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
 Mean0.061
 SD0.355
 Sharpe ratio (Glass type estimate) 0.172
 Sharpe ratio (Hedges UMVUE)0.170
 df59.000
 t0.385
 p0.351
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.706
 Upperbound of 95% confidence interval for Sharpe Ratio1.048
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.707
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.047
Statistics related to Sortino ratio
 Sortino ratio0.205
 Upside Potential Ratio1.098
 Upside part of mean0.328
 Downside part of mean-0.267
 Upside SD0.187
 Downside SD0.299
 N nonnegative terms33.000
 N negative terms27.000
Statistics related to linear regression on benchmark
 N of observations60.000
 Mean of predictor0.183
 Mean of criterion0.061
 SD of predictor0.180
 SD of criterion0.355
 Covariance0.001
 r0.020
 b (slope, estimate of beta)0.038
 a (intercept, estimate of alpha)0.054
 Mean Square Error0.128
 DF error58.000
 t(b)0.149
 p(b)0.441
 t(a)0.324
 p(a)0.374
 Lowerbound of 95% confidence interval for beta-0.480
 Upperbound of 95% confidence interval for beta0.557
 Lowerbound of 95% confidence interval for alpha-0.280
 Upperbound of 95% confidence interval for alpha0.388
 Treynor index (mean / b)1.587
 Jensen alpha (a)0.054
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.458
 Sharpe ratio (Glass type estimate) -0.054
 Sharpe ratio (Hedges UMVUE)-0.053
 df59.000
 t-0.120
 p0.548
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.930
 Upperbound of 95% confidence interval for Sharpe Ratio0.823
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.930
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.823
Statistics related to Sortino ratio
 Sortino ratio-0.059
 Upside Potential Ratio0.740
 Upside part of mean0.311
 Downside part of mean-0.335
 Upside SD0.174
 Downside SD0.420
 N nonnegative terms33.000
 N negative terms27.000
Statistics related to linear regression on benchmark
 N of observations60.000
 Mean of predictor0.166
 Mean of criterion-0.025
 SD of predictor0.176
 SD of criterion0.458
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.054
 a (intercept, estimate of alpha)-0.016
 Mean Square Error0.213
 DF error58.000
 t(b)-0.159
 p(b)0.563
 t(a)-0.073
 p(a)0.529
 Lowerbound of 95% confidence interval for beta-0.739
 Upperbound of 95% confidence interval for beta0.630
 Lowerbound of 95% confidence interval for alpha-0.444
 Upperbound of 95% confidence interval for alpha0.413
 Treynor index (mean / b)0.453
 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%)0.197
 Expected Shortfall on VaR0.239
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 observations60.000
 Minimum0.429
 Quartile 10.998
 Median1.012
 Quartile 31.035
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.002
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.036
 Number outliers low3.000
 Percentage of outliers low0.050
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.083
 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)0.053
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.053
 Expected Shortfall (regression method)4.682
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)0.020
 Calmar ratio (compounded annual return / max draw down)0.028
 Compounded annual return / average of 25% largest draw downs0.071
 Compounded annual return / Expected Shortfall lognormal0.082
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.008
 SD0.251
 Sharpe ratio (Glass type estimate) 0.032
 Sharpe ratio (Hedges UMVUE)0.032
 df1744.000
 t0.072
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.838
 Upperbound of 95% confidence interval for Sharpe Ratio0.902
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.838
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.902
Statistics related to Sortino ratio
 Sortino ratio0.040
 Upside Potential Ratio4.137
 Upside part of mean0.830
 Downside part of mean-0.821
 Upside SD0.151
 Downside SD0.201
 N nonnegative terms522.000
 N negative terms1223.000
Statistics related to linear regression on benchmark
 N of observations1745.000
 Mean of predictor0.195
 Mean of criterion0.008
 SD of predictor0.199
 SD of criterion0.251
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.026
 a (intercept, estimate of alpha)0.013
 Mean Square Error0.063
 DF error1743.000
 t(b)-0.845
 p(b)0.513
 t(a)0.117
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.085
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.206
 Upperbound of 95% confidence interval for alpha0.232
 Treynor index (mean / b)-0.315
 Jensen alpha (a)0.013
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.260
 Sharpe ratio (Glass type estimate) -0.096
 Sharpe ratio (Hedges UMVUE)-0.096
 df1744.000
 t-0.216
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.966
 Upperbound of 95% confidence interval for Sharpe Ratio0.774
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.966
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.774
Statistics related to Sortino ratio
 Sortino ratio-0.116
 Upside Potential Ratio3.816
 Upside part of mean0.818
 Downside part of mean-0.843
 Upside SD0.147
 Downside SD0.214
 N nonnegative terms522.000
 N negative terms1223.000
Statistics related to linear regression on benchmark
 N of observations1745.000
 Mean of predictor0.175
 Mean of criterion-0.025
 SD of predictor0.199
 SD of criterion0.260
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.029
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.068
 DF error1743.000
 t(b)-0.930
 p(b)0.514
 t(a)-0.171
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.091
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.246
 Upperbound of 95% confidence interval for alpha0.207
 Treynor index (mean / b)0.854
 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 VaR0.029
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 observations1745.000
 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 41.010
 Inter Quartile Range0.002
 Number outliers low234.000
 Percentage of outliers low0.134
 Mean of outliers low0.985
 Number of outliers high264.000
 Percentage of outliers high0.151
 Mean of outliers high1.014
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)0.037
 Extreme Value Index (regression method)0.547
 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)0.020
 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 downs0.207
 Compounded annual return / Expected Shortfall lognormal0.676
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 predictor0.047
 Mean of criterion-0.044
 SD of predictor0.243
 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 predictor0.018
 Mean of criterion-0.044
 SD of predictor0.244
 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)-5595501853821346.000
 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)-43203607183157050433819841134592.000
 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
 Mean0.061
 SD0.355
 Sharpe ratio (Glass type estimate) 0.172
 Sharpe ratio (Hedges UMVUE)0.170
 df59.000
 t0.385
 p0.351
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.706
 Upperbound of 95% confidence interval for Sharpe Ratio1.048
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.707
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.047
Statistics related to Sortino ratio
 Sortino ratio0.205
 Upside Potential Ratio1.098
 Upside part of mean0.328
 Downside part of mean-0.267
 Upside SD0.187
 Downside SD0.299
 N nonnegative terms33.000
 N negative terms27.000
Statistics related to linear regression on benchmark
 N of observations60.000
 Mean of predictor0.183
 Mean of criterion0.061
 SD of predictor0.180
 SD of criterion0.355
 Covariance0.001
 r0.020
 b (slope, estimate of beta)0.038
 a (intercept, estimate of alpha)0.054
 Mean Square Error0.128
 DF error58.000
 t(b)0.149
 p(b)0.441
 t(a)0.324
 p(a)0.374
 Lowerbound of 95% confidence interval for beta-0.480
 Upperbound of 95% confidence interval for beta0.557
 Lowerbound of 95% confidence interval for alpha-0.280
 Upperbound of 95% confidence interval for alpha0.388
 Treynor index (mean / b)1.587
 Jensen alpha (a)0.054
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.458
 Sharpe ratio (Glass type estimate) -0.054
 Sharpe ratio (Hedges UMVUE)-0.053
 df59.000
 t-0.120
 p0.548
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.930
 Upperbound of 95% confidence interval for Sharpe Ratio0.823
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.930
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.823
Statistics related to Sortino ratio
 Sortino ratio-0.059
 Upside Potential Ratio0.740
 Upside part of mean0.311
 Downside part of mean-0.335
 Upside SD0.174
 Downside SD0.420
 N nonnegative terms33.000
 N negative terms27.000
Statistics related to linear regression on benchmark
 N of observations60.000
 Mean of predictor0.166
 Mean of criterion-0.025
 SD of predictor0.176
 SD of criterion0.458
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.054
 a (intercept, estimate of alpha)-0.016
 Mean Square Error0.213
 DF error58.000
 t(b)-0.159
 p(b)0.563
 t(a)-0.073
 p(a)0.529
 Lowerbound of 95% confidence interval for beta-0.739
 Upperbound of 95% confidence interval for beta0.630
 Lowerbound of 95% confidence interval for alpha-0.444
 Upperbound of 95% confidence interval for alpha0.413
 Treynor index (mean / b)0.453
 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%)0.197
 Expected Shortfall on VaR0.239
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 observations60.000
 Minimum0.429
 Quartile 10.998
 Median1.012
 Quartile 31.035
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.002
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.036
 Number outliers low3.000
 Percentage of outliers low0.050
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.083
 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)0.053
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.053
 Expected Shortfall (regression method)4.682
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)0.020
 Calmar ratio (compounded annual return / max draw down)0.028
 Compounded annual return / average of 25% largest draw downs0.071
 Compounded annual return / Expected Shortfall lognormal0.082
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.008
 SD0.251
 Sharpe ratio (Glass type estimate) 0.032
 Sharpe ratio (Hedges UMVUE)0.032
 df1744.000
 t0.072
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.838
 Upperbound of 95% confidence interval for Sharpe Ratio0.902
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.838
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.902
Statistics related to Sortino ratio
 Sortino ratio0.040
 Upside Potential Ratio4.137
 Upside part of mean0.830
 Downside part of mean-0.821
 Upside SD0.151
 Downside SD0.201
 N nonnegative terms522.000
 N negative terms1223.000
Statistics related to linear regression on benchmark
 N of observations1745.000
 Mean of predictor0.195
 Mean of criterion0.008
 SD of predictor0.199
 SD of criterion0.251
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.026
 a (intercept, estimate of alpha)0.013
 Mean Square Error0.063
 DF error1743.000
 t(b)-0.845
 p(b)0.513
 t(a)0.117
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.085
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.206
 Upperbound of 95% confidence interval for alpha0.232
 Treynor index (mean / b)-0.315
 Jensen alpha (a)0.013
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.260
 Sharpe ratio (Glass type estimate) -0.096
 Sharpe ratio (Hedges UMVUE)-0.096
 df1744.000
 t-0.216
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.966
 Upperbound of 95% confidence interval for Sharpe Ratio0.774
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.966
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.774
Statistics related to Sortino ratio
 Sortino ratio-0.116
 Upside Potential Ratio3.816
 Upside part of mean0.818
 Downside part of mean-0.843
 Upside SD0.147
 Downside SD0.214
 N nonnegative terms522.000
 N negative terms1223.000
Statistics related to linear regression on benchmark
 N of observations1745.000
 Mean of predictor0.175
 Mean of criterion-0.025
 SD of predictor0.199
 SD of criterion0.260
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.029
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.068
 DF error1743.000
 t(b)-0.930
 p(b)0.514
 t(a)-0.171
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.091
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.246
 Upperbound of 95% confidence interval for alpha0.207
 Treynor index (mean / b)0.854
 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 VaR0.029
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 observations1745.000
 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 41.010
 Inter Quartile Range0.002
 Number outliers low234.000
 Percentage of outliers low0.134
 Mean of outliers low0.985
 Number of outliers high264.000
 Percentage of outliers high0.151
 Mean of outliers high1.014
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)0.037
 Extreme Value Index (regression method)0.547
 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)0.020
 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 downs0.207
 Compounded annual return / Expected Shortfall lognormal0.676
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 predictor0.047
 Mean of criterion-0.044
 SD of predictor0.243
 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 predictor0.018
 Mean of criterion-0.044
 SD of predictor0.244
 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)-5595501853821346.000
 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)-43203607183157050433819841134592.000
 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