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Advanced Statistics: MaxProfits

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
 Mean3.135
 SD1.598
 Sharpe ratio (Glass type estimate) 1.962
 Sharpe ratio (Hedges UMVUE)1.771
 df8.000
 t1.699
 p0.064
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.542
 Upperbound of 95% confidence interval for Sharpe Ratio4.363
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.653
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.195
Statistics related to Sortino ratio
 Sortino ratio5.250
 Upside Potential Ratio6.841
 Upside part of mean4.086
 Downside part of mean-0.951
 Upside SD1.653
 Downside SD0.597
 N nonnegative terms5.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations9.000
 Mean of predictor0.138
 Mean of criterion3.135
 SD of predictor0.183
 SD of criterion1.598
 Covariance-0.016
 r-0.055
 b (slope, estimate of beta)-0.481
 a (intercept, estimate of alpha)3.202
 Mean Square Error2.910
 DF error7.000
 t(b)-0.146
 p(b)0.556
 t(a)1.584
 p(a)0.079
 Lowerbound of 95% confidence interval for beta-8.255
 Upperbound of 95% confidence interval for beta7.293
 Lowerbound of 95% confidence interval for alpha-1.579
 Upperbound of 95% confidence interval for alpha7.983
 Treynor index (mean / b)-6.517
 Jensen alpha (a)3.202
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean1.940
 SD1.435
 Sharpe ratio (Glass type estimate) 1.352
 Sharpe ratio (Hedges UMVUE)1.220
 df8.000
 t1.171
 p0.138
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.042
 Upperbound of 95% confidence interval for Sharpe Ratio3.669
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.121
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.561
Statistics related to Sortino ratio
 Sortino ratio2.536
 Upside Potential Ratio4.097
 Upside part of mean3.134
 Downside part of mean-1.194
 Upside SD1.249
 Downside SD0.765
 N nonnegative terms5.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations9.000
 Mean of predictor0.123
 Mean of criterion1.940
 SD of predictor0.180
 SD of criterion1.435
 Covariance-0.020
 r-0.078
 b (slope, estimate of beta)-0.622
 a (intercept, estimate of alpha)2.016
 Mean Square Error2.340
 DF error7.000
 t(b)-0.206
 p(b)0.579
 t(a)1.117
 p(a)0.150
 Lowerbound of 95% confidence interval for beta-7.744
 Upperbound of 95% confidence interval for beta6.501
 Lowerbound of 95% confidence interval for alpha-2.251
 Upperbound of 95% confidence interval for alpha6.284
 Treynor index (mean / b)-3.121
 Jensen alpha (a)2.016
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.405
 Expected Shortfall on VaR0.494
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.168
 Expected Shortfall on VaR0.344
ORDER STATISTICS
Quartiles of return rates
 Number of observations9.000
 Minimum0.555
 Quartile 11.000
 Median1.359
 Quartile 31.592
 Maximum1.924
 Mean of quarter 10.767
 Mean of quarter 21.180
 Mean of quarter 31.563
 Mean of quarter 41.799
 Inter Quartile Range0.592
 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)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)-1.396
 VaR(95%) (regression method)0.586
 Expected Shortfall (regression method)0.617
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.445
 Quartile 10.445
 Median0.445
 Quartile 30.445
 Maximum0.445
 Mean of quarter 1NA
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 4NA
 Inter Quartile Range0.000
 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)4.571
 Compounded annual return (geometric extrapolation)6.273
 Calmar ratio (compounded annual return / max draw down)14.085
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal12.688
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean2.420
 SD1.028
 Sharpe ratio (Glass type estimate) 2.355
 Sharpe ratio (Hedges UMVUE)2.348
 df263.000
 t2.063
 p0.020
 Lowerbound of 95% confidence interval for Sharpe Ratio0.106
 Upperbound of 95% confidence interval for Sharpe Ratio4.599
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.102
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.594
Statistics related to Sortino ratio
 Sortino ratio3.856
 Upside Potential Ratio10.997
 Upside part of mean6.902
 Downside part of mean-4.482
 Upside SD0.822
 Downside SD0.628
 N nonnegative terms109.000
 N negative terms155.000
Statistics related to linear regression on benchmark
 N of observations264.000
 Mean of predictor0.228
 Mean of criterion2.420
 SD of predictor0.155
 SD of criterion1.028
 Covariance-0.018
 r-0.114
 b (slope, estimate of beta)-0.751
 a (intercept, estimate of alpha)2.591
 Mean Square Error1.047
 DF error262.000
 t(b)-1.850
 p(b)0.967
 t(a)2.212
 p(a)0.014
 Lowerbound of 95% confidence interval for beta-1.551
 Upperbound of 95% confidence interval for beta0.049
 Lowerbound of 95% confidence interval for alpha0.284
 Upperbound of 95% confidence interval for alpha4.897
 Treynor index (mean / b)-3.220
 Jensen alpha (a)2.591
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean1.895
 SD1.018
 Sharpe ratio (Glass type estimate) 1.861
 Sharpe ratio (Hedges UMVUE)1.856
 df263.000
 t1.630
 p0.052
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.384
 Upperbound of 95% confidence interval for Sharpe Ratio4.102
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.387
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.099
Statistics related to Sortino ratio
 Sortino ratio2.812
 Upside Potential Ratio9.782
 Upside part of mean6.593
 Downside part of mean-4.698
 Upside SD0.768
 Downside SD0.674
 N nonnegative terms109.000
 N negative terms155.000
Statistics related to linear regression on benchmark
 N of observations264.000
 Mean of predictor0.215
 Mean of criterion1.895
 SD of predictor0.155
 SD of criterion1.018
 Covariance-0.019
 r-0.118
 b (slope, estimate of beta)-0.777
 a (intercept, estimate of alpha)2.062
 Mean Square Error1.026
 DF error262.000
 t(b)-1.925
 p(b)0.972
 t(a)1.778
 p(a)0.038
 Lowerbound of 95% confidence interval for beta-1.572
 Upperbound of 95% confidence interval for beta0.018
 Lowerbound of 95% confidence interval for alpha-0.221
 Upperbound of 95% confidence interval for alpha4.346
 Treynor index (mean / b)-2.438
 Jensen alpha (a)2.062
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 VaR0.102
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.033
 Expected Shortfall on VaR0.069
ORDER STATISTICS
Quartiles of return rates
 Number of observations264.000
 Minimum0.765
 Quartile 10.992
 Median1.000
 Quartile 31.024
 Maximum1.314
 Mean of quarter 10.949
 Mean of quarter 20.999
 Mean of quarter 31.008
 Mean of quarter 41.073
 Inter Quartile Range0.032
 Number outliers low22.000
 Percentage of outliers low0.083
 Mean of outliers low0.901
 Number of outliers high27.000
 Percentage of outliers high0.102
 Mean of outliers high1.118
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.329
 VaR(95%) (moments method)0.034
 Expected Shortfall (moments method)0.065
 Extreme Value Index (regression method)0.149
 VaR(95%) (regression method)0.052
 Expected Shortfall (regression method)0.087
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.002
 Quartile 10.015
 Median0.054
 Quartile 30.130
 Maximum0.559
 Mean of quarter 10.008
 Mean of quarter 20.031
 Mean of quarter 30.108
 Mean of quarter 40.326
 Inter Quartile Range0.115
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.091
 Mean of outliers high0.559
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-3.750
 VaR(95%) (moments method)0.317
 Expected Shortfall (moments method)0.319
 Extreme Value Index (regression method)-0.157
 VaR(95%) (regression method)0.596
 Expected Shortfall (regression method)0.814
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)4.468
 Compounded annual return (geometric extrapolation)5.952
 Calmar ratio (compounded annual return / max draw down)10.641
 Compounded annual return / average of 25% largest draw downs18.246
 Compounded annual return / Expected Shortfall lognormal58.377
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.500
 SD0.960
 Sharpe ratio (Glass type estimate) 0.521
 Sharpe ratio (Hedges UMVUE)0.518
 df171.000
 t0.368
 p0.482
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.252
 Upperbound of 95% confidence interval for Sharpe Ratio3.292
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.254
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.291
Statistics related to Sortino ratio
 Sortino ratio0.724
 Upside Potential Ratio7.944
 Upside part of mean5.484
 Downside part of mean-4.984
 Upside SD0.664
 Downside SD0.690
 N nonnegative terms56.000
 N negative terms116.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.427
 Mean of criterion0.500
 SD of predictor0.164
 SD of criterion0.960
 Covariance-0.013
 r-0.080
 b (slope, estimate of beta)-0.469
 a (intercept, estimate of alpha)0.700
 Mean Square Error0.921
 DF error170.000
 t(b)-1.049
 p(b)0.540
 t(a)0.511
 p(a)0.480
 Lowerbound of 95% confidence interval for beta-1.352
 Upperbound of 95% confidence interval for beta0.414
 Lowerbound of 95% confidence interval for alpha-2.005
 Upperbound of 95% confidence interval for alpha3.406
 Treynor index (mean / b)-1.066
 Jensen alpha (a)0.700
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.030
 SD0.980
 Sharpe ratio (Glass type estimate) 0.030
 Sharpe ratio (Hedges UMVUE)0.030
 df171.000
 t0.022
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.741
 Upperbound of 95% confidence interval for Sharpe Ratio2.802
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.741
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.802
Statistics related to Sortino ratio
 Sortino ratio0.040
 Upside Potential Ratio7.074
 Upside part of mean5.277
 Downside part of mean-5.247
 Upside SD0.631
 Downside SD0.746
 N nonnegative terms56.000
 N negative terms116.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.414
 Mean of criterion0.030
 SD of predictor0.163
 SD of criterion0.980
 Covariance-0.014
 r-0.089
 b (slope, estimate of beta)-0.536
 a (intercept, estimate of alpha)0.252
 Mean Square Error0.958
 DF error170.000
 t(b)-1.170
 p(b)0.545
 t(a)0.180
 p(a)0.493
 Lowerbound of 95% confidence interval for beta-1.441
 Upperbound of 95% confidence interval for beta0.368
 Lowerbound of 95% confidence interval for alpha-2.507
 Upperbound of 95% confidence interval for alpha3.010
 Treynor index (mean / b)-0.056
 Jensen alpha (a)0.252
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.083
 Expected Shortfall on VaR0.103
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.040
 Expected Shortfall on VaR0.082
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.765
 Quartile 10.991
 Median1.000
 Quartile 31.019
 Maximum1.200
 Mean of quarter 10.943
 Mean of quarter 20.999
 Mean of quarter 31.003
 Mean of quarter 41.061
 Inter Quartile Range0.029
 Number outliers low16.000
 Percentage of outliers low0.093
 Mean of outliers low0.898
 Number of outliers high18.000
 Percentage of outliers high0.105
 Mean of outliers high1.096
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.029
 VaR(95%) (moments method)0.034
 Expected Shortfall (moments method)0.048
 Extreme Value Index (regression method)0.141
 VaR(95%) (regression method)0.062
 Expected Shortfall (regression method)0.105
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.054
 Quartile 10.090
 Median0.127
 Quartile 30.343
 Maximum0.559
 Mean of quarter 10.054
 Mean of quarter 20.127
 Mean of quarter 3NA
 Mean of quarter 40.559
 Inter Quartile Range0.253
 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)0.075
 Compounded annual return (geometric extrapolation)0.077
 Calmar ratio (compounded annual return / max draw down)0.137
 Compounded annual return / average of 25% largest draw downs0.137
 Compounded annual return / Expected Shortfall lognormal0.744