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Advanced Statistics: ES Bomber

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
 Mean-1.371
 SD0.220
 Sharpe ratio (Glass type estimate) -6.234
 Sharpe ratio (Hedges UMVUE)-3.517
 df2.000
 t-3.117
 p0.955
 Lowerbound of 95% confidence interval for Sharpe Ratio-12.980
 Upperbound of 95% confidence interval for Sharpe Ratio0.712
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8.737
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.703
Statistics related to Sortino ratio
 Sortino ratio-3.155
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-1.371
 Upside SD0.000
 Downside SD0.434
 N nonnegative terms0.000
 N negative terms3.000
Statistics related to linear regression on benchmark
 N of observations3.000
 Mean of predictor0.440
 Mean of criterion-1.371
 SD of predictor0.108
 SD of criterion0.220
 Covariance-0.001
 r-0.034
 b (slope, estimate of beta)-0.070
 a (intercept, estimate of alpha)-1.340
 Mean Square Error0.097
 DF error1.000
 t(b)-0.034
 p(b)0.511
 t(a)-1.225
 p(a)0.782
 Lowerbound of 95% confidence interval for beta-26.040
 Upperbound of 95% confidence interval for beta25.901
 Lowerbound of 95% confidence interval for alpha-15.240
 Upperbound of 95% confidence interval for alpha12.560
 Treynor index (mean / b)19.655
 Jensen alpha (a)-1.340
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.471
 SD0.253
 Sharpe ratio (Glass type estimate) -5.824
 Sharpe ratio (Hedges UMVUE)-3.286
 df2.000
 t-2.912
 p0.950
 Lowerbound of 95% confidence interval for Sharpe Ratio-12.255
 Upperbound of 95% confidence interval for Sharpe Ratio0.849
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8.359
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.787
Statistics related to Sortino ratio
 Sortino ratio-3.116
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-1.471
 Upside SD0.000
 Downside SD0.472
 N nonnegative terms0.000
 N negative terms3.000
Statistics related to linear regression on benchmark
 N of observations3.000
 Mean of predictor0.427
 Mean of criterion-1.471
 SD of predictor0.103
 SD of criterion0.253
 Covariance-0.001
 r-0.037
 b (slope, estimate of beta)-0.091
 a (intercept, estimate of alpha)-1.432
 Mean Square Error0.127
 DF error1.000
 t(b)-0.037
 p(b)0.512
 t(a)-1.131
 p(a)0.770
 Lowerbound of 95% confidence interval for beta-31.157
 Upperbound of 95% confidence interval for beta30.976
 Lowerbound of 95% confidence interval for alpha-17.513
 Upperbound of 95% confidence interval for alpha14.649
 Treynor index (mean / b)16.199
 Jensen alpha (a)-1.432
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.215
 Expected Shortfall on VaR0.239
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.173
 Expected Shortfall on VaR0.173
ORDER STATISTICS
Quartiles of return rates
 Number of observations3.000
 Minimum0.816
 Quartile 10.868
 Median0.920
 Quartile 30.926
 Maximum0.932
 Mean of quarter 10.816
 Mean of quarter 20.920
 Mean of quarter 3NA
 Mean of quarter 40.932
 Inter Quartile Range0.058
 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)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.300
 Quartile 10.300
 Median0.300
 Quartile 30.300
 Maximum0.300
 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)-1.200
 Compounded annual return (geometric extrapolation)-0.760
 Calmar ratio (compounded annual return / max draw down)-2.533
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-3.185
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-1.189
 SD0.481
 Sharpe ratio (Glass type estimate) -2.475
 Sharpe ratio (Hedges UMVUE)-2.456
 df96.000
 t-1.314
 p0.904
 Lowerbound of 95% confidence interval for Sharpe Ratio-6.176
 Upperbound of 95% confidence interval for Sharpe Ratio1.239
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.163
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.251
Statistics related to Sortino ratio
 Sortino ratio-2.903
 Upside Potential Ratio4.734
 Upside part of mean1.940
 Downside part of mean-3.129
 Upside SD0.254
 Downside SD0.410
 N nonnegative terms32.000
 N negative terms65.000
Statistics related to linear regression on benchmark
 N of observations97.000
 Mean of predictor0.720
 Mean of criterion-1.189
 SD of predictor0.212
 SD of criterion0.481
 Covariance-0.049
 r-0.482
 b (slope, estimate of beta)-1.092
 a (intercept, estimate of alpha)-0.404
 Mean Square Error0.179
 DF error95.000
 t(b)-5.367
 p(b)1.000
 t(a)-0.498
 p(a)0.690
 Lowerbound of 95% confidence interval for beta-1.496
 Upperbound of 95% confidence interval for beta-0.688
 Lowerbound of 95% confidence interval for alpha-2.012
 Upperbound of 95% confidence interval for alpha1.205
 Treynor index (mean / b)1.089
 Jensen alpha (a)-0.404
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.309
 SD0.490
 Sharpe ratio (Glass type estimate) -2.670
 Sharpe ratio (Hedges UMVUE)-2.649
 df96.000
 t-1.418
 p0.920
 Lowerbound of 95% confidence interval for Sharpe Ratio-6.373
 Upperbound of 95% confidence interval for Sharpe Ratio1.047
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.359
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.061
Statistics related to Sortino ratio
 Sortino ratio-3.079
 Upside Potential Ratio4.487
 Upside part of mean1.908
 Downside part of mean-3.217
 Upside SD0.249
 Downside SD0.425
 N nonnegative terms32.000
 N negative terms65.000
Statistics related to linear regression on benchmark
 N of observations97.000
 Mean of predictor0.697
 Mean of criterion-1.309
 SD of predictor0.211
 SD of criterion0.490
 Covariance-0.050
 r-0.483
 b (slope, estimate of beta)-1.123
 a (intercept, estimate of alpha)-0.526
 Mean Square Error0.186
 DF error95.000
 t(b)-5.378
 p(b)1.000
 t(a)-0.637
 p(a)0.737
 Lowerbound of 95% confidence interval for beta-1.538
 Upperbound of 95% confidence interval for beta-0.709
 Lowerbound of 95% confidence interval for alpha-2.165
 Upperbound of 95% confidence interval for alpha1.113
 Treynor index (mean / b)1.165
 Jensen alpha (a)-0.526
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.046
 Expected Shortfall on VaR0.057
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.025
 Expected Shortfall on VaR0.050
ORDER STATISTICS
Quartiles of return rates
 Number of observations97.000
 Minimum0.899
 Quartile 10.994
 Median1.000
 Quartile 31.003
 Maximum1.057
 Mean of quarter 10.965
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.022
 Inter Quartile Range0.009
 Number outliers low17.000
 Percentage of outliers low0.175
 Mean of outliers low0.955
 Number of outliers high13.000
 Percentage of outliers high0.134
 Mean of outliers high1.034
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.311
 VaR(95%) (moments method)0.021
 Expected Shortfall (moments method)0.027
 Extreme Value Index (regression method)-0.143
 VaR(95%) (regression method)0.041
 Expected Shortfall (regression method)0.057
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.005
 Quartile 10.033
 Median0.061
 Quartile 30.198
 Maximum0.334
 Mean of quarter 10.005
 Mean of quarter 20.061
 Mean of quarter 3NA
 Mean of quarter 40.334
 Inter Quartile Range0.165
 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)-1.064
 Compounded annual return (geometric extrapolation)-0.718
 Calmar ratio (compounded annual return / max draw down)-2.148
 Compounded annual return / average of 25% largest draw downs-2.148
 Compounded annual return / Expected Shortfall lognormal-12.676