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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
 Mean0.044
 SD0.338
 Sharpe ratio (Glass type estimate) 0.130
 Sharpe ratio (Hedges UMVUE)0.129
 df60.000
 t0.294
 p0.385
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.740
 Upperbound of 95% confidence interval for Sharpe Ratio0.999
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.741
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.998
Statistics related to Sortino ratio
 Sortino ratio0.160
 Upside Potential Ratio1.116
 Upside part of mean0.306
 Downside part of mean-0.262
 Upside SD0.192
 Downside SD0.274
 N nonnegative terms27.000
 N negative terms34.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.226
 Mean of criterion0.044
 SD of predictor0.196
 SD of criterion0.338
 Covariance0.001
 r0.017
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)0.037
 Mean Square Error0.116
 DF error59.000
 t(b)0.132
 p(b)0.448
 t(a)0.234
 p(a)0.408
 Lowerbound of 95% confidence interval for beta-0.418
 Upperbound of 95% confidence interval for beta0.477
 Lowerbound of 95% confidence interval for alpha-0.281
 Upperbound of 95% confidence interval for alpha0.356
 Treynor index (mean / b)1.495
 Jensen alpha (a)0.037
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.416
 Sharpe ratio (Glass type estimate) -0.069
 Sharpe ratio (Hedges UMVUE)-0.069
 df60.000
 t-0.156
 p0.562
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.939
 Upperbound of 95% confidence interval for Sharpe Ratio0.800
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.938
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.801
Statistics related to Sortino ratio
 Sortino ratio-0.077
 Upside Potential Ratio0.775
 Upside part of mean0.289
 Downside part of mean-0.318
 Upside SD0.177
 Downside SD0.372
 N nonnegative terms27.000
 N negative terms34.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.205
 Mean of criterion-0.029
 SD of predictor0.192
 SD of criterion0.416
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)-0.028
 Mean Square Error0.176
 DF error59.000
 t(b)-0.021
 p(b)0.508
 t(a)-0.142
 p(a)0.556
 Lowerbound of 95% confidence interval for beta-0.570
 Upperbound of 95% confidence interval for beta0.558
 Lowerbound of 95% confidence interval for alpha-0.417
 Upperbound of 95% confidence interval for alpha0.362
 Treynor index (mean / b)4.818
 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%)0.181
 Expected Shortfall on VaR0.220
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 observations61.000
 Minimum0.466
 Quartile 10.999
 Median1.001
 Quartile 31.038
 Maximum1.268
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.017
 Mean of quarter 41.094
 Inter Quartile Range0.039
 Number outliers low4.000
 Percentage of outliers low0.066
 Mean of outliers low0.758
 Number of outliers high5.000
 Percentage of outliers high0.082
 Mean of outliers high1.169
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.673
 VaR(95%) (moments method)0.011
 Expected Shortfall (moments method)0.041
 Extreme Value Index (regression method)1.107
 VaR(95%) (regression method)0.069
 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 downs0.057
 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
 SD0.352
 Sharpe ratio (Glass type estimate) 0.095
 Sharpe ratio (Hedges UMVUE)0.095
 df1352.000
 t0.215
 p0.497
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.768
 Upperbound of 95% confidence interval for Sharpe Ratio0.957
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.768
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.957
Statistics related to Sortino ratio
 Sortino ratio0.134
 Upside Potential Ratio4.480
 Upside part of mean1.113
 Downside part of mean-1.080
 Upside SD0.249
 Downside SD0.249
 N nonnegative terms457.000
 N negative terms896.000
Statistics related to linear regression on benchmark
 N of observations1353.000
 Mean of predictor0.255
 Mean of criterion0.033
 SD of predictor0.285
 SD of criterion0.352
 Covariance0.011
 r0.113
 b (slope, estimate of beta)0.140
 a (intercept, estimate of alpha)-0.002
 Mean Square Error0.122
 DF error1351.000
 t(b)4.187
 p(b)0.428
 t(a)-0.015
 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-0.305
 Upperbound of 95% confidence interval for alpha0.300
 Treynor index (mean / b)0.239
 Jensen alpha (a)-0.002
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.355
 Sharpe ratio (Glass type estimate) -0.082
 Sharpe ratio (Hedges UMVUE)-0.082
 df1352.000
 t-0.186
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.944
 Upperbound of 95% confidence interval for Sharpe Ratio0.781
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.944
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.781
Statistics related to Sortino ratio
 Sortino ratio-0.110
 Upside Potential Ratio4.085
 Upside part of mean1.085
 Downside part of mean-1.114
 Upside SD0.235
 Downside SD0.266
 N nonnegative terms457.000
 N negative terms896.000
Statistics related to linear regression on benchmark
 N of observations1353.000
 Mean of predictor0.215
 Mean of criterion-0.029
 SD of predictor0.282
 SD of criterion0.355
 Covariance0.011
 r0.108
 b (slope, estimate of beta)0.136
 a (intercept, estimate of alpha)-0.058
 Mean Square Error0.124
 DF error1351.000
 t(b)3.999
 p(b)0.431
 t(a)-0.375
 p(a)0.506
 Lowerbound of 95% confidence interval for beta0.069
 Upperbound of 95% confidence interval for beta0.203
 Lowerbound of 95% confidence interval for alpha-0.363
 Upperbound of 95% confidence interval for alpha0.247
 Treynor index (mean / b)-0.214
 Jensen alpha (a)-0.058
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.036
 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 observations1353.000
 Minimum0.802
 Quartile 10.998
 Median1.000
 Quartile 31.003
 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 low154.000
 Percentage of outliers low0.114
 Mean of outliers low0.970
 Number of outliers high157.000
 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)0.926
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.175
 Extreme Value Index (regression method)0.519
 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)0.016
 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 downs0.117
 Compounded annual return / Expected Shortfall lognormal0.340
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 predictor0.452
 Mean of criterion-0.044
 SD of predictor0.228
 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 predictor0.426
 Mean of criterion-0.044
 SD of predictor0.228
 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)-8741300142219704.000
 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)66370252328278802356570240843776.000
 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
 Mean0.044
 SD0.338
 Sharpe ratio (Glass type estimate) 0.130
 Sharpe ratio (Hedges UMVUE)0.129
 df60.000
 t0.294
 p0.385
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.740
 Upperbound of 95% confidence interval for Sharpe Ratio0.999
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.741
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.998
Statistics related to Sortino ratio
 Sortino ratio0.160
 Upside Potential Ratio1.116
 Upside part of mean0.306
 Downside part of mean-0.262
 Upside SD0.192
 Downside SD0.274
 N nonnegative terms27.000
 N negative terms34.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.226
 Mean of criterion0.044
 SD of predictor0.196
 SD of criterion0.338
 Covariance0.001
 r0.017
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)0.037
 Mean Square Error0.116
 DF error59.000
 t(b)0.132
 p(b)0.448
 t(a)0.234
 p(a)0.408
 Lowerbound of 95% confidence interval for beta-0.418
 Upperbound of 95% confidence interval for beta0.477
 Lowerbound of 95% confidence interval for alpha-0.281
 Upperbound of 95% confidence interval for alpha0.356
 Treynor index (mean / b)1.495
 Jensen alpha (a)0.037
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.416
 Sharpe ratio (Glass type estimate) -0.069
 Sharpe ratio (Hedges UMVUE)-0.069
 df60.000
 t-0.156
 p0.562
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.939
 Upperbound of 95% confidence interval for Sharpe Ratio0.800
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.938
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.801
Statistics related to Sortino ratio
 Sortino ratio-0.077
 Upside Potential Ratio0.775
 Upside part of mean0.289
 Downside part of mean-0.318
 Upside SD0.177
 Downside SD0.372
 N nonnegative terms27.000
 N negative terms34.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.205
 Mean of criterion-0.029
 SD of predictor0.192
 SD of criterion0.416
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)-0.028
 Mean Square Error0.176
 DF error59.000
 t(b)-0.021
 p(b)0.508
 t(a)-0.142
 p(a)0.556
 Lowerbound of 95% confidence interval for beta-0.570
 Upperbound of 95% confidence interval for beta0.558
 Lowerbound of 95% confidence interval for alpha-0.417
 Upperbound of 95% confidence interval for alpha0.362
 Treynor index (mean / b)4.818
 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%)0.181
 Expected Shortfall on VaR0.220
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 observations61.000
 Minimum0.466
 Quartile 10.999
 Median1.001
 Quartile 31.038
 Maximum1.268
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.017
 Mean of quarter 41.094
 Inter Quartile Range0.039
 Number outliers low4.000
 Percentage of outliers low0.066
 Mean of outliers low0.758
 Number of outliers high5.000
 Percentage of outliers high0.082
 Mean of outliers high1.169
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.673
 VaR(95%) (moments method)0.011
 Expected Shortfall (moments method)0.041
 Extreme Value Index (regression method)1.107
 VaR(95%) (regression method)0.069
 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 downs0.057
 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
 SD0.352
 Sharpe ratio (Glass type estimate) 0.095
 Sharpe ratio (Hedges UMVUE)0.095
 df1352.000
 t0.215
 p0.497
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.768
 Upperbound of 95% confidence interval for Sharpe Ratio0.957
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.768
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.957
Statistics related to Sortino ratio
 Sortino ratio0.134
 Upside Potential Ratio4.480
 Upside part of mean1.113
 Downside part of mean-1.080
 Upside SD0.249
 Downside SD0.249
 N nonnegative terms457.000
 N negative terms896.000
Statistics related to linear regression on benchmark
 N of observations1353.000
 Mean of predictor0.255
 Mean of criterion0.033
 SD of predictor0.285
 SD of criterion0.352
 Covariance0.011
 r0.113
 b (slope, estimate of beta)0.140
 a (intercept, estimate of alpha)-0.002
 Mean Square Error0.122
 DF error1351.000
 t(b)4.187
 p(b)0.428
 t(a)-0.015
 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-0.305
 Upperbound of 95% confidence interval for alpha0.300
 Treynor index (mean / b)0.239
 Jensen alpha (a)-0.002
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.029
 SD0.355
 Sharpe ratio (Glass type estimate) -0.082
 Sharpe ratio (Hedges UMVUE)-0.082
 df1352.000
 t-0.186
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.944
 Upperbound of 95% confidence interval for Sharpe Ratio0.781
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.944
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.781
Statistics related to Sortino ratio
 Sortino ratio-0.110
 Upside Potential Ratio4.085
 Upside part of mean1.085
 Downside part of mean-1.114
 Upside SD0.235
 Downside SD0.266
 N nonnegative terms457.000
 N negative terms896.000
Statistics related to linear regression on benchmark
 N of observations1353.000
 Mean of predictor0.215
 Mean of criterion-0.029
 SD of predictor0.282
 SD of criterion0.355
 Covariance0.011
 r0.108
 b (slope, estimate of beta)0.136
 a (intercept, estimate of alpha)-0.058
 Mean Square Error0.124
 DF error1351.000
 t(b)3.999
 p(b)0.431
 t(a)-0.375
 p(a)0.506
 Lowerbound of 95% confidence interval for beta0.069
 Upperbound of 95% confidence interval for beta0.203
 Lowerbound of 95% confidence interval for alpha-0.363
 Upperbound of 95% confidence interval for alpha0.247
 Treynor index (mean / b)-0.214
 Jensen alpha (a)-0.058
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.036
 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 observations1353.000
 Minimum0.802
 Quartile 10.998
 Median1.000
 Quartile 31.003
 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 low154.000
 Percentage of outliers low0.114
 Mean of outliers low0.970
 Number of outliers high157.000
 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)0.926
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.175
 Extreme Value Index (regression method)0.519
 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)0.016
 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 downs0.117
 Compounded annual return / Expected Shortfall lognormal0.340
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 predictor0.452
 Mean of criterion-0.044
 SD of predictor0.228
 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 predictor0.426
 Mean of criterion-0.044
 SD of predictor0.228
 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)-8741300142219704.000
 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)66370252328278802356570240843776.000
 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