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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
 Mean0.041
 SD0.332
 Sharpe ratio (Glass type estimate) 0.124
 Sharpe ratio (Hedges UMVUE)0.122
 df62.000
 t0.284
 p0.389
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.732
 Upperbound of 95% confidence interval for Sharpe Ratio0.979
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.733
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.978
Statistics related to Sortino ratio
 Sortino ratio0.153
 Upside Potential Ratio1.098
 Upside part of mean0.297
 Downside part of mean-0.255
 Upside SD0.189
 Downside SD0.270
 N nonnegative terms27.000
 N negative terms36.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.244
 Mean of criterion0.041
 SD of predictor0.195
 SD of criterion0.332
 Covariance0.001
 r0.015
 b (slope, estimate of beta)0.025
 a (intercept, estimate of alpha)0.035
 Mean Square Error0.112
 DF error61.000
 t(b)0.117
 p(b)0.454
 t(a)0.225
 p(a)0.411
 Lowerbound of 95% confidence interval for beta-0.410
 Upperbound of 95% confidence interval for beta0.461
 Lowerbound of 95% confidence interval for alpha-0.276
 Upperbound of 95% confidence interval for alpha0.346
 Treynor index (mean / b)1.623
 Jensen alpha (a)0.035
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.409
 Sharpe ratio (Glass type estimate) -0.072
 Sharpe ratio (Hedges UMVUE)-0.071
 df62.000
 t-0.164
 p0.565
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.927
 Upperbound of 95% confidence interval for Sharpe Ratio0.784
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.926
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.785
Statistics related to Sortino ratio
 Sortino ratio-0.080
 Upside Potential Ratio0.763
 Upside part of mean0.280
 Downside part of mean-0.309
 Upside SD0.174
 Downside SD0.366
 N nonnegative terms27.000
 N negative terms36.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.223
 Mean of criterion-0.029
 SD of predictor0.191
 SD of criterion0.409
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)-0.028
 Mean Square Error0.170
 DF error61.000
 t(b)-0.024
 p(b)0.509
 t(a)-0.147
 p(a)0.558
 Lowerbound of 95% confidence interval for beta-0.555
 Upperbound of 95% confidence interval for beta0.542
 Lowerbound of 95% confidence interval for alpha-0.408
 Upperbound of 95% confidence interval for alpha0.352
 Treynor index (mean / b)4.542
 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%)0.178
 Expected Shortfall on VaR0.217
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.052
 Expected Shortfall on VaR0.117
ORDER STATISTICS
Quartiles of return rates
 Number of observations63.000
 Minimum0.466
 Quartile 11.000
 Median1.000
 Quartile 31.033
 Maximum1.268
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.014
 Mean of quarter 41.091
 Inter Quartile Range0.033
 Number outliers low5.000
 Percentage of outliers low0.079
 Mean of outliers low0.796
 Number of outliers high6.000
 Percentage of outliers high0.095
 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)0.066
 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)0.015
 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 downs0.055
 Compounded annual return / Expected Shortfall lognormal0.068
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.031
 SD0.347
 Sharpe ratio (Glass type estimate) 0.090
 Sharpe ratio (Hedges UMVUE)0.090
 df1389.000
 t0.207
 p0.496
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.761
 Upperbound of 95% confidence interval for Sharpe Ratio0.941
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.761
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.941
Statistics related to Sortino ratio
 Sortino ratio0.127
 Upside Potential Ratio4.420
 Upside part of mean1.084
 Downside part of mean-1.053
 Upside SD0.246
 Downside SD0.245
 N nonnegative terms457.000
 N negative terms933.000
Statistics related to linear regression on benchmark
 N of observations1390.000
 Mean of predictor0.262
 Mean of criterion0.031
 SD of predictor0.284
 SD of criterion0.347
 Covariance0.011
 r0.112
 b (slope, estimate of beta)0.137
 a (intercept, estimate of alpha)-0.005
 Mean Square Error0.119
 DF error1388.000
 t(b)4.201
 p(b)0.444
 t(a)-0.031
 p(a)0.500
 Lowerbound of 95% confidence interval for beta0.073
 Upperbound of 95% confidence interval for beta0.201
 Lowerbound of 95% confidence interval for alpha-0.299
 Upperbound of 95% confidence interval for alpha0.290
 Treynor index (mean / b)0.229
 Jensen alpha (a)-0.005
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.350
 Sharpe ratio (Glass type estimate) -0.084
 Sharpe ratio (Hedges UMVUE)-0.084
 df1389.000
 t-0.194
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.935
 Upperbound of 95% confidence interval for Sharpe Ratio0.767
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.935
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.767
Statistics related to Sortino ratio
 Sortino ratio-0.113
 Upside Potential Ratio4.030
 Upside part of mean1.056
 Downside part of mean-1.085
 Upside SD0.232
 Downside SD0.262
 N nonnegative terms457.000
 N negative terms933.000
Statistics related to linear regression on benchmark
 N of observations1390.000
 Mean of predictor0.222
 Mean of criterion-0.029
 SD of predictor0.281
 SD of criterion0.350
 Covariance0.011
 r0.107
 b (slope, estimate of beta)0.133
 a (intercept, estimate of alpha)-0.059
 Mean Square Error0.121
 DF error1388.000
 t(b)4.012
 p(b)0.446
 t(a)-0.390
 p(a)0.505
 Lowerbound of 95% confidence interval for beta0.068
 Upperbound of 95% confidence interval for beta0.198
 Lowerbound of 95% confidence interval for alpha-0.356
 Upperbound of 95% confidence interval for alpha0.238
 Treynor index (mean / b)-0.221
 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 VaR0.024
ORDER STATISTICS
Quartiles of return rates
 Number of observations1390.000
 Minimum0.802
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.246
 Mean of quarter 10.985
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.016
 Inter Quartile Range0.004
 Number outliers low162.000
 Percentage of outliers low0.117
 Mean of outliers low0.971
 Number of outliers high163.000
 Percentage of outliers high0.117
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.956
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.284
 Extreme Value Index (regression method)0.524
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.029
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 downs0.114
 Compounded annual return / Expected Shortfall lognormal0.335
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 predictor0.646
 Mean of criterion-0.044
 SD of predictor0.202
 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 predictor0.625
 Mean of criterion-0.044
 SD of predictor0.202
 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)-8642541404474975.000
 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)-96940686304297140863215486369792.000
 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
 Mean0.041
 SD0.332
 Sharpe ratio (Glass type estimate) 0.124
 Sharpe ratio (Hedges UMVUE)0.122
 df62.000
 t0.284
 p0.389
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.732
 Upperbound of 95% confidence interval for Sharpe Ratio0.979
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.733
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.978
Statistics related to Sortino ratio
 Sortino ratio0.153
 Upside Potential Ratio1.098
 Upside part of mean0.297
 Downside part of mean-0.255
 Upside SD0.189
 Downside SD0.270
 N nonnegative terms27.000
 N negative terms36.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.244
 Mean of criterion0.041
 SD of predictor0.195
 SD of criterion0.332
 Covariance0.001
 r0.015
 b (slope, estimate of beta)0.025
 a (intercept, estimate of alpha)0.035
 Mean Square Error0.112
 DF error61.000
 t(b)0.117
 p(b)0.454
 t(a)0.225
 p(a)0.411
 Lowerbound of 95% confidence interval for beta-0.410
 Upperbound of 95% confidence interval for beta0.461
 Lowerbound of 95% confidence interval for alpha-0.276
 Upperbound of 95% confidence interval for alpha0.346
 Treynor index (mean / b)1.623
 Jensen alpha (a)0.035
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.409
 Sharpe ratio (Glass type estimate) -0.072
 Sharpe ratio (Hedges UMVUE)-0.071
 df62.000
 t-0.164
 p0.565
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.927
 Upperbound of 95% confidence interval for Sharpe Ratio0.784
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.926
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.785
Statistics related to Sortino ratio
 Sortino ratio-0.080
 Upside Potential Ratio0.763
 Upside part of mean0.280
 Downside part of mean-0.309
 Upside SD0.174
 Downside SD0.366
 N nonnegative terms27.000
 N negative terms36.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.223
 Mean of criterion-0.029
 SD of predictor0.191
 SD of criterion0.409
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)-0.028
 Mean Square Error0.170
 DF error61.000
 t(b)-0.024
 p(b)0.509
 t(a)-0.147
 p(a)0.558
 Lowerbound of 95% confidence interval for beta-0.555
 Upperbound of 95% confidence interval for beta0.542
 Lowerbound of 95% confidence interval for alpha-0.408
 Upperbound of 95% confidence interval for alpha0.352
 Treynor index (mean / b)4.542
 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%)0.178
 Expected Shortfall on VaR0.217
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.052
 Expected Shortfall on VaR0.117
ORDER STATISTICS
Quartiles of return rates
 Number of observations63.000
 Minimum0.466
 Quartile 11.000
 Median1.000
 Quartile 31.033
 Maximum1.268
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.014
 Mean of quarter 41.091
 Inter Quartile Range0.033
 Number outliers low5.000
 Percentage of outliers low0.079
 Mean of outliers low0.796
 Number of outliers high6.000
 Percentage of outliers high0.095
 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)0.066
 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)0.015
 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 downs0.055
 Compounded annual return / Expected Shortfall lognormal0.068
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.031
 SD0.347
 Sharpe ratio (Glass type estimate) 0.090
 Sharpe ratio (Hedges UMVUE)0.090
 df1389.000
 t0.207
 p0.496
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.761
 Upperbound of 95% confidence interval for Sharpe Ratio0.941
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.761
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.941
Statistics related to Sortino ratio
 Sortino ratio0.127
 Upside Potential Ratio4.420
 Upside part of mean1.084
 Downside part of mean-1.053
 Upside SD0.246
 Downside SD0.245
 N nonnegative terms457.000
 N negative terms933.000
Statistics related to linear regression on benchmark
 N of observations1390.000
 Mean of predictor0.262
 Mean of criterion0.031
 SD of predictor0.284
 SD of criterion0.347
 Covariance0.011
 r0.112
 b (slope, estimate of beta)0.137
 a (intercept, estimate of alpha)-0.005
 Mean Square Error0.119
 DF error1388.000
 t(b)4.201
 p(b)0.444
 t(a)-0.031
 p(a)0.500
 Lowerbound of 95% confidence interval for beta0.073
 Upperbound of 95% confidence interval for beta0.201
 Lowerbound of 95% confidence interval for alpha-0.299
 Upperbound of 95% confidence interval for alpha0.290
 Treynor index (mean / b)0.229
 Jensen alpha (a)-0.005
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.350
 Sharpe ratio (Glass type estimate) -0.084
 Sharpe ratio (Hedges UMVUE)-0.084
 df1389.000
 t-0.194
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.935
 Upperbound of 95% confidence interval for Sharpe Ratio0.767
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.935
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.767
Statistics related to Sortino ratio
 Sortino ratio-0.113
 Upside Potential Ratio4.030
 Upside part of mean1.056
 Downside part of mean-1.085
 Upside SD0.232
 Downside SD0.262
 N nonnegative terms457.000
 N negative terms933.000
Statistics related to linear regression on benchmark
 N of observations1390.000
 Mean of predictor0.222
 Mean of criterion-0.029
 SD of predictor0.281
 SD of criterion0.350
 Covariance0.011
 r0.107
 b (slope, estimate of beta)0.133
 a (intercept, estimate of alpha)-0.059
 Mean Square Error0.121
 DF error1388.000
 t(b)4.012
 p(b)0.446
 t(a)-0.390
 p(a)0.505
 Lowerbound of 95% confidence interval for beta0.068
 Upperbound of 95% confidence interval for beta0.198
 Lowerbound of 95% confidence interval for alpha-0.356
 Upperbound of 95% confidence interval for alpha0.238
 Treynor index (mean / b)-0.221
 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 VaR0.024
ORDER STATISTICS
Quartiles of return rates
 Number of observations1390.000
 Minimum0.802
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.246
 Mean of quarter 10.985
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.016
 Inter Quartile Range0.004
 Number outliers low162.000
 Percentage of outliers low0.117
 Mean of outliers low0.971
 Number of outliers high163.000
 Percentage of outliers high0.117
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.956
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.284
 Extreme Value Index (regression method)0.524
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.029
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 downs0.114
 Compounded annual return / Expected Shortfall lognormal0.335
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 predictor0.646
 Mean of criterion-0.044
 SD of predictor0.202
 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 predictor0.625
 Mean of criterion-0.044
 SD of predictor0.202
 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)-8642541404474975.000
 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)-96940686304297140863215486369792.000
 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