Collective2 Collective2
Featured Strategy QUANT AI Gold and Silver +36.6% Cumul. Return since Sep 23, 2025 Hypothetical

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Advanced Statistics: discourse

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
 Mean0.039
 SD0.099
 Sharpe ratio (Glass type estimate) 0.394
 Sharpe ratio (Hedges UMVUE)0.390
 df72.000
 t0.971
 p0.167
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.405
 Upperbound of 95% confidence interval for Sharpe Ratio1.190
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.408
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.187
Statistics related to Sortino ratio
 Sortino ratio0.823
 Upside Potential Ratio2.653
 Upside part of mean0.125
 Downside part of mean-0.086
 Upside SD0.087
 Downside SD0.047
 N nonnegative terms35.000
 N negative terms38.000
Statistics related to linear regression on benchmark
 N of observations73.000
 Mean of predictor0.233
 Mean of criterion0.039
 SD of predictor0.220
 SD of criterion0.099
 Covariance0.012
 r0.558
 b (slope, estimate of beta)0.250
 a (intercept, estimate of alpha)-0.019
 Mean Square Error0.007
 DF error71.000
 t(b)5.663
 p(b)0.000
 t(a)-0.554
 p(a)0.709
 Lowerbound of 95% confidence interval for beta0.162
 Upperbound of 95% confidence interval for beta0.338
 Lowerbound of 95% confidence interval for alpha-0.089
 Upperbound of 95% confidence interval for alpha0.050
 Treynor index (mean / b)0.155
 Jensen alpha (a)-0.019
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.034
 SD0.095
 Sharpe ratio (Glass type estimate) 0.358
 Sharpe ratio (Hedges UMVUE)0.354
 df72.000
 t0.883
 p0.190
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.440
 Upperbound of 95% confidence interval for Sharpe Ratio1.154
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.443
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.151
Statistics related to Sortino ratio
 Sortino ratio0.712
 Upside Potential Ratio2.535
 Upside part of mean0.121
 Downside part of mean-0.087
 Upside SD0.082
 Downside SD0.048
 N nonnegative terms35.000
 N negative terms38.000
Statistics related to linear regression on benchmark
 N of observations73.000
 Mean of predictor0.208
 Mean of criterion0.034
 SD of predictor0.204
 SD of criterion0.095
 Covariance0.011
 r0.544
 b (slope, estimate of beta)0.253
 a (intercept, estimate of alpha)-0.019
 Mean Square Error0.006
 DF error71.000
 t(b)5.457
 p(b)0.000
 t(a)-0.549
 p(a)0.708
 Lowerbound of 95% confidence interval for beta0.161
 Upperbound of 95% confidence interval for beta0.346
 Lowerbound of 95% confidence interval for alpha-0.086
 Upperbound of 95% confidence interval for alpha0.049
 Treynor index (mean / b)0.134
 Jensen alpha (a)-0.019
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.041
 Expected Shortfall on VaR0.052
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.017
 Expected Shortfall on VaR0.032
ORDER STATISTICS
Quartiles of return rates
 Number of observations73.000
 Minimum0.954
 Quartile 10.993
 Median1.002
 Quartile 31.015
 Maximum1.154
 Mean of quarter 10.980
 Mean of quarter 20.999
 Mean of quarter 31.008
 Mean of quarter 41.041
 Inter Quartile Range0.021
 Number outliers low2.000
 Percentage of outliers low0.027
 Mean of outliers low0.956
 Number of outliers high2.000
 Percentage of outliers high0.027
 Mean of outliers high1.128
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.008
 VaR(95%) (moments method)0.017
 Expected Shortfall (moments method)0.023
 Extreme Value Index (regression method)-0.052
 VaR(95%) (regression method)0.021
 Expected Shortfall (regression method)0.028
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.005
 Quartile 10.008
 Median0.015
 Quartile 30.052
 Maximum0.083
 Mean of quarter 10.006
 Mean of quarter 20.012
 Mean of quarter 30.027
 Mean of quarter 40.077
 Inter Quartile Range0.044
 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)-1.225
 VaR(95%) (moments method)0.082
 Expected Shortfall (moments method)0.083
 Extreme Value Index (regression method)0.244
 VaR(95%) (regression method)0.084
 Expected Shortfall (regression method)0.095
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.100
 Compounded annual return (geometric extrapolation)0.081
 Calmar ratio (compounded annual return / max draw down)0.976
 Compounded annual return / average of 25% largest draw downs1.054
 Compounded annual return / Expected Shortfall lognormal1.552
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.038
 SD0.100
 Sharpe ratio (Glass type estimate) 0.380
 Sharpe ratio (Hedges UMVUE)0.380
 df1608.000
 t0.942
 p0.488
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.411
 Upperbound of 95% confidence interval for Sharpe Ratio1.171
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.411
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.171
Statistics related to Sortino ratio
 Sortino ratio0.608
 Upside Potential Ratio7.215
 Upside part of mean0.451
 Downside part of mean-0.413
 Upside SD0.078
 Downside SD0.063
 N nonnegative terms749.000
 N negative terms860.000
Statistics related to linear regression on benchmark
 N of observations1609.000
 Mean of predictor0.261
 Mean of criterion0.038
 SD of predictor0.224
 SD of criterion0.100
 Covariance0.012
 r0.520
 b (slope, estimate of beta)0.232
 a (intercept, estimate of alpha)-0.023
 Mean Square Error0.007
 DF error1607.000
 t(b)24.406
 p(b)0.185
 t(a)-0.652
 p(a)0.510
 Lowerbound of 95% confidence interval for beta0.214
 Upperbound of 95% confidence interval for beta0.251
 Lowerbound of 95% confidence interval for alpha-0.090
 Upperbound of 95% confidence interval for alpha0.045
 Treynor index (mean / b)0.164
 Jensen alpha (a)-0.023
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.033
 SD0.100
 Sharpe ratio (Glass type estimate) 0.332
 Sharpe ratio (Hedges UMVUE)0.332
 df1608.000
 t0.823
 p0.490
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.459
 Upperbound of 95% confidence interval for Sharpe Ratio1.123
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.459
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.123
Statistics related to Sortino ratio
 Sortino ratio0.523
 Upside Potential Ratio7.085
 Upside part of mean0.448
 Downside part of mean-0.415
 Upside SD0.077
 Downside SD0.063
 N nonnegative terms749.000
 N negative terms860.000
Statistics related to linear regression on benchmark
 N of observations1609.000
 Mean of predictor0.235
 Mean of criterion0.033
 SD of predictor0.225
 SD of criterion0.100
 Covariance0.012
 r0.525
 b (slope, estimate of beta)0.232
 a (intercept, estimate of alpha)-0.021
 Mean Square Error0.007
 DF error1607.000
 t(b)24.712
 p(b)0.182
 t(a)-0.627
 p(a)0.510
 Lowerbound of 95% confidence interval for beta0.213
 Upperbound of 95% confidence interval for beta0.250
 Lowerbound of 95% confidence interval for alpha-0.089
 Upperbound of 95% confidence interval for alpha0.046
 Treynor index (mean / b)0.143
 Jensen alpha (a)-0.021
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.012
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.008
ORDER STATISTICS
Quartiles of return rates
 Number of observations1609.000
 Minimum0.939
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.085
 Mean of quarter 10.995
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.006
 Inter Quartile Range0.003
 Number outliers low78.000
 Percentage of outliers low0.048
 Mean of outliers low0.987
 Number of outliers high97.000
 Percentage of outliers high0.060
 Mean of outliers high1.015
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.440
 VaR(95%) (moments method)0.005
 Expected Shortfall (moments method)0.011
 Extreme Value Index (regression method)0.322
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.008
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations61.000
 Minimum0.000
 Quartile 10.002
 Median0.005
 Quartile 30.017
 Maximum0.128
 Mean of quarter 10.001
 Mean of quarter 20.003
 Mean of quarter 30.009
 Mean of quarter 40.054
 Inter Quartile Range0.015
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high7.000
 Percentage of outliers high0.115
 Mean of outliers high0.086
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.469
 VaR(95%) (moments method)0.054
 Expected Shortfall (moments method)0.117
 Extreme Value Index (regression method)0.365
 VaR(95%) (regression method)0.054
 Expected Shortfall (regression method)0.100
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.099
 Compounded annual return (geometric extrapolation)0.080
 Calmar ratio (compounded annual return / max draw down)0.628
 Compounded annual return / average of 25% largest draw downs1.488
 Compounded annual return / Expected Shortfall lognormal6.422
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.099
 SD0.041
 Sharpe ratio (Glass type estimate) -2.419
 Sharpe ratio (Hedges UMVUE)-2.405
 df130.000
 t-1.710
 p0.574
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.202
 Upperbound of 95% confidence interval for Sharpe Ratio0.373
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.192
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.382
Statistics related to Sortino ratio
 Sortino ratio-3.140
 Upside Potential Ratio4.315
 Upside part of mean0.136
 Downside part of mean-0.235
 Upside SD0.027
 Downside SD0.032
 N nonnegative terms29.000
 N negative terms102.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor1.408
 Mean of criterion-0.099
 SD of predictor0.372
 SD of criterion0.041
 Covariance0.003
 r0.188
 b (slope, estimate of beta)0.021
 a (intercept, estimate of alpha)-0.128
 Mean Square Error0.002
 DF error129.000
 t(b)2.175
 p(b)0.381
 t(a)-2.186
 p(a)0.620
 Lowerbound of 95% confidence interval for beta0.002
 Upperbound of 95% confidence interval for beta0.040
 Lowerbound of 95% confidence interval for alpha-0.245
 Upperbound of 95% confidence interval for alpha-0.012
 Treynor index (mean / b)-4.780
 Jensen alpha (a)-0.128
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.100
 SD0.041
 Sharpe ratio (Glass type estimate) -2.440
 Sharpe ratio (Hedges UMVUE)-2.426
 df130.000
 t-1.725
 p0.575
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.223
 Upperbound of 95% confidence interval for Sharpe Ratio0.352
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.213
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.361
Statistics related to Sortino ratio
 Sortino ratio-3.158
 Upside Potential Ratio4.292
 Upside part of mean0.136
 Downside part of mean-0.236
 Upside SD0.026
 Downside SD0.032
 N nonnegative terms29.000
 N negative terms102.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor1.337
 Mean of criterion-0.100
 SD of predictor0.366
 SD of criterion0.041
 Covariance0.003
 r0.191
 b (slope, estimate of beta)0.021
 a (intercept, estimate of alpha)-0.129
 Mean Square Error0.002
 DF error129.000
 t(b)2.207
 p(b)0.379
 t(a)-2.195
 p(a)0.620
 Lowerbound of 95% confidence interval for beta0.002
 Upperbound of 95% confidence interval for beta0.041
 Lowerbound of 95% confidence interval for alpha-0.244
 Upperbound of 95% confidence interval for alpha-0.013
 Treynor index (mean / b)-4.681
 Jensen alpha (a)-0.129
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.006
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations131.000
 Minimum0.991
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.012
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.002
 Inter Quartile Range0.000
 Number outliers low31.000
 Percentage of outliers low0.237
 Mean of outliers low0.997
 Number of outliers high29.000
 Percentage of outliers high0.221
 Mean of outliers high1.003
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.415
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)-0.233
 VaR(95%) (regression method)0.004
 Expected Shortfall (regression method)0.005
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.019
 Quartile 10.024
 Median0.029
 Quartile 30.035
 Maximum0.040
 Mean of quarter 10.019
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.040
 Inter Quartile Range0.011
 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)-0.055
 Compounded annual return (geometric extrapolation)-0.054
 Calmar ratio (compounded annual return / max draw down)-1.348
 Compounded annual return / average of 25% largest draw downs-1.348
 Compounded annual return / Expected Shortfall lognormal-9.743

Advanced Statistics: discourse

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
 Mean0.039
 SD0.099
 Sharpe ratio (Glass type estimate) 0.394
 Sharpe ratio (Hedges UMVUE)0.390
 df72.000
 t0.971
 p0.167
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.405
 Upperbound of 95% confidence interval for Sharpe Ratio1.190
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.408
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.187
Statistics related to Sortino ratio
 Sortino ratio0.823
 Upside Potential Ratio2.653
 Upside part of mean0.125
 Downside part of mean-0.086
 Upside SD0.087
 Downside SD0.047
 N nonnegative terms35.000
 N negative terms38.000
Statistics related to linear regression on benchmark
 N of observations73.000
 Mean of predictor0.233
 Mean of criterion0.039
 SD of predictor0.220
 SD of criterion0.099
 Covariance0.012
 r0.558
 b (slope, estimate of beta)0.250
 a (intercept, estimate of alpha)-0.019
 Mean Square Error0.007
 DF error71.000
 t(b)5.663
 p(b)0.000
 t(a)-0.554
 p(a)0.709
 Lowerbound of 95% confidence interval for beta0.162
 Upperbound of 95% confidence interval for beta0.338
 Lowerbound of 95% confidence interval for alpha-0.089
 Upperbound of 95% confidence interval for alpha0.050
 Treynor index (mean / b)0.155
 Jensen alpha (a)-0.019
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.034
 SD0.095
 Sharpe ratio (Glass type estimate) 0.358
 Sharpe ratio (Hedges UMVUE)0.354
 df72.000
 t0.883
 p0.190
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.440
 Upperbound of 95% confidence interval for Sharpe Ratio1.154
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.443
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.151
Statistics related to Sortino ratio
 Sortino ratio0.712
 Upside Potential Ratio2.535
 Upside part of mean0.121
 Downside part of mean-0.087
 Upside SD0.082
 Downside SD0.048
 N nonnegative terms35.000
 N negative terms38.000
Statistics related to linear regression on benchmark
 N of observations73.000
 Mean of predictor0.208
 Mean of criterion0.034
 SD of predictor0.204
 SD of criterion0.095
 Covariance0.011
 r0.544
 b (slope, estimate of beta)0.253
 a (intercept, estimate of alpha)-0.019
 Mean Square Error0.006
 DF error71.000
 t(b)5.457
 p(b)0.000
 t(a)-0.549
 p(a)0.708
 Lowerbound of 95% confidence interval for beta0.161
 Upperbound of 95% confidence interval for beta0.346
 Lowerbound of 95% confidence interval for alpha-0.086
 Upperbound of 95% confidence interval for alpha0.049
 Treynor index (mean / b)0.134
 Jensen alpha (a)-0.019
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.041
 Expected Shortfall on VaR0.052
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.017
 Expected Shortfall on VaR0.032
ORDER STATISTICS
Quartiles of return rates
 Number of observations73.000
 Minimum0.954
 Quartile 10.993
 Median1.002
 Quartile 31.015
 Maximum1.154
 Mean of quarter 10.980
 Mean of quarter 20.999
 Mean of quarter 31.008
 Mean of quarter 41.041
 Inter Quartile Range0.021
 Number outliers low2.000
 Percentage of outliers low0.027
 Mean of outliers low0.956
 Number of outliers high2.000
 Percentage of outliers high0.027
 Mean of outliers high1.128
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.008
 VaR(95%) (moments method)0.017
 Expected Shortfall (moments method)0.023
 Extreme Value Index (regression method)-0.052
 VaR(95%) (regression method)0.021
 Expected Shortfall (regression method)0.028
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.005
 Quartile 10.008
 Median0.015
 Quartile 30.052
 Maximum0.083
 Mean of quarter 10.006
 Mean of quarter 20.012
 Mean of quarter 30.027
 Mean of quarter 40.077
 Inter Quartile Range0.044
 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)-1.225
 VaR(95%) (moments method)0.082
 Expected Shortfall (moments method)0.083
 Extreme Value Index (regression method)0.244
 VaR(95%) (regression method)0.084
 Expected Shortfall (regression method)0.095
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.100
 Compounded annual return (geometric extrapolation)0.081
 Calmar ratio (compounded annual return / max draw down)0.976
 Compounded annual return / average of 25% largest draw downs1.054
 Compounded annual return / Expected Shortfall lognormal1.552
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.038
 SD0.100
 Sharpe ratio (Glass type estimate) 0.380
 Sharpe ratio (Hedges UMVUE)0.380
 df1608.000
 t0.942
 p0.488
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.411
 Upperbound of 95% confidence interval for Sharpe Ratio1.171
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.411
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.171
Statistics related to Sortino ratio
 Sortino ratio0.608
 Upside Potential Ratio7.215
 Upside part of mean0.451
 Downside part of mean-0.413
 Upside SD0.078
 Downside SD0.063
 N nonnegative terms749.000
 N negative terms860.000
Statistics related to linear regression on benchmark
 N of observations1609.000
 Mean of predictor0.261
 Mean of criterion0.038
 SD of predictor0.224
 SD of criterion0.100
 Covariance0.012
 r0.520
 b (slope, estimate of beta)0.232
 a (intercept, estimate of alpha)-0.023
 Mean Square Error0.007
 DF error1607.000
 t(b)24.406
 p(b)0.185
 t(a)-0.652
 p(a)0.510
 Lowerbound of 95% confidence interval for beta0.214
 Upperbound of 95% confidence interval for beta0.251
 Lowerbound of 95% confidence interval for alpha-0.090
 Upperbound of 95% confidence interval for alpha0.045
 Treynor index (mean / b)0.164
 Jensen alpha (a)-0.023
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.033
 SD0.100
 Sharpe ratio (Glass type estimate) 0.332
 Sharpe ratio (Hedges UMVUE)0.332
 df1608.000
 t0.823
 p0.490
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.459
 Upperbound of 95% confidence interval for Sharpe Ratio1.123
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.459
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.123
Statistics related to Sortino ratio
 Sortino ratio0.523
 Upside Potential Ratio7.085
 Upside part of mean0.448
 Downside part of mean-0.415
 Upside SD0.077
 Downside SD0.063
 N nonnegative terms749.000
 N negative terms860.000
Statistics related to linear regression on benchmark
 N of observations1609.000
 Mean of predictor0.235
 Mean of criterion0.033
 SD of predictor0.225
 SD of criterion0.100
 Covariance0.012
 r0.525
 b (slope, estimate of beta)0.232
 a (intercept, estimate of alpha)-0.021
 Mean Square Error0.007
 DF error1607.000
 t(b)24.712
 p(b)0.182
 t(a)-0.627
 p(a)0.510
 Lowerbound of 95% confidence interval for beta0.213
 Upperbound of 95% confidence interval for beta0.250
 Lowerbound of 95% confidence interval for alpha-0.089
 Upperbound of 95% confidence interval for alpha0.046
 Treynor index (mean / b)0.143
 Jensen alpha (a)-0.021
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.012
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.008
ORDER STATISTICS
Quartiles of return rates
 Number of observations1609.000
 Minimum0.939
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.085
 Mean of quarter 10.995
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.006
 Inter Quartile Range0.003
 Number outliers low78.000
 Percentage of outliers low0.048
 Mean of outliers low0.987
 Number of outliers high97.000
 Percentage of outliers high0.060
 Mean of outliers high1.015
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.440
 VaR(95%) (moments method)0.005
 Expected Shortfall (moments method)0.011
 Extreme Value Index (regression method)0.322
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.008
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations61.000
 Minimum0.000
 Quartile 10.002
 Median0.005
 Quartile 30.017
 Maximum0.128
 Mean of quarter 10.001
 Mean of quarter 20.003
 Mean of quarter 30.009
 Mean of quarter 40.054
 Inter Quartile Range0.015
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high7.000
 Percentage of outliers high0.115
 Mean of outliers high0.086
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.469
 VaR(95%) (moments method)0.054
 Expected Shortfall (moments method)0.117
 Extreme Value Index (regression method)0.365
 VaR(95%) (regression method)0.054
 Expected Shortfall (regression method)0.100
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.099
 Compounded annual return (geometric extrapolation)0.080
 Calmar ratio (compounded annual return / max draw down)0.628
 Compounded annual return / average of 25% largest draw downs1.488
 Compounded annual return / Expected Shortfall lognormal6.422
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.099
 SD0.041
 Sharpe ratio (Glass type estimate) -2.419
 Sharpe ratio (Hedges UMVUE)-2.405
 df130.000
 t-1.710
 p0.574
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.202
 Upperbound of 95% confidence interval for Sharpe Ratio0.373
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.192
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.382
Statistics related to Sortino ratio
 Sortino ratio-3.140
 Upside Potential Ratio4.315
 Upside part of mean0.136
 Downside part of mean-0.235
 Upside SD0.027
 Downside SD0.032
 N nonnegative terms29.000
 N negative terms102.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor1.408
 Mean of criterion-0.099
 SD of predictor0.372
 SD of criterion0.041
 Covariance0.003
 r0.188
 b (slope, estimate of beta)0.021
 a (intercept, estimate of alpha)-0.128
 Mean Square Error0.002
 DF error129.000
 t(b)2.175
 p(b)0.381
 t(a)-2.186
 p(a)0.620
 Lowerbound of 95% confidence interval for beta0.002
 Upperbound of 95% confidence interval for beta0.040
 Lowerbound of 95% confidence interval for alpha-0.245
 Upperbound of 95% confidence interval for alpha-0.012
 Treynor index (mean / b)-4.780
 Jensen alpha (a)-0.128
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.100
 SD0.041
 Sharpe ratio (Glass type estimate) -2.440
 Sharpe ratio (Hedges UMVUE)-2.426
 df130.000
 t-1.725
 p0.575
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.223
 Upperbound of 95% confidence interval for Sharpe Ratio0.352
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.213
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.361
Statistics related to Sortino ratio
 Sortino ratio-3.158
 Upside Potential Ratio4.292
 Upside part of mean0.136
 Downside part of mean-0.236
 Upside SD0.026
 Downside SD0.032
 N nonnegative terms29.000
 N negative terms102.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor1.337
 Mean of criterion-0.100
 SD of predictor0.366
 SD of criterion0.041
 Covariance0.003
 r0.191
 b (slope, estimate of beta)0.021
 a (intercept, estimate of alpha)-0.129
 Mean Square Error0.002
 DF error129.000
 t(b)2.207
 p(b)0.379
 t(a)-2.195
 p(a)0.620
 Lowerbound of 95% confidence interval for beta0.002
 Upperbound of 95% confidence interval for beta0.041
 Lowerbound of 95% confidence interval for alpha-0.244
 Upperbound of 95% confidence interval for alpha-0.013
 Treynor index (mean / b)-4.681
 Jensen alpha (a)-0.129
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.006
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations131.000
 Minimum0.991
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.012
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.002
 Inter Quartile Range0.000
 Number outliers low31.000
 Percentage of outliers low0.237
 Mean of outliers low0.997
 Number of outliers high29.000
 Percentage of outliers high0.221
 Mean of outliers high1.003
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.415
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)-0.233
 VaR(95%) (regression method)0.004
 Expected Shortfall (regression method)0.005
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.019
 Quartile 10.024
 Median0.029
 Quartile 30.035
 Maximum0.040
 Mean of quarter 10.019
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.040
 Inter Quartile Range0.011
 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)-0.055
 Compounded annual return (geometric extrapolation)-0.054
 Calmar ratio (compounded annual return / max draw down)-1.348
 Compounded annual return / average of 25% largest draw downs-1.348
 Compounded annual return / Expected Shortfall lognormal-9.743