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Advanced Statistics: 2d

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
 Mean0.315
 SD0.303
 Sharpe ratio (Glass type estimate) 1.039
 Sharpe ratio (Hedges UMVUE)0.997
 df19.000
 t1.341
 p0.316
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.528
 Upperbound of 95% confidence interval for Sharpe Ratio2.579
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.554
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.548
Statistics related to Sortino ratio
 Sortino ratio2.446
 Upside Potential Ratio3.870
 Upside part of mean0.499
 Downside part of mean-0.183
 Upside SD0.281
 Downside SD0.129
 N nonnegative terms14.000
 N negative terms6.000
Statistics related to linear regression on benchmark
 N of observations20.000
 Mean of predictor0.133
 Mean of criterion0.315
 SD of predictor0.087
 SD of criterion0.303
 Covariance-0.003
 r-0.132
 b (slope, estimate of beta)-0.458
 a (intercept, estimate of alpha)0.376
 Mean Square Error0.095
 DF error18.000
 t(b)-0.563
 p(b)0.566
 t(a)1.432
 p(a)0.340
 Lowerbound of 95% confidence interval for beta-2.165
 Upperbound of 95% confidence interval for beta1.250
 Lowerbound of 95% confidence interval for alpha-0.176
 Upperbound of 95% confidence interval for alpha0.928
 Treynor index (mean / b)-0.689
 Jensen alpha (a)0.376
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.271
 SD0.282
 Sharpe ratio (Glass type estimate) 0.960
 Sharpe ratio (Hedges UMVUE)0.922
 df19.000
 t1.240
 p0.328
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.600
 Upperbound of 95% confidence interval for Sharpe Ratio2.497
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.624
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.468
Statistics related to Sortino ratio
 Sortino ratio1.989
 Upside Potential Ratio3.396
 Upside part of mean0.463
 Downside part of mean-0.192
 Upside SD0.251
 Downside SD0.136
 N nonnegative terms14.000
 N negative terms6.000
Statistics related to linear regression on benchmark
 N of observations20.000
 Mean of predictor0.128
 Mean of criterion0.271
 SD of predictor0.086
 SD of criterion0.282
 Covariance-0.003
 r-0.117
 b (slope, estimate of beta)-0.386
 a (intercept, estimate of alpha)0.321
 Mean Square Error0.083
 DF error18.000
 t(b)-0.501
 p(b)0.559
 t(a)1.314
 p(a)0.352
 Lowerbound of 95% confidence interval for beta-2.003
 Upperbound of 95% confidence interval for beta1.231
 Lowerbound of 95% confidence interval for alpha-0.192
 Upperbound of 95% confidence interval for alpha0.833
 Treynor index (mean / b)-0.702
 Jensen alpha (a)0.321
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.105
 Expected Shortfall on VaR0.135
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.024
 Expected Shortfall on VaR0.055
ORDER STATISTICS
Quartiles of return rates
 Number of observations20.000
 Minimum0.871
 Quartile 10.987
 Median1.027
 Quartile 31.038
 Maximum1.308
 Mean of quarter 10.946
 Mean of quarter 21.011
 Mean of quarter 31.032
 Mean of quarter 41.131
 Inter Quartile Range0.051
 Number outliers low1.000
 Percentage of outliers low0.050
 Mean of outliers low0.871
 Number of outliers high2.000
 Percentage of outliers high0.100
 Mean of outliers high1.227
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.844
 VaR(95%) (moments method)0.061
 Expected Shortfall (moments method)0.403
 Extreme Value Index (regression method)2.178
 VaR(95%) (regression method)0.047
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.019
 Quartile 10.025
 Median0.031
 Quartile 30.125
 Maximum0.219
 Mean of quarter 10.019
 Mean of quarter 20.031
 Mean of quarter 3NA
 Mean of quarter 40.219
 Inter Quartile Range0.100
 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)0.414
 Compounded annual return (geometric extrapolation)0.370
 Calmar ratio (compounded annual return / max draw down)1.692
 Compounded annual return / average of 25% largest draw downs1.692
 Compounded annual return / Expected Shortfall lognormal2.744
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.381
 SD0.457
 Sharpe ratio (Glass type estimate) 0.833
 Sharpe ratio (Hedges UMVUE)0.832
 df588.000
 t1.090
 p0.138
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.666
 Upperbound of 95% confidence interval for Sharpe Ratio2.331
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.667
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.330
Statistics related to Sortino ratio
 Sortino ratio1.219
 Upside Potential Ratio6.470
 Upside part of mean2.020
 Downside part of mean-1.639
 Upside SD0.334
 Downside SD0.312
 N nonnegative terms341.000
 N negative terms248.000
Statistics related to linear regression on benchmark
 N of observations589.000
 Mean of predictor0.162
 Mean of criterion0.381
 SD of predictor0.161
 SD of criterion0.457
 Covariance-0.009
 r-0.125
 b (slope, estimate of beta)-0.356
 a (intercept, estimate of alpha)0.438
 Mean Square Error0.206
 DF error587.000
 t(b)-3.058
 p(b)0.999
 t(a)1.262
 p(a)0.104
 Lowerbound of 95% confidence interval for beta-0.584
 Upperbound of 95% confidence interval for beta-0.127
 Lowerbound of 95% confidence interval for alpha-0.244
 Upperbound of 95% confidence interval for alpha1.121
 Treynor index (mean / b)-1.070
 Jensen alpha (a)0.438
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.275
 SD0.460
 Sharpe ratio (Glass type estimate) 0.598
 Sharpe ratio (Hedges UMVUE)0.598
 df588.000
 t0.783
 p0.217
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.900
 Upperbound of 95% confidence interval for Sharpe Ratio2.096
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.901
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.096
Statistics related to Sortino ratio
 Sortino ratio0.834
 Upside Potential Ratio5.954
 Upside part of mean1.967
 Downside part of mean-1.691
 Upside SD0.320
 Downside SD0.330
 N nonnegative terms341.000
 N negative terms248.000
Statistics related to linear regression on benchmark
 N of observations589.000
 Mean of predictor0.149
 Mean of criterion0.275
 SD of predictor0.161
 SD of criterion0.460
 Covariance-0.009
 r-0.125
 b (slope, estimate of beta)-0.358
 a (intercept, estimate of alpha)0.329
 Mean Square Error0.209
 DF error587.000
 t(b)-3.055
 p(b)0.999
 t(a)0.940
 p(a)0.174
 Lowerbound of 95% confidence interval for beta-0.588
 Upperbound of 95% confidence interval for beta-0.128
 Lowerbound of 95% confidence interval for alpha-0.358
 Upperbound of 95% confidence interval for alpha1.015
 Treynor index (mean / b)-0.770
 Jensen alpha (a)0.329
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.039
 Expected Shortfall on VaR0.049
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.022
ORDER STATISTICS
Quartiles of return rates
 Number of observations589.000
 Minimum0.819
 Quartile 10.998
 Median1.001
 Quartile 31.003
 Maximum1.176
 Mean of quarter 10.982
 Mean of quarter 21.000
 Mean of quarter 31.002
 Mean of quarter 41.022
 Inter Quartile Range0.005
 Number outliers low69.000
 Percentage of outliers low0.117
 Mean of outliers low0.965
 Number of outliers high70.000
 Percentage of outliers high0.119
 Mean of outliers high1.040
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.154
 VaR(95%) (moments method)0.015
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.688
 VaR(95%) (regression method)0.013
 Expected Shortfall (regression method)0.050
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations76.000
 Minimum0.000
 Quartile 10.001
 Median0.002
 Quartile 30.009
 Maximum0.475
 Mean of quarter 10.000
 Mean of quarter 20.002
 Mean of quarter 30.005
 Mean of quarter 40.064
 Inter Quartile Range0.009
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high11.000
 Percentage of outliers high0.145
 Mean of outliers high0.103
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.072
 VaR(95%) (moments method)0.058
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)1.173
 VaR(95%) (regression method)0.057
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.425
 Compounded annual return (geometric extrapolation)0.376
 Calmar ratio (compounded annual return / max draw down)0.792
 Compounded annual return / average of 25% largest draw downs5.839
 Compounded annual return / Expected Shortfall lognormal7.666
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.285
 SD0.272
 Sharpe ratio (Glass type estimate) 1.050
 Sharpe ratio (Hedges UMVUE)1.046
 df171.000
 t0.743
 p0.464
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.725
 Upperbound of 95% confidence interval for Sharpe Ratio3.823
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.728
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.820
Statistics related to Sortino ratio
 Sortino ratio1.968
 Upside Potential Ratio9.731
 Upside part of mean1.411
 Downside part of mean-1.126
 Upside SD0.229
 Downside SD0.145
 N nonnegative terms84.000
 N negative terms88.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.380
 Mean of criterion0.285
 SD of predictor0.116
 SD of criterion0.272
 Covariance-0.003
 r-0.103
 b (slope, estimate of beta)-0.242
 a (intercept, estimate of alpha)0.377
 Mean Square Error0.073
 DF error170.000
 t(b)-1.356
 p(b)0.552
 t(a)0.969
 p(a)0.463
 Lowerbound of 95% confidence interval for beta-0.594
 Upperbound of 95% confidence interval for beta0.110
 Lowerbound of 95% confidence interval for alpha-0.391
 Upperbound of 95% confidence interval for alpha1.146
 Treynor index (mean / b)-1.180
 Jensen alpha (a)0.377
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.249
 SD0.267
 Sharpe ratio (Glass type estimate) 0.934
 Sharpe ratio (Hedges UMVUE)0.930
 df171.000
 t0.660
 p0.468
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.841
 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 ratio1.695
 Upside Potential Ratio9.417
 Upside part of mean1.386
 Downside part of mean-1.136
 Upside SD0.222
 Downside SD0.147
 N nonnegative terms84.000
 N negative terms88.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.373
 Mean of criterion0.249
 SD of predictor0.116
 SD of criterion0.267
 Covariance-0.003
 r-0.107
 b (slope, estimate of beta)-0.246
 a (intercept, estimate of alpha)0.341
 Mean Square Error0.071
 DF error170.000
 t(b)-1.401
 p(b)0.553
 t(a)0.892
 p(a)0.466
 Lowerbound of 95% confidence interval for beta-0.593
 Upperbound of 95% confidence interval for beta0.101
 Lowerbound of 95% confidence interval for alpha-0.413
 Upperbound of 95% confidence interval for alpha1.096
 Treynor index (mean / b)-1.014
 Jensen alpha (a)0.341
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.008
 Expected Shortfall on VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.951
 Quartile 10.997
 Median1.000
 Quartile 31.003
 Maximum1.092
 Mean of quarter 10.988
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.016
 Inter Quartile Range0.005
 Number outliers low20.000
 Percentage of outliers low0.116
 Mean of outliers low0.980
 Number of outliers high19.000
 Percentage of outliers high0.110
 Mean of outliers high1.028
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.357
 VaR(95%) (moments method)0.010
 Expected Shortfall (moments method)0.019
 Extreme Value Index (regression method)0.083
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.016
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations24.000
 Minimum0.000
 Quartile 10.001
 Median0.002
 Quartile 30.012
 Maximum0.091
 Mean of quarter 10.000
 Mean of quarter 20.001
 Mean of quarter 30.006
 Mean of quarter 40.052
 Inter Quartile Range0.011
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high4.000
 Percentage of outliers high0.167
 Mean of outliers high0.067
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.169
 VaR(95%) (moments method)0.045
 Expected Shortfall (moments method)0.049
 Extreme Value Index (regression method)-0.931
 VaR(95%) (regression method)0.076
 Expected Shortfall (regression method)0.084
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.316
 Compounded annual return (geometric extrapolation)0.341
 Calmar ratio (compounded annual return / max draw down)3.738
 Compounded annual return / average of 25% largest draw downs6.555
 Compounded annual return / Expected Shortfall lognormal11.947