.398
 Jensen alpha (a)1.485
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.772
 SD1.115
 Sharpe ratio (Glass type estimate) 0.692
 Sharpe ratio (Hedges UMVUE)0.691
 df745.000
 t1.019
 p0.154
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.639
 Upperbound of 95% confidence interval for Sharpe Ratio2.023
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.640
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.023
Statistics related to Sortino ratio
 Sortino ratio1.073
 Upside Potential Ratio6.823
 Upside part of mean4.908
 Downside part of mean-4.137
 Upside SD0.852
 Downside SD0.719
 N nonnegative terms332.000
 N negative terms414.000
Statistics related to linear regression on benchmark
 N of observations746.000
 Mean of predictor0.077
 Mean of criterion0.772
 SD of predictor0.183
 SD of criterion1.115
 Covariance-0.020
 r-0.097
 b (slope, estimate of beta)-0.589
 a (intercept, estimate of alpha)0.817
 Mean Square Error1.233
 DF error744.000
 t(b)-2.647
 p(b)0.996
 t(a)1.083
 p(a)0.140
 Lowerbound of 95% confidence interval for beta-1.026
 Upperbound of 95% confidence interval for beta-0.152
 Lowerbound of 95% confidence interval for alpha-0.664
 Upperbound of 95% confidence interval for alpha2.298
 Treynor index (mean / b)-1.310
 Jensen alpha (a)0.817
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.092
 Expected Shortfall on VaR0.114
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.027
 Expected Shortfall on VaR0.059
ORDER STATISTICS
Quartiles of return rates
 Number of observations746.000
 Minimum0.483
 Quartile 10.992
 Median1.000
 Quartile 31.013
 Maximum2.224
 Mean of quarter 10.956
 Mean of quarter 20.998
 Mean of quarter 31.004
 Mean of quarter 41.058
 Inter Quartile Range0.021
 Number outliers low77.000
 Percentage of outliers low0.103
 Mean of outliers low0.922
 Number of outliers high66.000
 Percentage of outliers high0.088
 Mean of outliers high1.116
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.438
 VaR(95%) (moments method)0.033
 Expected Shortfall (moments method)0.072
 Extreme Value Index (regression method)0.230
 VaR(95%) (regression method)0.036
 Expected Shortfall (regression method)0.063
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations28.000
 Minimum0.003
 Quartile 10.010
 Median0.059
 Quartile 30.147
 Maximum0.676
 Mean of quarter 10.005
 Mean of quarter 20.022
 Mean of quarter 30.099
 Mean of quarter 40.390
 Inter Quartile Range0.137
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high4.000
 Percentage of outliers high0.143
 Mean of outliers high0.506
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.304
 VaR(95%) (moments method)0.396
 Expected Shortfall (moments method)0.418
 Extreme Value Index (regression method)-0.474
 VaR(95%) (regression method)0.555
 Expected Shortfall (regression method)0.663
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)2.243
 Compounded annual return (geometric extrapolation)1.261
 Calmar ratio (compounded annual return / max draw down)1.866
 Compounded annual return / average of 25% largest draw downs3.232
 Compounded annual return / Expected Shortfall lognormal11.019
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.257
 SD1.126
 Sharpe ratio (Glass type estimate) 1.117
 Sharpe ratio (Hedges UMVUE)1.112
 df171.000
 t0.789
 p0.462
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.659
 Upperbound of 95% confidence interval for Sharpe Ratio3.889
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.663
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.886
Statistics related to Sortino ratio
 Sortino ratio2.874
 Upside Potential Ratio9.731
 Upside part of mean4.255
 Downside part of mean-2.999
 Upside SD1.036
 Downside SD0.437
 N nonnegative terms47.000
 N negative terms125.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.340
 Mean of criterion1.257
 SD of predictor0.119
 SD of criterion1.126
 Covariance-0.001
 r-0.008
 b (slope, estimate of beta)-0.077
 a (intercept, estimate of alpha)1.283
 Mean Square Error1.275
 DF error170.000
 t(b)-0.106
 p(b)0.504
 t(a)0.794
 p(a)0.470
 Lowerbound of 95% confidence interval for beta-1.507
 Upperbound of 95% confidence interval for beta1.353
 Lowerbound of 95% confidence interval for alpha-1.906
 Upperbound of 95% confidence interval for alpha4.472
 Treynor index (mean / b)-16.334
 Jensen alpha (a)1.283
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.741
 SD0.971
 Sharpe ratio (Glass type estimate) 0.763
 Sharpe ratio (Hedges UMVUE)0.760
 df171.000
 t0.539
 p0.474
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.011
 Upperbound of 95% confidence interval for Sharpe Ratio3.535
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.013
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.533
Statistics related to Sortino ratio
 Sortino ratio1.617
 Upside Potential Ratio8.381
 Upside part of mean3.841
 Downside part of mean-3.100
 Upside SD0.854
 Downside SD0.458
 N nonnegative terms47.000
 N negative terms125.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.333
 Mean of criterion0.741
 SD of predictor0.119
 SD of criterion0.971
 Covariance-0.002
 r-0.018
 b (slope, estimate of beta)-0.148
 a (intercept, estimate of alpha)0.790
 Mean Square Error0.949
 DF error170.000
 t(b)-0.237
 p(b)0.509
 t(a)0.567
 p(a)0.478
 Lowerbound of 95% confidence interval for beta-1.384
 Upperbound of 95% confidence interval for beta1.088
 Lowerbound of 95% confidence interval for alpha-1.960
 Upperbound of 95% confidence interval for alpha3.541
 Treynor index (mean / b)-5.002
 Jensen alpha (a)0.790
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.081
 Expected Shortfall on VaR0.100
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.025
 Expected Shortfall on VaR0.052
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.858
 Quartile 10.997
 Median1.000
 Quartile 31.002
 Maximum1.599
 Mean of quarter 10.966
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.050
 Inter Quartile Range0.005
 Number outliers low32.000
 Percentage of outliers low0.186
 Mean of outliers low0.956
 Number of outliers high31.000
 Percentage of outliers high0.180
 Mean of outliers high1.067
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.588
 VaR(95%) (moments method)0.020
 Expected Shortfall (moments method)0.059
 Extreme Value Index (regression method)0.284
 VaR(95%) (regression method)0.029
 Expected Shortfall (regression method)0.057
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations8.000
 Minimum0.014
 Quartile 10.044
 Median0.069
 Quartile 30.121
 Maximum0.393
 Mean of quarter 10.026
 Mean of quarter 20.052
 Mean of quarter 30.097
 Mean of quarter 40.267
 Inter Quartile Range0.077
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.125
 Mean of outliers high0.393
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)0.962
 Compounded annual return (geometric extrapolation)1.193
 Calmar ratio (compounded annual return / max draw down)3.031
 Compounded annual return / average of 25% largest draw downs4.468
 Compounded annual return / Expected Shortfall lognormal11.891