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Advanced Statistics: Kubera

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-0.003
 SD0.325
 Sharpe ratio (Glass type estimate) -0.010
 Sharpe ratio (Hedges UMVUE)-0.010
 df10.000
 t-0.010
 p0.504
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.057
 Upperbound of 95% confidence interval for Sharpe Ratio2.037
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.057
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.038
Statistics related to Sortino ratio
 Sortino ratio-0.013
 Upside Potential Ratio1.274
 Upside part of mean0.319
 Downside part of mean-0.322
 Upside SD0.184
 Downside SD0.250
 N nonnegative terms3.000
 N negative terms8.000
Statistics related to linear regression on benchmark
 N of observations11.000
 Mean of predictor0.151
 Mean of criterion-0.003
 SD of predictor0.270
 SD of criterion0.325
 Covariance0.017
 r0.189
 b (slope, estimate of beta)0.228
 a (intercept, estimate of alpha)-0.038
 Mean Square Error0.113
 DF error9.000
 t(b)0.579
 p(b)0.289
 t(a)-0.106
 p(a)0.541
 Lowerbound of 95% confidence interval for beta-0.664
 Upperbound of 95% confidence interval for beta1.120
 Lowerbound of 95% confidence interval for alpha-0.845
 Upperbound of 95% confidence interval for alpha0.769
 Treynor index (mean / b)-0.015
 Jensen alpha (a)-0.038
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.056
 SD0.348
 Sharpe ratio (Glass type estimate) -0.160
 Sharpe ratio (Hedges UMVUE)-0.148
 df10.000
 t-0.153
 p0.559
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.205
 Upperbound of 95% confidence interval for Sharpe Ratio1.892
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.196
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.900
Statistics related to Sortino ratio
 Sortino ratio-0.197
 Upside Potential Ratio1.064
 Upside part of mean0.302
 Downside part of mean-0.358
 Upside SD0.173
 Downside SD0.284
 N nonnegative terms3.000
 N negative terms8.000
Statistics related to linear regression on benchmark
 N of observations11.000
 Mean of predictor0.118
 Mean of criterion-0.056
 SD of predictor0.262
 SD of criterion0.348
 Covariance0.019
 r0.205
 b (slope, estimate of beta)0.272
 a (intercept, estimate of alpha)-0.088
 Mean Square Error0.129
 DF error9.000
 t(b)0.627
 p(b)0.273
 t(a)-0.232
 p(a)0.589
 Lowerbound of 95% confidence interval for beta-0.709
 Upperbound of 95% confidence interval for beta1.252
 Lowerbound of 95% confidence interval for alpha-0.945
 Upperbound of 95% confidence interval for alpha0.769
 Treynor index (mean / b)-0.205
 Jensen alpha (a)-0.088
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.156
 Expected Shortfall on VaR0.190
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.077
 Expected Shortfall on VaR0.160
ORDER STATISTICS
Quartiles of return rates
 Number of observations11.000
 Minimum0.766
 Quartile 10.996
 Median1.000
 Quartile 31.039
 Maximum1.141
 Mean of quarter 10.911
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.101
 Inter Quartile Range0.043
 Number outliers low1.000
 Percentage of outliers low0.091
 Mean of outliers low0.766
 Number of outliers high1.000
 Percentage of outliers high0.091
 Mean of outliers high1.141
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.659
 VaR(95%) (moments method)0.042
 Expected Shortfall (moments method)0.160
 Extreme Value Index (regression method)2.576
 VaR(95%) (regression method)0.305
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.258
 Quartile 10.258
 Median0.258
 Quartile 30.258
 Maximum0.258
 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)-0.012
 Compounded annual return (geometric extrapolation)-0.012
 Calmar ratio (compounded annual return / max draw down)-0.045
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.061
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.036
 SD0.200
 Sharpe ratio (Glass type estimate) -0.179
 Sharpe ratio (Hedges UMVUE)-0.179
 df316.000
 t-0.172
 p0.568
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.221
 Upperbound of 95% confidence interval for Sharpe Ratio1.863
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.221
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.863
Statistics related to Sortino ratio
 Sortino ratio-0.281
 Upside Potential Ratio5.291
 Upside part of mean0.676
 Downside part of mean-0.712
 Upside SD0.154
 Downside SD0.128
 N nonnegative terms32.000
 N negative terms285.000
Statistics related to linear regression on benchmark
 N of observations317.000
 Mean of predictor0.203
 Mean of criterion-0.036
 SD of predictor0.271
 SD of criterion0.200
 Covariance0.005
 r0.090
 b (slope, estimate of beta)0.066
 a (intercept, estimate of alpha)-0.049
 Mean Square Error0.040
 DF error315.000
 t(b)1.599
 p(b)0.055
 t(a)-0.237
 p(a)0.594
 Lowerbound of 95% confidence interval for beta-0.015
 Upperbound of 95% confidence interval for beta0.148
 Lowerbound of 95% confidence interval for alpha-0.460
 Upperbound of 95% confidence interval for alpha0.361
 Treynor index (mean / b)-0.541
 Jensen alpha (a)-0.049
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.056
 SD0.199
 Sharpe ratio (Glass type estimate) -0.280
 Sharpe ratio (Hedges UMVUE)-0.280
 df316.000
 t-0.269
 p0.606
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.322
 Upperbound of 95% confidence interval for Sharpe Ratio1.762
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.322
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.762
Statistics related to Sortino ratio
 Sortino ratio-0.430
 Upside Potential Ratio5.128
 Upside part of mean0.664
 Downside part of mean-0.720
 Upside SD0.150
 Downside SD0.130
 N nonnegative terms32.000
 N negative terms285.000
Statistics related to linear regression on benchmark
 N of observations317.000
 Mean of predictor0.166
 Mean of criterion-0.056
 SD of predictor0.271
 SD of criterion0.199
 Covariance0.005
 r0.090
 b (slope, estimate of beta)0.066
 a (intercept, estimate of alpha)-0.067
 Mean Square Error0.039
 DF error315.000
 t(b)1.608
 p(b)0.054
 t(a)-0.323
 p(a)0.627
 Lowerbound of 95% confidence interval for beta-0.015
 Upperbound of 95% confidence interval for beta0.147
 Lowerbound of 95% confidence interval for alpha-0.473
 Upperbound of 95% confidence interval for alpha0.340
 Treynor index (mean / b)-0.843
 Jensen alpha (a)-0.067
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.022
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.014
ORDER STATISTICS
Quartiles of return rates
 Number of observations317.000
 Minimum0.958
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.078
 Mean of quarter 10.992
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.008
 Inter Quartile Range0.000
 Number outliers low33.000
 Percentage of outliers low0.104
 Mean of outliers low0.981
 Number of outliers high32.000
 Percentage of outliers high0.101
 Mean of outliers high1.020
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)-0.266
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.011
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.006
 Quartile 10.050
 Median0.093
 Quartile 30.203
 Maximum0.313
 Mean of quarter 10.006
 Mean of quarter 20.093
 Mean of quarter 3NA
 Mean of quarter 40.313
 Inter Quartile Range0.153
 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)-0.012
 Compounded annual return (geometric extrapolation)-0.012
 Calmar ratio (compounded annual return / max draw down)-0.037
 Compounded annual return / average of 25% largest draw downs-0.037
 Compounded annual return / Expected Shortfall lognormal-0.529
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.278
 SD0.142
 Sharpe ratio (Glass type estimate) 1.958
 Sharpe ratio (Hedges UMVUE)1.949
 df171.000
 t1.384
 p0.433
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.824
 Upperbound of 95% confidence interval for Sharpe Ratio4.735
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.830
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.729
Statistics related to Sortino ratio
 Sortino ratio5.593
 Upside Potential Ratio7.850
 Upside part of mean0.390
 Downside part of mean-0.112
 Upside SD0.133
 Downside SD0.050
 N nonnegative terms7.000
 N negative terms165.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.728
 Mean of criterion0.278
 SD of predictor0.267
 SD of criterion0.142
 Covariance0.002
 r0.064
 b (slope, estimate of beta)0.034
 a (intercept, estimate of alpha)0.254
 Mean Square Error0.020
 DF error170.000
 t(b)0.832
 p(b)0.468
 t(a)1.247
 p(a)0.452
 Lowerbound of 95% confidence interval for beta-0.046
 Upperbound of 95% confidence interval for beta0.114
 Lowerbound of 95% confidence interval for alpha-0.148
 Upperbound of 95% confidence interval for alpha0.655
 Treynor index (mean / b)8.223
 Jensen alpha (a)0.254
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.268
 SD0.139
 Sharpe ratio (Glass type estimate) 1.928
 Sharpe ratio (Hedges UMVUE)1.919
 df171.000
 t1.363
 p0.434
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.855
 Upperbound of 95% confidence interval for Sharpe Ratio4.704
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.860
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.698
Statistics related to Sortino ratio
 Sortino ratio5.300
 Upside Potential Ratio7.541
 Upside part of mean0.382
 Downside part of mean-0.113
 Upside SD0.130
 Downside SD0.051
 N nonnegative terms7.000
 N negative terms165.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.692
 Mean of criterion0.268
 SD of predictor0.266
 SD of criterion0.139
 Covariance0.002
 r0.064
 b (slope, estimate of beta)0.033
 a (intercept, estimate of alpha)0.245
 Mean Square Error0.019
 DF error170.000
 t(b)0.834
 p(b)0.468
 t(a)1.233
 p(a)0.453
 Lowerbound of 95% confidence interval for beta-0.046
 Upperbound of 95% confidence interval for beta0.112
 Lowerbound of 95% confidence interval for alpha-0.147
 Upperbound of 95% confidence interval for alpha0.638
 Treynor index (mean / b)8.049
 Jensen alpha (a)0.245
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.015
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.003
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.965
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.070
 Mean of quarter 10.999
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.005
 Inter Quartile Range0.000
 Number outliers low1.000
 Percentage of outliers low0.006
 Mean of outliers low0.965
 Number of outliers high7.000
 Percentage of outliers high0.041
 Mean of outliers high1.028
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
 Minimum0.035
 Quartile 10.035
 Median0.035
 Quartile 30.035
 Maximum0.035
 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)0.338
 Compounded annual return (geometric extrapolation)0.367
 Calmar ratio (compounded annual return / max draw down)10.472
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal25.128