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Advanced Statistics: Buzo Principle

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
 Mean0.029
 SD0.306
 Sharpe ratio (Glass type estimate) 0.093
 Sharpe ratio (Hedges UMVUE)0.092
 df73.000
 t0.231
 p0.409
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.697
 Upperbound of 95% confidence interval for Sharpe Ratio0.882
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.697
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.882
Statistics related to Sortino ratio
 Sortino ratio0.114
 Upside Potential Ratio1.013
 Upside part of mean0.253
 Downside part of mean-0.224
 Upside SD0.175
 Downside SD0.249
 N nonnegative terms27.000
 N negative terms47.000
Statistics related to linear regression on benchmark
 N of observations74.000
 Mean of predictor0.288
 Mean of criterion0.029
 SD of predictor0.234
 SD of criterion0.306
 Covariance0.001
 r0.008
 b (slope, estimate of beta)0.010
 a (intercept, estimate of alpha)0.026
 Mean Square Error0.095
 DF error72.000
 t(b)0.066
 p(b)0.474
 t(a)0.194
 p(a)0.423
 Lowerbound of 95% confidence interval for beta-0.298
 Upperbound of 95% confidence interval for beta0.318
 Lowerbound of 95% confidence interval for alpha-0.237
 Upperbound of 95% confidence interval for alpha0.289
 Treynor index (mean / b)2.820
 Jensen alpha (a)0.026
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.032
 SD0.377
 Sharpe ratio (Glass type estimate) -0.084
 Sharpe ratio (Hedges UMVUE)-0.083
 df73.000
 t-0.208
 p0.582
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.873
 Upperbound of 95% confidence interval for Sharpe Ratio0.706
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.872
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.707
Statistics related to Sortino ratio
 Sortino ratio-0.093
 Upside Potential Ratio0.704
 Upside part of mean0.238
 Downside part of mean-0.270
 Upside SD0.161
 Downside SD0.338
 N nonnegative terms27.000
 N negative terms47.000
Statistics related to linear regression on benchmark
 N of observations74.000
 Mean of predictor0.259
 Mean of criterion-0.032
 SD of predictor0.225
 SD of criterion0.377
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)-0.030
 Mean Square Error0.144
 DF error72.000
 t(b)-0.024
 p(b)0.509
 t(a)-0.188
 p(a)0.574
 Lowerbound of 95% confidence interval for beta-0.398
 Upperbound of 95% confidence interval for beta0.389
 Lowerbound of 95% confidence interval for alpha-0.351
 Upperbound of 95% confidence interval for alpha0.291
 Treynor index (mean / b)6.715
 Jensen alpha (a)-0.030
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.166
 Expected Shortfall on VaR0.202
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.049
 Expected Shortfall on VaR0.109
ORDER STATISTICS
Quartiles of return rates
 Number of observations74.000
 Minimum0.466
 Quartile 11.000
 Median1.000
 Quartile 31.025
 Maximum1.268
 Mean of quarter 10.936
 Mean of quarter 21.000
 Mean of quarter 31.007
 Mean of quarter 41.081
 Inter Quartile Range0.025
 Number outliers low7.000
 Percentage of outliers low0.095
 Mean of outliers low0.843
 Number of outliers high8.000
 Percentage of outliers high0.108
 Mean of outliers high1.136
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.673
 VaR(95%) (moments method)0.009
 Expected Shortfall (moments method)0.035
 Extreme Value Index (regression method)1.107
 VaR(95%) (regression method)0.053
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.003
 Quartile 10.016
 Median0.038
 Quartile 30.048
 Maximum0.694
 Mean of quarter 10.008
 Mean of quarter 20.027
 Mean of quarter 30.043
 Mean of quarter 40.269
 Inter Quartile Range0.032
 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 high0.694
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.237
 VaR(95%) (moments method)0.282
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)5.421
 VaR(95%) (regression method)1.915
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.013
 Compounded annual return (geometric extrapolation)0.013
 Calmar ratio (compounded annual return / max draw down)0.018
 Compounded annual return / average of 25% largest draw downs0.047
 Compounded annual return / Expected Shortfall lognormal0.062
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.020
 SD0.320
 Sharpe ratio (Glass type estimate) 0.063
 Sharpe ratio (Hedges UMVUE)0.062
 df1633.000
 t0.156
 p0.498
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.722
 Upperbound of 95% confidence interval for Sharpe Ratio0.847
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.722
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.847
Statistics related to Sortino ratio
 Sortino ratio0.089
 Upside Potential Ratio4.077
 Upside part of mean0.922
 Downside part of mean-0.902
 Upside SD0.227
 Downside SD0.226
 N nonnegative terms457.000
 N negative terms1177.000
Statistics related to linear regression on benchmark
 N of observations1634.000
 Mean of predictor0.332
 Mean of criterion0.020
 SD of predictor0.319
 SD of criterion0.320
 Covariance0.009
 r0.092
 b (slope, estimate of beta)0.092
 a (intercept, estimate of alpha)-0.011
 Mean Square Error0.102
 DF error1632.000
 t(b)3.732
 p(b)0.454
 t(a)-0.083
 p(a)0.501
 Lowerbound of 95% confidence interval for beta0.044
 Upperbound of 95% confidence interval for beta0.141
 Lowerbound of 95% confidence interval for alpha-0.262
 Upperbound of 95% confidence interval for alpha0.240
 Treynor index (mean / b)0.217
 Jensen alpha (a)-0.011
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.032
 SD0.323
 Sharpe ratio (Glass type estimate) -0.098
 Sharpe ratio (Hedges UMVUE)-0.098
 df1633.000
 t-0.245
 p0.504
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.883
 Upperbound of 95% confidence interval for Sharpe Ratio0.687
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.883
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.687
Statistics related to Sortino ratio
 Sortino ratio-0.131
 Upside Potential Ratio3.717
 Upside part of mean0.898
 Downside part of mean-0.930
 Upside SD0.214
 Downside SD0.242
 N nonnegative terms457.000
 N negative terms1177.000
Statistics related to linear regression on benchmark
 N of observations1634.000
 Mean of predictor0.281
 Mean of criterion-0.032
 SD of predictor0.318
 SD of criterion0.323
 Covariance0.009
 r0.087
 b (slope, estimate of beta)0.089
 a (intercept, estimate of alpha)-0.057
 Mean Square Error0.103
 DF error1632.000
 t(b)3.542
 p(b)0.456
 t(a)-0.439
 p(a)0.505
 Lowerbound of 95% confidence interval for beta0.040
 Upperbound of 95% confidence interval for beta0.138
 Lowerbound of 95% confidence interval for alpha-0.310
 Upperbound of 95% confidence interval for alpha0.196
 Treynor index (mean / b)-0.357
 Jensen alpha (a)-0.057
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.032
 Expected Shortfall on VaR0.040
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.022
ORDER STATISTICS
Quartiles of return rates
 Number of observations1634.000
 Minimum0.802
 Quartile 10.999
 Median1.000
 Quartile 31.001
 Maximum1.246
 Mean of quarter 10.987
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.014
 Inter Quartile Range0.002
 Number outliers low283.000
 Percentage of outliers low0.173
 Mean of outliers low0.982
 Number of outliers high306.000
 Percentage of outliers high0.187
 Mean of outliers high1.018
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.007
 VaR(95%) (moments method)0.008
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.538
 VaR(95%) (regression method)0.009
 Expected Shortfall (regression method)0.027
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations63.000
 Minimum0.000
 Quartile 10.007
 Median0.019
 Quartile 30.045
 Maximum0.703
 Mean of quarter 10.003
 Mean of quarter 20.014
 Mean of quarter 30.030
 Mean of quarter 40.129
 Inter Quartile Range0.038
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high7.000
 Percentage of outliers high0.111
 Mean of outliers high0.215
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.539
 VaR(95%) (moments method)0.132
 Expected Shortfall (moments method)0.312
 Extreme Value Index (regression method)0.459
 VaR(95%) (regression method)0.124
 Expected Shortfall (regression method)0.252
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.013
 Compounded annual return (geometric extrapolation)0.012
 Calmar ratio (compounded annual return / max draw down)0.018
 Compounded annual return / average of 25% largest draw downs0.097
 Compounded annual return / Expected Shortfall lognormal0.308
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) NA
 Sharpe ratio (Hedges UMVUE)NA
 dfNA
 tNA
 pNA
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
Statistics related to Sortino ratio
 Sortino ratio-16.186
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.003
 N nonnegative terms0.000
 N negative terms131.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor0.561
 Mean of criterion-0.044
 SD of predictor0.411
 SD of criterion0.000
 Covariance0.000
 rNA
 b (slope, estimate of beta)NA
 a (intercept, estimate of alpha)NA
 Mean Square ErrorNA
 DF errorNA
 t(b)NA
 p(b)NA
 t(a)NA
 p(a)NA
 Lowerbound of 95% confidence interval for betaNA
 Upperbound of 95% confidence interval for betaNA
 Lowerbound of 95% confidence interval for alphaNA
 Upperbound of 95% confidence interval for alphaNA
 Treynor index (mean / b)NA
 Jensen alpha (a)NA
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) -12492933348697024.000
 Sharpe ratio (Hedges UMVUE)-12420719861132300.000
 df130.000
 t-8833837887775228.000
 p1.000
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-13930479873814932.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-10910959848449668.000
Statistics related to Sortino ratio
 Sortino ratio-16.186
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.003
 N nonnegative terms0.000
 N negative terms131.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor0.476
 Mean of criterion-0.044
 SD of predictor0.414
 SD of criterion0.000
 Covariance0.000
 r0.000
 b (slope, estimate of beta)0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error129.000
 t(b)0.000
 p(b)0.500
 t(a)-8777492766489210.000
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.000
 Upperbound of 95% confidence interval for beta0.000
 Lowerbound of 95% confidence interval for alpha-0.044
 Upperbound of 95% confidence interval for alpha-0.044
 Treynor index (mean / b)-283715057818448445353199717580800.000
 Jensen alpha (a)-0.044
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
ORDER STATISTICS
Quartiles of return rates
 Number of observations131.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 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 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 observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 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 lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 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)0.000
 Compounded annual return (geometric extrapolation)0.000
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.000

Advanced Statistics: Buzo Principle

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
 Mean0.029
 SD0.306
 Sharpe ratio (Glass type estimate) 0.093
 Sharpe ratio (Hedges UMVUE)0.092
 df73.000
 t0.231
 p0.409
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.697
 Upperbound of 95% confidence interval for Sharpe Ratio0.882
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.697
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.882
Statistics related to Sortino ratio
 Sortino ratio0.114
 Upside Potential Ratio1.013
 Upside part of mean0.253
 Downside part of mean-0.224
 Upside SD0.175
 Downside SD0.249
 N nonnegative terms27.000
 N negative terms47.000
Statistics related to linear regression on benchmark
 N of observations74.000
 Mean of predictor0.288
 Mean of criterion0.029
 SD of predictor0.234
 SD of criterion0.306
 Covariance0.001
 r0.008
 b (slope, estimate of beta)0.010
 a (intercept, estimate of alpha)0.026
 Mean Square Error0.095
 DF error72.000
 t(b)0.066
 p(b)0.474
 t(a)0.194
 p(a)0.423
 Lowerbound of 95% confidence interval for beta-0.298
 Upperbound of 95% confidence interval for beta0.318
 Lowerbound of 95% confidence interval for alpha-0.237
 Upperbound of 95% confidence interval for alpha0.289
 Treynor index (mean / b)2.820
 Jensen alpha (a)0.026
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.032
 SD0.377
 Sharpe ratio (Glass type estimate) -0.084
 Sharpe ratio (Hedges UMVUE)-0.083
 df73.000
 t-0.208
 p0.582
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.873
 Upperbound of 95% confidence interval for Sharpe Ratio0.706
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.872
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.707
Statistics related to Sortino ratio
 Sortino ratio-0.093
 Upside Potential Ratio0.704
 Upside part of mean0.238
 Downside part of mean-0.270
 Upside SD0.161
 Downside SD0.338
 N nonnegative terms27.000
 N negative terms47.000
Statistics related to linear regression on benchmark
 N of observations74.000
 Mean of predictor0.259
 Mean of criterion-0.032
 SD of predictor0.225
 SD of criterion0.377
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)-0.030
 Mean Square Error0.144
 DF error72.000
 t(b)-0.024
 p(b)0.509
 t(a)-0.188
 p(a)0.574
 Lowerbound of 95% confidence interval for beta-0.398
 Upperbound of 95% confidence interval for beta0.389
 Lowerbound of 95% confidence interval for alpha-0.351
 Upperbound of 95% confidence interval for alpha0.291
 Treynor index (mean / b)6.715
 Jensen alpha (a)-0.030
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.166
 Expected Shortfall on VaR0.202
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.049
 Expected Shortfall on VaR0.109
ORDER STATISTICS
Quartiles of return rates
 Number of observations74.000
 Minimum0.466
 Quartile 11.000
 Median1.000
 Quartile 31.025
 Maximum1.268
 Mean of quarter 10.936
 Mean of quarter 21.000
 Mean of quarter 31.007
 Mean of quarter 41.081
 Inter Quartile Range0.025
 Number outliers low7.000
 Percentage of outliers low0.095
 Mean of outliers low0.843
 Number of outliers high8.000
 Percentage of outliers high0.108
 Mean of outliers high1.136
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.673
 VaR(95%) (moments method)0.009
 Expected Shortfall (moments method)0.035
 Extreme Value Index (regression method)1.107
 VaR(95%) (regression method)0.053
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.003
 Quartile 10.016
 Median0.038
 Quartile 30.048
 Maximum0.694
 Mean of quarter 10.008
 Mean of quarter 20.027
 Mean of quarter 30.043
 Mean of quarter 40.269
 Inter Quartile Range0.032
 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 high0.694
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.237
 VaR(95%) (moments method)0.282
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)5.421
 VaR(95%) (regression method)1.915
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.013
 Compounded annual return (geometric extrapolation)0.013
 Calmar ratio (compounded annual return / max draw down)0.018
 Compounded annual return / average of 25% largest draw downs0.047
 Compounded annual return / Expected Shortfall lognormal0.062
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.020
 SD0.320
 Sharpe ratio (Glass type estimate) 0.063
 Sharpe ratio (Hedges UMVUE)0.062
 df1633.000
 t0.156
 p0.498
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.722
 Upperbound of 95% confidence interval for Sharpe Ratio0.847
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.722
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.847
Statistics related to Sortino ratio
 Sortino ratio0.089
 Upside Potential Ratio4.077
 Upside part of mean0.922
 Downside part of mean-0.902
 Upside SD0.227
 Downside SD0.226
 N nonnegative terms457.000
 N negative terms1177.000
Statistics related to linear regression on benchmark
 N of observations1634.000
 Mean of predictor0.332
 Mean of criterion0.020
 SD of predictor0.319
 SD of criterion0.320
 Covariance0.009
 r0.092
 b (slope, estimate of beta)0.092
 a (intercept, estimate of alpha)-0.011
 Mean Square Error0.102
 DF error1632.000
 t(b)3.732
 p(b)0.454
 t(a)-0.083
 p(a)0.501
 Lowerbound of 95% confidence interval for beta0.044
 Upperbound of 95% confidence interval for beta0.141
 Lowerbound of 95% confidence interval for alpha-0.262
 Upperbound of 95% confidence interval for alpha0.240
 Treynor index (mean / b)0.217
 Jensen alpha (a)-0.011
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.032
 SD0.323
 Sharpe ratio (Glass type estimate) -0.098
 Sharpe ratio (Hedges UMVUE)-0.098
 df1633.000
 t-0.245
 p0.504
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.883
 Upperbound of 95% confidence interval for Sharpe Ratio0.687
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.883
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.687
Statistics related to Sortino ratio
 Sortino ratio-0.131
 Upside Potential Ratio3.717
 Upside part of mean0.898
 Downside part of mean-0.930
 Upside SD0.214
 Downside SD0.242
 N nonnegative terms457.000
 N negative terms1177.000
Statistics related to linear regression on benchmark
 N of observations1634.000
 Mean of predictor0.281
 Mean of criterion-0.032
 SD of predictor0.318
 SD of criterion0.323
 Covariance0.009
 r0.087
 b (slope, estimate of beta)0.089
 a (intercept, estimate of alpha)-0.057
 Mean Square Error0.103
 DF error1632.000
 t(b)3.542
 p(b)0.456
 t(a)-0.439
 p(a)0.505
 Lowerbound of 95% confidence interval for beta0.040
 Upperbound of 95% confidence interval for beta0.138
 Lowerbound of 95% confidence interval for alpha-0.310
 Upperbound of 95% confidence interval for alpha0.196
 Treynor index (mean / b)-0.357
 Jensen alpha (a)-0.057
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.032
 Expected Shortfall on VaR0.040
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.022
ORDER STATISTICS
Quartiles of return rates
 Number of observations1634.000
 Minimum0.802
 Quartile 10.999
 Median1.000
 Quartile 31.001
 Maximum1.246
 Mean of quarter 10.987
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.014
 Inter Quartile Range0.002
 Number outliers low283.000
 Percentage of outliers low0.173
 Mean of outliers low0.982
 Number of outliers high306.000
 Percentage of outliers high0.187
 Mean of outliers high1.018
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.007
 VaR(95%) (moments method)0.008
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.538
 VaR(95%) (regression method)0.009
 Expected Shortfall (regression method)0.027
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations63.000
 Minimum0.000
 Quartile 10.007
 Median0.019
 Quartile 30.045
 Maximum0.703
 Mean of quarter 10.003
 Mean of quarter 20.014
 Mean of quarter 30.030
 Mean of quarter 40.129
 Inter Quartile Range0.038
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high7.000
 Percentage of outliers high0.111
 Mean of outliers high0.215
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.539
 VaR(95%) (moments method)0.132
 Expected Shortfall (moments method)0.312
 Extreme Value Index (regression method)0.459
 VaR(95%) (regression method)0.124
 Expected Shortfall (regression method)0.252
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.013
 Compounded annual return (geometric extrapolation)0.012
 Calmar ratio (compounded annual return / max draw down)0.018
 Compounded annual return / average of 25% largest draw downs0.097
 Compounded annual return / Expected Shortfall lognormal0.308
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) NA
 Sharpe ratio (Hedges UMVUE)NA
 dfNA
 tNA
 pNA
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
Statistics related to Sortino ratio
 Sortino ratio-16.186
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.003
 N nonnegative terms0.000
 N negative terms131.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor0.561
 Mean of criterion-0.044
 SD of predictor0.411
 SD of criterion0.000
 Covariance0.000
 rNA
 b (slope, estimate of beta)NA
 a (intercept, estimate of alpha)NA
 Mean Square ErrorNA
 DF errorNA
 t(b)NA
 p(b)NA
 t(a)NA
 p(a)NA
 Lowerbound of 95% confidence interval for betaNA
 Upperbound of 95% confidence interval for betaNA
 Lowerbound of 95% confidence interval for alphaNA
 Upperbound of 95% confidence interval for alphaNA
 Treynor index (mean / b)NA
 Jensen alpha (a)NA
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) -12492933348697024.000
 Sharpe ratio (Hedges UMVUE)-12420719861132300.000
 df130.000
 t-8833837887775228.000
 p1.000
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-13930479873814932.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-10910959848449668.000
Statistics related to Sortino ratio
 Sortino ratio-16.186
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.003
 N nonnegative terms0.000
 N negative terms131.000
Statistics related to linear regression on benchmark
 N of observations131.000
 Mean of predictor0.476
 Mean of criterion-0.044
 SD of predictor0.414
 SD of criterion0.000
 Covariance0.000
 r0.000
 b (slope, estimate of beta)0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error129.000
 t(b)0.000
 p(b)0.500
 t(a)-8777492766489210.000
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.000
 Upperbound of 95% confidence interval for beta0.000
 Lowerbound of 95% confidence interval for alpha-0.044
 Upperbound of 95% confidence interval for alpha-0.044
 Treynor index (mean / b)-283715057818448445353199717580800.000
 Jensen alpha (a)-0.044
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
ORDER STATISTICS
Quartiles of return rates
 Number of observations131.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 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 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 observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 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 lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 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)0.000
 Compounded annual return (geometric extrapolation)0.000
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.000