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
 Mean0.065
 SD0.361
 Sharpe ratio (Glass type estimate) 0.179
 Sharpe ratio (Hedges UMVUE)0.177
 df57.000
 t0.394
 p0.348
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.714
 Upperbound of 95% confidence interval for Sharpe Ratio1.071
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.715
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.069
Statistics related to Sortino ratio
 Sortino ratio0.213
 Upside Potential Ratio1.116
 Upside part of mean0.339
 Downside part of mean-0.274
 Upside SD0.190
 Downside SD0.304
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.204
 Mean of criterion0.065
 SD of predictor0.180
 SD of criterion0.361
 Covariance0.001
 r0.017
 b (slope, estimate of beta)0.034
 a (intercept, estimate of alpha)0.058
 Mean Square Error0.133
 DF error56.000
 t(b)0.126
 p(b)0.450
 t(a)0.331
 p(a)0.371
 Lowerbound of 95% confidence interval for beta-0.503
 Upperbound of 95% confidence interval for beta0.571
 Lowerbound of 95% confidence interval for alpha-0.292
 Upperbound of 95% confidence interval for alpha0.407
 Treynor index (mean / b)1.908
 Jensen alpha (a)0.058
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.466
 Sharpe ratio (Glass type estimate) -0.051
 Sharpe ratio (Hedges UMVUE)-0.051
 df57.000
 t-0.113
 p0.545
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.943
 Upperbound of 95% confidence interval for Sharpe Ratio0.840
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.942
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.841
Statistics related to Sortino ratio
 Sortino ratio-0.056
 Upside Potential Ratio0.753
 Upside part of mean0.321
 Downside part of mean-0.345
 Upside SD0.177
 Downside SD0.427
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.186
 Mean of criterion-0.024
 SD of predictor0.176
 SD of criterion0.466
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.057
 a (intercept, estimate of alpha)-0.013
 Mean Square Error0.221
 DF error56.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.059
 p(a)0.524
 Lowerbound of 95% confidence interval for beta-0.766
 Upperbound of 95% confidence interval for beta0.652
 Lowerbound of 95% confidence interval for alpha-0.461
 Upperbound of 95% confidence interval for alpha0.435
 Treynor index (mean / b)0.417
 Jensen alpha (a)-0.013
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.200
 Expected Shortfall on VaR0.243
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations58.000
 Minimum0.429
 Quartile 10.995
 Median1.013
 Quartile 31.036
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.003
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.041
 Number outliers low3.000
 Percentage of outliers low0.052
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.086
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.182
 VaR(95%) (moments method)0.056
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.055
 Expected Shortfall (regression method)4.839
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.006
 Quartile 10.018
 Median0.040
 Quartile 30.044
 Maximum0.703
 Mean of quarter 10.010
 Mean of quarter 20.030
 Mean of quarter 30.042
 Mean of quarter 40.276
 Inter Quartile Range0.026
 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 high0.703
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.030
 VaR(95%) (moments method)0.248
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)3.283
 VaR(95%) (regression method)1.059
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.073
 Compounded annual return / Expected Shortfall lognormal0.083
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.011
 SD0.257
 Sharpe ratio (Glass type estimate) 0.041
 Sharpe ratio (Hedges UMVUE)0.041
 df1663.000
 t0.091
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.850
 Upperbound of 95% confidence interval for Sharpe Ratio0.932
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.850
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.932
Statistics related to Sortino ratio
 Sortino ratio0.052
 Upside Potential Ratio4.236
 Upside part of mean0.870
 Downside part of mean-0.859
 Upside SD0.155
 Downside SD0.205
 N nonnegative terms522.000
 N negative terms1142.000
Statistics related to linear regression on benchmark
 N of observations1664.000
 Mean of predictor0.208
 Mean of criterion0.011
 SD of predictor0.192
 SD of criterion0.257
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.029
 a (intercept, estimate of alpha)0.017
 Mean Square Error0.066
 DF error1662.000
 t(b)-0.877
 p(b)0.511
 t(a)0.141
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.093
 Upperbound of 95% confidence interval for beta0.036
 Lowerbound of 95% confidence interval for alpha-0.213
 Upperbound of 95% confidence interval for alpha0.247
 Treynor index (mean / b)-0.367
 Jensen alpha (a)0.017
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.266
 Sharpe ratio (Glass type estimate) -0.090
 Sharpe ratio (Hedges UMVUE)-0.090
 df1663.000
 t-0.198
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.981
 Upperbound of 95% confidence interval for Sharpe Ratio0.801
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.981
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.801
Statistics related to Sortino ratio
 Sortino ratio-0.109
 Upside Potential Ratio3.908
 Upside part of mean0.858
 Downside part of mean-0.882
 Upside SD0.150
 Downside SD0.220
 N nonnegative terms522.000
 N negative terms1142.000
Statistics related to linear regression on benchmark
 N of observations1664.000
 Mean of predictor0.189
 Mean of criterion-0.024
 SD of predictor0.192
 SD of criterion0.266
 Covariance-0.001
 r-0.024
 b (slope, estimate of beta)-0.033
 a (intercept, estimate of alpha)-0.018
 Mean Square Error0.071
 DF error1662.000
 t(b)-0.964
 p(b)0.512
 t(a)-0.147
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.100
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.255
 Upperbound of 95% confidence interval for alpha0.220
 Treynor index (mean / b)0.730
 Jensen alpha (a)-0.018
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1664.000
 Minimum0.810
 Quartile 10.999
 Median1.000
 Quartile 31.002
 Maximum1.158
 Mean of quarter 10.990
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.010
 Inter Quartile Range0.003
 Number outliers low195.000
 Percentage of outliers low0.117
 Mean of outliers low0.982
 Number of outliers high220.000
 Percentage of outliers high0.132
 Mean of outliers high1.016
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.828
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.042
 Extreme Value Index (regression method)0.556
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.017
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations71.000
 Minimum0.000
 Quartile 10.003
 Median0.008
 Quartile 30.023
 Maximum0.703
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.016
 Mean of quarter 40.093
 Inter Quartile Range0.020
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high11.000
 Percentage of outliers high0.155
 Mean of outliers high0.134
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.721
 VaR(95%) (moments method)0.089
 Expected Shortfall (moments method)0.338
 Extreme Value Index (regression method)0.541
 VaR(95%) (regression method)0.064
 Expected Shortfall (regression method)0.146
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.217
 Compounded annual return / Expected Shortfall lognormal0.693
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-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.140
 Mean of criterion-0.044
 SD of predictor0.158
 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) -7936535306446244.000
 Sharpe ratio (Hedges UMVUE)-7901674975671223.000
 df171.000
 t-5611977934314593.000
 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)-8739115425704417.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-7064234525638030.000
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.127
 Mean of criterion-0.044
 SD of predictor0.158
 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 error170.000
 t(b)0.000
 p(b)0.500
 t(a)-5590245688970973.000
 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)-181259795233523290266330036436992.000
 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 observations172.000
 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
 Mean0.065
 SD0.361
 Sharpe ratio (Glass type estimate) 0.179
 Sharpe ratio (Hedges UMVUE)0.177
 df57.000
 t0.394
 p0.348
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.714
 Upperbound of 95% confidence interval for Sharpe Ratio1.071
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.715
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.069
Statistics related to Sortino ratio
 Sortino ratio0.213
 Upside Potential Ratio1.116
 Upside part of mean0.339
 Downside part of mean-0.274
 Upside SD0.190
 Downside SD0.304
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.204
 Mean of criterion0.065
 SD of predictor0.180
 SD of criterion0.361
 Covariance0.001
 r0.017
 b (slope, estimate of beta)0.034
 a (intercept, estimate of alpha)0.058
 Mean Square Error0.133
 DF error56.000
 t(b)0.126
 p(b)0.450
 t(a)0.331
 p(a)0.371
 Lowerbound of 95% confidence interval for beta-0.503
 Upperbound of 95% confidence interval for beta0.571
 Lowerbound of 95% confidence interval for alpha-0.292
 Upperbound of 95% confidence interval for alpha0.407
 Treynor index (mean / b)1.908
 Jensen alpha (a)0.058
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.466
 Sharpe ratio (Glass type estimate) -0.051
 Sharpe ratio (Hedges UMVUE)-0.051
 df57.000
 t-0.113
 p0.545
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.943
 Upperbound of 95% confidence interval for Sharpe Ratio0.840
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.942
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.841
Statistics related to Sortino ratio
 Sortino ratio-0.056
 Upside Potential Ratio0.753
 Upside part of mean0.321
 Downside part of mean-0.345
 Upside SD0.177
 Downside SD0.427
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.186
 Mean of criterion-0.024
 SD of predictor0.176
 SD of criterion0.466
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.057
 a (intercept, estimate of alpha)-0.013
 Mean Square Error0.221
 DF error56.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.059
 p(a)0.524
 Lowerbound of 95% confidence interval for beta-0.766
 Upperbound of 95% confidence interval for beta0.652
 Lowerbound of 95% confidence interval for alpha-0.461
 Upperbound of 95% confidence interval for alpha0.435
 Treynor index (mean / b)0.417
 Jensen alpha (a)-0.013
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.200
 Expected Shortfall on VaR0.243
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations58.000
 Minimum0.429
 Quartile 10.995
 Median1.013
 Quartile 31.036
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.003
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.041
 Number outliers low3.000
 Percentage of outliers low0.052
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.086
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.182
 VaR(95%) (moments method)0.056
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.055
 Expected Shortfall (regression method)4.839
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.006
 Quartile 10.018
 Median0.040
 Quartile 30.044
 Maximum0.703
 Mean of quarter 10.010
 Mean of quarter 20.030
 Mean of quarter 30.042
 Mean of quarter 40.276
 Inter Quartile Range0.026
 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 high0.703
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.030
 VaR(95%) (moments method)0.248
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)3.283
 VaR(95%) (regression method)1.059
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.073
 Compounded annual return / Expected Shortfall lognormal0.083
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.011
 SD0.257
 Sharpe ratio (Glass type estimate) 0.041
 Sharpe ratio (Hedges UMVUE)0.041
 df1663.000
 t0.091
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.850
 Upperbound of 95% confidence interval for Sharpe Ratio0.932
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.850
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.932
Statistics related to Sortino ratio
 Sortino ratio0.052
 Upside Potential Ratio4.236
 Upside part of mean0.870
 Downside part of mean-0.859
 Upside SD0.155
 Downside SD0.205
 N nonnegative terms522.000
 N negative terms1142.000
Statistics related to linear regression on benchmark
 N of observations1664.000
 Mean of predictor0.208
 Mean of criterion0.011
 SD of predictor0.192
 SD of criterion0.257
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.029
 a (intercept, estimate of alpha)0.017
 Mean Square Error0.066
 DF error1662.000
 t(b)-0.877
 p(b)0.511
 t(a)0.141
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.093
 Upperbound of 95% confidence interval for beta0.036
 Lowerbound of 95% confidence interval for alpha-0.213
 Upperbound of 95% confidence interval for alpha0.247
 Treynor index (mean / b)-0.367
 Jensen alpha (a)0.017
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.266
 Sharpe ratio (Glass type estimate) -0.090
 Sharpe ratio (Hedges UMVUE)-0.090
 df1663.000
 t-0.198
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.981
 Upperbound of 95% confidence interval for Sharpe Ratio0.801
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.981
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.801
Statistics related to Sortino ratio
 Sortino ratio-0.109
 Upside Potential Ratio3.908
 Upside part of mean0.858
 Downside part of mean-0.882
 Upside SD0.150
 Downside SD0.220
 N nonnegative terms522.000
 N negative terms1142.000
Statistics related to linear regression on benchmark
 N of observations1664.000
 Mean of predictor0.189
 Mean of criterion-0.024
 SD of predictor0.192
 SD of criterion0.266
 Covariance-0.001
 r-0.024
 b (slope, estimate of beta)-0.033
 a (intercept, estimate of alpha)-0.018
 Mean Square Error0.071
 DF error1662.000
 t(b)-0.964
 p(b)0.512
 t(a)-0.147
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.100
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.255
 Upperbound of 95% confidence interval for alpha0.220
 Treynor index (mean / b)0.730
 Jensen alpha (a)-0.018
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1664.000
 Minimum0.810
 Quartile 10.999
 Median1.000
 Quartile 31.002
 Maximum1.158
 Mean of quarter 10.990
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.010
 Inter Quartile Range0.003
 Number outliers low195.000
 Percentage of outliers low0.117
 Mean of outliers low0.982
 Number of outliers high220.000
 Percentage of outliers high0.132
 Mean of outliers high1.016
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.828
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.042
 Extreme Value Index (regression method)0.556
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.017
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations71.000
 Minimum0.000
 Quartile 10.003
 Median0.008
 Quartile 30.023
 Maximum0.703
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.016
 Mean of quarter 40.093
 Inter Quartile Range0.020
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high11.000
 Percentage of outliers high0.155
 Mean of outliers high0.134
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.721
 VaR(95%) (moments method)0.089
 Expected Shortfall (moments method)0.338
 Extreme Value Index (regression method)0.541
 VaR(95%) (regression method)0.064
 Expected Shortfall (regression method)0.146
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.217
 Compounded annual return / Expected Shortfall lognormal0.693
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-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.140
 Mean of criterion-0.044
 SD of predictor0.158
 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) -7936535306446244.000
 Sharpe ratio (Hedges UMVUE)-7901674975671223.000
 df171.000
 t-5611977934314593.000
 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)-8739115425704417.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-7064234525638030.000
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.127
 Mean of criterion-0.044
 SD of predictor0.158
 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 error170.000
 t(b)0.000
 p(b)0.500
 t(a)-5590245688970973.000
 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)-181259795233523290266330036436992.000
 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 observations172.000
 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