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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
 Mean0.043
 SD0.335
 Sharpe ratio (Glass type estimate) 0.127
 Sharpe ratio (Hedges UMVUE)0.126
 df61.000
 t0.289
 p0.387
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.736
 Upperbound of 95% confidence interval for Sharpe Ratio0.989
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.737
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.988
Statistics related to Sortino ratio
 Sortino ratio0.156
 Upside Potential Ratio1.107
 Upside part of mean0.301
 Downside part of mean-0.259
 Upside SD0.191
 Downside SD0.272
 N nonnegative terms27.000
 N negative terms35.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.236
 Mean of criterion0.043
 SD of predictor0.196
 SD of criterion0.335
 Covariance0.001
 r0.016
 b (slope, estimate of beta)0.027
 a (intercept, estimate of alpha)0.036
 Mean Square Error0.114
 DF error60.000
 t(b)0.123
 p(b)0.451
 t(a)0.230
 p(a)0.410
 Lowerbound of 95% confidence interval for beta-0.414
 Upperbound of 95% confidence interval for beta0.468
 Lowerbound of 95% confidence interval for alpha-0.279
 Upperbound of 95% confidence interval for alpha0.351
 Treynor index (mean / b)1.572
 Jensen alpha (a)0.036
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.412
 Sharpe ratio (Glass type estimate) -0.071
 Sharpe ratio (Hedges UMVUE)-0.070
 df61.000
 t-0.160
 p0.563
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.933
 Upperbound of 95% confidence interval for Sharpe Ratio0.792
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.932
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.793
Statistics related to Sortino ratio
 Sortino ratio-0.079
 Upside Potential Ratio0.769
 Upside part of mean0.284
 Downside part of mean-0.313
 Upside SD0.176
 Downside SD0.369
 N nonnegative terms27.000
 N negative terms35.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.215
 Mean of criterion-0.029
 SD of predictor0.192
 SD of criterion0.412
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)-0.028
 Mean Square Error0.173
 DF error60.000
 t(b)-0.022
 p(b)0.509
 t(a)-0.144
 p(a)0.557
 Lowerbound of 95% confidence interval for beta-0.561
 Upperbound of 95% confidence interval for beta0.549
 Lowerbound of 95% confidence interval for alpha-0.413
 Upperbound of 95% confidence interval for alpha0.357
 Treynor index (mean / b)4.657
 Jensen alpha (a)-0.028
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.180
 Expected Shortfall on VaR0.219
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.052
 Expected Shortfall on VaR0.118
ORDER STATISTICS
Quartiles of return rates
 Number of observations62.000
 Minimum0.466
 Quartile 10.999
 Median1.000
 Quartile 31.035
 Maximum1.268
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.014
 Mean of quarter 41.091
 Inter Quartile Range0.036
 Number outliers low4.000
 Percentage of outliers low0.065
 Mean of outliers low0.758
 Number of outliers high6.000
 Percentage of outliers high0.097
 Mean of outliers high1.156
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.673
 VaR(95%) (moments method)0.010
 Expected Shortfall (moments method)0.040
 Extreme Value Index (regression method)1.107
 VaR(95%) (regression method)0.067
 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)0.016
 Compounded annual return (geometric extrapolation)0.015
 Calmar ratio (compounded annual return / max draw down)0.022
 Compounded annual return / average of 25% largest draw downs0.056
 Compounded annual return / Expected Shortfall lognormal0.069
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.033
 SD0.351
 Sharpe ratio (Glass type estimate) 0.094
 Sharpe ratio (Hedges UMVUE)0.093
 df1361.000
 t0.213
 p0.496
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.766
 Upperbound of 95% confidence interval for Sharpe Ratio0.953
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.766
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.953
Statistics related to Sortino ratio
 Sortino ratio0.132
 Upside Potential Ratio4.465
 Upside part of mean1.106
 Downside part of mean-1.073
 Upside SD0.248
 Downside SD0.248
 N nonnegative terms457.000
 N negative terms905.000
Statistics related to linear regression on benchmark
 N of observations1362.000
 Mean of predictor0.259
 Mean of criterion0.033
 SD of predictor0.285
 SD of criterion0.351
 Covariance0.011
 r0.113
 b (slope, estimate of beta)0.139
 a (intercept, estimate of alpha)-0.003
 Mean Square Error0.122
 DF error1360.000
 t(b)4.199
 p(b)0.443
 t(a)-0.022
 p(a)0.500
 Lowerbound of 95% confidence interval for beta0.074
 Upperbound of 95% confidence interval for beta0.205
 Lowerbound of 95% confidence interval for alpha-0.304
 Upperbound of 95% confidence interval for alpha0.297
 Treynor index (mean / b)0.235
 Jensen alpha (a)-0.003
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.354
 Sharpe ratio (Glass type estimate) -0.083
 Sharpe ratio (Hedges UMVUE)-0.082
 df1361.000
 t-0.188
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.942
 Upperbound of 95% confidence interval for Sharpe Ratio0.777
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.942
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.777
Statistics related to Sortino ratio
 Sortino ratio-0.110
 Upside Potential Ratio4.071
 Upside part of mean1.077
 Downside part of mean-1.107
 Upside SD0.234
 Downside SD0.265
 N nonnegative terms457.000
 N negative terms905.000
Statistics related to linear regression on benchmark
 N of observations1362.000
 Mean of predictor0.219
 Mean of criterion-0.029
 SD of predictor0.281
 SD of criterion0.354
 Covariance0.011
 r0.108
 b (slope, estimate of beta)0.136
 a (intercept, estimate of alpha)-0.059
 Mean Square Error0.124
 DF error1360.000
 t(b)4.011
 p(b)0.446
 t(a)-0.382
 p(a)0.505
 Lowerbound of 95% confidence interval for beta0.069
 Upperbound of 95% confidence interval for beta0.202
 Lowerbound of 95% confidence interval for alpha-0.362
 Upperbound of 95% confidence interval for alpha0.244
 Treynor index (mean / b)-0.215
 Jensen alpha (a)-0.059
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.035
 Expected Shortfall on VaR0.044
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.025
ORDER STATISTICS
Quartiles of return rates
 Number of observations1362.000
 Minimum0.802
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.246
 Mean of quarter 10.984
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.017
 Inter Quartile Range0.004
 Number outliers low155.000
 Percentage of outliers low0.114
 Mean of outliers low0.971
 Number of outliers high158.000
 Percentage of outliers high0.116
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.936
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.204
 Extreme Value Index (regression method)0.526
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.030
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)0.015
 Compounded annual return (geometric extrapolation)0.015
 Calmar ratio (compounded annual return / max draw down)0.021
 Compounded annual return / average of 25% largest draw downs0.116
 Compounded annual return / Expected Shortfall lognormal0.339
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 predictor0.618
 Mean of criterion-0.044
 SD of predictor0.208
 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 predictor0.596
 Mean of criterion-0.044
 SD of predictor0.207
 SD of criterion0.000
 Covariance-0.000
 r-0.000
 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)-8662854878524105.000
 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)37742888083290751192576276037632.000
 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
 Mean0.043
 SD0.335
 Sharpe ratio (Glass type estimate) 0.127
 Sharpe ratio (Hedges UMVUE)0.126
 df61.000
 t0.289
 p0.387
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.736
 Upperbound of 95% confidence interval for Sharpe Ratio0.989
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.737
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.988
Statistics related to Sortino ratio
 Sortino ratio0.156
 Upside Potential Ratio1.107
 Upside part of mean0.301
 Downside part of mean-0.259
 Upside SD0.191
 Downside SD0.272
 N nonnegative terms27.000
 N negative terms35.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.236
 Mean of criterion0.043
 SD of predictor0.196
 SD of criterion0.335
 Covariance0.001
 r0.016
 b (slope, estimate of beta)0.027
 a (intercept, estimate of alpha)0.036
 Mean Square Error0.114
 DF error60.000
 t(b)0.123
 p(b)0.451
 t(a)0.230
 p(a)0.410
 Lowerbound of 95% confidence interval for beta-0.414
 Upperbound of 95% confidence interval for beta0.468
 Lowerbound of 95% confidence interval for alpha-0.279
 Upperbound of 95% confidence interval for alpha0.351
 Treynor index (mean / b)1.572
 Jensen alpha (a)0.036
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.412
 Sharpe ratio (Glass type estimate) -0.071
 Sharpe ratio (Hedges UMVUE)-0.070
 df61.000
 t-0.160
 p0.563
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.933
 Upperbound of 95% confidence interval for Sharpe Ratio0.792
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.932
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.793
Statistics related to Sortino ratio
 Sortino ratio-0.079
 Upside Potential Ratio0.769
 Upside part of mean0.284
 Downside part of mean-0.313
 Upside SD0.176
 Downside SD0.369
 N nonnegative terms27.000
 N negative terms35.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.215
 Mean of criterion-0.029
 SD of predictor0.192
 SD of criterion0.412
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)-0.028
 Mean Square Error0.173
 DF error60.000
 t(b)-0.022
 p(b)0.509
 t(a)-0.144
 p(a)0.557
 Lowerbound of 95% confidence interval for beta-0.561
 Upperbound of 95% confidence interval for beta0.549
 Lowerbound of 95% confidence interval for alpha-0.413
 Upperbound of 95% confidence interval for alpha0.357
 Treynor index (mean / b)4.657
 Jensen alpha (a)-0.028
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.180
 Expected Shortfall on VaR0.219
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.052
 Expected Shortfall on VaR0.118
ORDER STATISTICS
Quartiles of return rates
 Number of observations62.000
 Minimum0.466
 Quartile 10.999
 Median1.000
 Quartile 31.035
 Maximum1.268
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.014
 Mean of quarter 41.091
 Inter Quartile Range0.036
 Number outliers low4.000
 Percentage of outliers low0.065
 Mean of outliers low0.758
 Number of outliers high6.000
 Percentage of outliers high0.097
 Mean of outliers high1.156
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.673
 VaR(95%) (moments method)0.010
 Expected Shortfall (moments method)0.040
 Extreme Value Index (regression method)1.107
 VaR(95%) (regression method)0.067
 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)0.016
 Compounded annual return (geometric extrapolation)0.015
 Calmar ratio (compounded annual return / max draw down)0.022
 Compounded annual return / average of 25% largest draw downs0.056
 Compounded annual return / Expected Shortfall lognormal0.069
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.033
 SD0.351
 Sharpe ratio (Glass type estimate) 0.094
 Sharpe ratio (Hedges UMVUE)0.093
 df1361.000
 t0.213
 p0.496
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.766
 Upperbound of 95% confidence interval for Sharpe Ratio0.953
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.766
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.953
Statistics related to Sortino ratio
 Sortino ratio0.132
 Upside Potential Ratio4.465
 Upside part of mean1.106
 Downside part of mean-1.073
 Upside SD0.248
 Downside SD0.248
 N nonnegative terms457.000
 N negative terms905.000
Statistics related to linear regression on benchmark
 N of observations1362.000
 Mean of predictor0.259
 Mean of criterion0.033
 SD of predictor0.285
 SD of criterion0.351
 Covariance0.011
 r0.113
 b (slope, estimate of beta)0.139
 a (intercept, estimate of alpha)-0.003
 Mean Square Error0.122
 DF error1360.000
 t(b)4.199
 p(b)0.443
 t(a)-0.022
 p(a)0.500
 Lowerbound of 95% confidence interval for beta0.074
 Upperbound of 95% confidence interval for beta0.205
 Lowerbound of 95% confidence interval for alpha-0.304
 Upperbound of 95% confidence interval for alpha0.297
 Treynor index (mean / b)0.235
 Jensen alpha (a)-0.003
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.354
 Sharpe ratio (Glass type estimate) -0.083
 Sharpe ratio (Hedges UMVUE)-0.082
 df1361.000
 t-0.188
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.942
 Upperbound of 95% confidence interval for Sharpe Ratio0.777
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.942
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.777
Statistics related to Sortino ratio
 Sortino ratio-0.110
 Upside Potential Ratio4.071
 Upside part of mean1.077
 Downside part of mean-1.107
 Upside SD0.234
 Downside SD0.265
 N nonnegative terms457.000
 N negative terms905.000
Statistics related to linear regression on benchmark
 N of observations1362.000
 Mean of predictor0.219
 Mean of criterion-0.029
 SD of predictor0.281
 SD of criterion0.354
 Covariance0.011
 r0.108
 b (slope, estimate of beta)0.136
 a (intercept, estimate of alpha)-0.059
 Mean Square Error0.124
 DF error1360.000
 t(b)4.011
 p(b)0.446
 t(a)-0.382
 p(a)0.505
 Lowerbound of 95% confidence interval for beta0.069
 Upperbound of 95% confidence interval for beta0.202
 Lowerbound of 95% confidence interval for alpha-0.362
 Upperbound of 95% confidence interval for alpha0.244
 Treynor index (mean / b)-0.215
 Jensen alpha (a)-0.059
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.035
 Expected Shortfall on VaR0.044
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.025
ORDER STATISTICS
Quartiles of return rates
 Number of observations1362.000
 Minimum0.802
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.246
 Mean of quarter 10.984
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.017
 Inter Quartile Range0.004
 Number outliers low155.000
 Percentage of outliers low0.114
 Mean of outliers low0.971
 Number of outliers high158.000
 Percentage of outliers high0.116
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.936
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.204
 Extreme Value Index (regression method)0.526
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.030
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)0.015
 Compounded annual return (geometric extrapolation)0.015
 Calmar ratio (compounded annual return / max draw down)0.021
 Compounded annual return / average of 25% largest draw downs0.116
 Compounded annual return / Expected Shortfall lognormal0.339
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 predictor0.618
 Mean of criterion-0.044
 SD of predictor0.208
 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 predictor0.596
 Mean of criterion-0.044
 SD of predictor0.207
 SD of criterion0.000
 Covariance-0.000
 r-0.000
 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)-8662854878524105.000
 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)37742888083290751192576276037632.000
 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