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
 Mean0.058
 SD0.349
 Sharpe ratio (Glass type estimate) 0.165
 Sharpe ratio (Hedges UMVUE)0.163
 df61.000
 t0.376
 p0.354
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.698
 Upperbound of 95% confidence interval for Sharpe Ratio1.027
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.700
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.026
Statistics related to Sortino ratio
 Sortino ratio0.196
 Upside Potential Ratio1.080
 Upside part of mean0.317
 Downside part of mean-0.259
 Upside SD0.184
 Downside SD0.294
 N nonnegative terms33.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.195
 Mean of criterion0.058
 SD of predictor0.178
 SD of criterion0.349
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.035
 a (intercept, estimate of alpha)0.051
 Mean Square Error0.124
 DF error60.000
 t(b)0.138
 p(b)0.445
 t(a)0.313
 p(a)0.378
 Lowerbound of 95% confidence interval for beta-0.471
 Upperbound of 95% confidence interval for beta0.540
 Lowerbound of 95% confidence interval for alpha-0.274
 Upperbound of 95% confidence interval for alpha0.376
 Treynor index (mean / b)1.656
 Jensen alpha (a)0.051
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.450
 Sharpe ratio (Glass type estimate) -0.056
 Sharpe ratio (Hedges UMVUE)-0.055
 df61.000
 t-0.127
 p0.550
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.918
 Upperbound of 95% confidence interval for Sharpe Ratio0.806
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.918
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.807
Statistics related to Sortino ratio
 Sortino ratio-0.061
 Upside Potential Ratio0.728
 Upside part of mean0.301
 Downside part of mean-0.326
 Upside SD0.171
 Downside SD0.413
 N nonnegative terms33.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.177
 Mean of criterion-0.025
 SD of predictor0.174
 SD of criterion0.450
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.054
 a (intercept, estimate of alpha)-0.016
 Mean Square Error0.206
 DF error60.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.075
 p(a)0.530
 Lowerbound of 95% confidence interval for beta-0.721
 Upperbound of 95% confidence interval for beta0.613
 Lowerbound of 95% confidence interval for alpha-0.432
 Upperbound of 95% confidence interval for alpha0.401
 Treynor index (mean / b)0.466
 Jensen alpha (a)-0.016
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.194
 Expected Shortfall on VaR0.236
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 observations62.000
 Minimum0.429
 Quartile 11.000
 Median1.010
 Quartile 31.034
 Maximum1.250
 Mean of quarter 10.923
 Mean of quarter 21.001
 Mean of quarter 31.020
 Mean of quarter 41.090
 Inter Quartile Range0.034
 Number outliers low3.000
 Percentage of outliers low0.048
 Mean of outliers low0.681
 Number of outliers high7.000
 Percentage of outliers high0.113
 Mean of outliers high1.140
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)0.787
 VaR(95%) (regression method)0.052
 Expected Shortfall (regression method)0.319
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)0.020
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.027
 Compounded annual return / average of 25% largest draw downs0.069
 Compounded annual return / Expected Shortfall lognormal0.080
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.007
 SD0.248
 Sharpe ratio (Glass type estimate) 0.028
 Sharpe ratio (Hedges UMVUE)0.028
 df1786.000
 t0.063
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.832
 Upperbound of 95% confidence interval for Sharpe Ratio0.887
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.832
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.887
Statistics related to Sortino ratio
 Sortino ratio0.034
 Upside Potential Ratio4.088
 Upside part of mean0.810
 Downside part of mean-0.803
 Upside SD0.150
 Downside SD0.198
 N nonnegative terms522.000
 N negative terms1265.000
Statistics related to linear regression on benchmark
 N of observations1787.000
 Mean of predictor0.202
 Mean of criterion0.007
 SD of predictor0.200
 SD of criterion0.248
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.025
 a (intercept, estimate of alpha)0.012
 Mean Square Error0.062
 DF error1785.000
 t(b)-0.839
 p(b)0.513
 t(a)0.108
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.082
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.202
 Upperbound of 95% confidence interval for alpha0.226
 Treynor index (mean / b)-0.278
 Jensen alpha (a)0.012
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.257
 Sharpe ratio (Glass type estimate) -0.099
 Sharpe ratio (Hedges UMVUE)-0.099
 df1786.000
 t-0.225
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.959
 Upperbound of 95% confidence interval for Sharpe Ratio0.761
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.959
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.761
Statistics related to Sortino ratio
 Sortino ratio-0.120
 Upside Potential Ratio3.771
 Upside part of mean0.799
 Downside part of mean-0.825
 Upside SD0.145
 Downside SD0.212
 N nonnegative terms522.000
 N negative terms1265.000
Statistics related to linear regression on benchmark
 N of observations1787.000
 Mean of predictor0.182
 Mean of criterion-0.025
 SD of predictor0.200
 SD of criterion0.257
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.066
 DF error1785.000
 t(b)-0.923
 p(b)0.514
 t(a)-0.179
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.088
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.242
 Upperbound of 95% confidence interval for alpha0.201
 Treynor index (mean / b)0.905
 Jensen alpha (a)-0.020
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 VaR0.028
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 observations1787.000
 Minimum0.810
 Quartile 10.999
 Median1.000
 Quartile 31.001
 Maximum1.158
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.002
 Number outliers low269.000
 Percentage of outliers low0.151
 Mean of outliers low0.986
 Number of outliers high296.000
 Percentage of outliers high0.166
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.817
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.036
 Extreme Value Index (regression method)0.547
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.016
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)0.020
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.027
 Compounded annual return / average of 25% largest draw downs0.202
 Compounded annual return / Expected Shortfall lognormal0.668
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 predictor0.131
 Mean of criterion-0.044
 SD of predictor0.259
 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 predictor0.097
 Mean of criterion-0.044
 SD of predictor0.259
 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 error170.000
 t(b)-0.000
 p(b)0.500
 t(a)-5594387212590421.000
 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)79568378689964546845016921735168.000
 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
 Mean0.058
 SD0.349
 Sharpe ratio (Glass type estimate) 0.165
 Sharpe ratio (Hedges UMVUE)0.163
 df61.000
 t0.376
 p0.354
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.698
 Upperbound of 95% confidence interval for Sharpe Ratio1.027
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.700
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.026
Statistics related to Sortino ratio
 Sortino ratio0.196
 Upside Potential Ratio1.080
 Upside part of mean0.317
 Downside part of mean-0.259
 Upside SD0.184
 Downside SD0.294
 N nonnegative terms33.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.195
 Mean of criterion0.058
 SD of predictor0.178
 SD of criterion0.349
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.035
 a (intercept, estimate of alpha)0.051
 Mean Square Error0.124
 DF error60.000
 t(b)0.138
 p(b)0.445
 t(a)0.313
 p(a)0.378
 Lowerbound of 95% confidence interval for beta-0.471
 Upperbound of 95% confidence interval for beta0.540
 Lowerbound of 95% confidence interval for alpha-0.274
 Upperbound of 95% confidence interval for alpha0.376
 Treynor index (mean / b)1.656
 Jensen alpha (a)0.051
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.450
 Sharpe ratio (Glass type estimate) -0.056
 Sharpe ratio (Hedges UMVUE)-0.055
 df61.000
 t-0.127
 p0.550
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.918
 Upperbound of 95% confidence interval for Sharpe Ratio0.806
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.918
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.807
Statistics related to Sortino ratio
 Sortino ratio-0.061
 Upside Potential Ratio0.728
 Upside part of mean0.301
 Downside part of mean-0.326
 Upside SD0.171
 Downside SD0.413
 N nonnegative terms33.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations62.000
 Mean of predictor0.177
 Mean of criterion-0.025
 SD of predictor0.174
 SD of criterion0.450
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.054
 a (intercept, estimate of alpha)-0.016
 Mean Square Error0.206
 DF error60.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.075
 p(a)0.530
 Lowerbound of 95% confidence interval for beta-0.721
 Upperbound of 95% confidence interval for beta0.613
 Lowerbound of 95% confidence interval for alpha-0.432
 Upperbound of 95% confidence interval for alpha0.401
 Treynor index (mean / b)0.466
 Jensen alpha (a)-0.016
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.194
 Expected Shortfall on VaR0.236
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 observations62.000
 Minimum0.429
 Quartile 11.000
 Median1.010
 Quartile 31.034
 Maximum1.250
 Mean of quarter 10.923
 Mean of quarter 21.001
 Mean of quarter 31.020
 Mean of quarter 41.090
 Inter Quartile Range0.034
 Number outliers low3.000
 Percentage of outliers low0.048
 Mean of outliers low0.681
 Number of outliers high7.000
 Percentage of outliers high0.113
 Mean of outliers high1.140
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)0.787
 VaR(95%) (regression method)0.052
 Expected Shortfall (regression method)0.319
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)0.020
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.027
 Compounded annual return / average of 25% largest draw downs0.069
 Compounded annual return / Expected Shortfall lognormal0.080
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.007
 SD0.248
 Sharpe ratio (Glass type estimate) 0.028
 Sharpe ratio (Hedges UMVUE)0.028
 df1786.000
 t0.063
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.832
 Upperbound of 95% confidence interval for Sharpe Ratio0.887
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.832
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.887
Statistics related to Sortino ratio
 Sortino ratio0.034
 Upside Potential Ratio4.088
 Upside part of mean0.810
 Downside part of mean-0.803
 Upside SD0.150
 Downside SD0.198
 N nonnegative terms522.000
 N negative terms1265.000
Statistics related to linear regression on benchmark
 N of observations1787.000
 Mean of predictor0.202
 Mean of criterion0.007
 SD of predictor0.200
 SD of criterion0.248
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.025
 a (intercept, estimate of alpha)0.012
 Mean Square Error0.062
 DF error1785.000
 t(b)-0.839
 p(b)0.513
 t(a)0.108
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.082
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.202
 Upperbound of 95% confidence interval for alpha0.226
 Treynor index (mean / b)-0.278
 Jensen alpha (a)0.012
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.257
 Sharpe ratio (Glass type estimate) -0.099
 Sharpe ratio (Hedges UMVUE)-0.099
 df1786.000
 t-0.225
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.959
 Upperbound of 95% confidence interval for Sharpe Ratio0.761
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.959
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.761
Statistics related to Sortino ratio
 Sortino ratio-0.120
 Upside Potential Ratio3.771
 Upside part of mean0.799
 Downside part of mean-0.825
 Upside SD0.145
 Downside SD0.212
 N nonnegative terms522.000
 N negative terms1265.000
Statistics related to linear regression on benchmark
 N of observations1787.000
 Mean of predictor0.182
 Mean of criterion-0.025
 SD of predictor0.200
 SD of criterion0.257
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.066
 DF error1785.000
 t(b)-0.923
 p(b)0.514
 t(a)-0.179
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.088
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.242
 Upperbound of 95% confidence interval for alpha0.201
 Treynor index (mean / b)0.905
 Jensen alpha (a)-0.020
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 VaR0.028
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 observations1787.000
 Minimum0.810
 Quartile 10.999
 Median1.000
 Quartile 31.001
 Maximum1.158
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.002
 Number outliers low269.000
 Percentage of outliers low0.151
 Mean of outliers low0.986
 Number of outliers high296.000
 Percentage of outliers high0.166
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.817
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.036
 Extreme Value Index (regression method)0.547
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.016
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)0.020
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.027
 Compounded annual return / average of 25% largest draw downs0.202
 Compounded annual return / Expected Shortfall lognormal0.668
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 predictor0.131
 Mean of criterion-0.044
 SD of predictor0.259
 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 predictor0.097
 Mean of criterion-0.044
 SD of predictor0.259
 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 error170.000
 t(b)-0.000
 p(b)0.500
 t(a)-5594387212590421.000
 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)79568378689964546845016921735168.000
 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