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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
 Mean0.059
 SD0.352
 Sharpe ratio (Glass type estimate) 0.169
 Sharpe ratio (Hedges UMVUE)0.167
 df60.000
 t0.380
 p0.353
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.702
 Upperbound of 95% confidence interval for Sharpe Ratio1.038
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.703
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.036
Statistics related to Sortino ratio
 Sortino ratio0.200
 Upside Potential Ratio1.089
 Upside part of mean0.322
 Downside part of mean-0.263
 Upside SD0.186
 Downside SD0.296
 N nonnegative terms33.000
 N negative terms28.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.193
 Mean of criterion0.059
 SD of predictor0.180
 SD of criterion0.352
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.035
 a (intercept, estimate of alpha)0.053
 Mean Square Error0.126
 DF error59.000
 t(b)0.139
 p(b)0.445
 t(a)0.319
 p(a)0.376
 Lowerbound of 95% confidence interval for beta-0.475
 Upperbound of 95% confidence interval for beta0.546
 Lowerbound of 95% confidence interval for alpha-0.277
 Upperbound of 95% confidence interval for alpha0.383
 Treynor index (mean / b)1.678
 Jensen alpha (a)0.053
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.454
 Sharpe ratio (Glass type estimate) -0.055
 Sharpe ratio (Hedges UMVUE)-0.054
 df60.000
 t-0.124
 p0.549
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.924
 Upperbound of 95% confidence interval for Sharpe Ratio0.815
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.924
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.815
Statistics related to Sortino ratio
 Sortino ratio-0.060
 Upside Potential Ratio0.734
 Upside part of mean0.306
 Downside part of mean-0.331
 Upside SD0.172
 Downside SD0.416
 N nonnegative terms33.000
 N negative terms28.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.175
 Mean of criterion-0.025
 SD of predictor0.176
 SD of criterion0.454
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.054
 a (intercept, estimate of alpha)-0.015
 Mean Square Error0.210
 DF error59.000
 t(b)-0.161
 p(b)0.564
 t(a)-0.073
 p(a)0.529
 Lowerbound of 95% confidence interval for beta-0.727
 Upperbound of 95% confidence interval for beta0.619
 Lowerbound of 95% confidence interval for alpha-0.439
 Upperbound of 95% confidence interval for alpha0.408
 Treynor index (mean / b)0.461
 Jensen alpha (a)-0.015
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.196
 Expected Shortfall on VaR0.238
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 observations61.000
 Minimum0.429
 Quartile 11.000
 Median1.012
 Quartile 31.034
 Maximum1.250
 Mean of quarter 10.923
 Mean of quarter 21.002
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.034
 Number outliers low3.000
 Percentage of outliers low0.049
 Mean of outliers low0.681
 Number of outliers high7.000
 Percentage of outliers high0.115
 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)0.053
 Expected Shortfall (regression method)0.323
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 downs0.070
 Compounded annual return / Expected Shortfall lognormal0.081
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.007
 SD0.249
 Sharpe ratio (Glass type estimate) 0.029
 Sharpe ratio (Hedges UMVUE)0.029
 df1771.000
 t0.066
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.834
 Upperbound of 95% confidence interval for Sharpe Ratio0.893
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.834
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.893
Statistics related to Sortino ratio
 Sortino ratio0.037
 Upside Potential Ratio4.105
 Upside part of mean0.817
 Downside part of mean-0.810
 Upside SD0.150
 Downside SD0.199
 N nonnegative terms522.000
 N negative terms1250.000
Statistics related to linear regression on benchmark
 N of observations1772.000
 Mean of predictor0.198
 Mean of criterion0.007
 SD of predictor0.200
 SD of criterion0.249
 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 error1770.000
 t(b)-0.840
 p(b)0.510
 t(a)0.111
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.083
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.204
 Upperbound of 95% confidence interval for alpha0.228
 Treynor index (mean / b)-0.292
 Jensen alpha (a)0.012
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.258
 Sharpe ratio (Glass type estimate) -0.098
 Sharpe ratio (Hedges UMVUE)-0.098
 df1771.000
 t-0.222
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.961
 Upperbound of 95% confidence interval for Sharpe Ratio0.766
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.961
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.766
Statistics related to Sortino ratio
 Sortino ratio-0.118
 Upside Potential Ratio3.787
 Upside part of mean0.806
 Downside part of mean-0.831
 Upside SD0.146
 Downside SD0.213
 N nonnegative terms522.000
 N negative terms1250.000
Statistics related to linear regression on benchmark
 N of observations1772.000
 Mean of predictor0.178
 Mean of criterion-0.025
 SD of predictor0.200
 SD of criterion0.258
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.067
 DF error1770.000
 t(b)-0.924
 p(b)0.511
 t(a)-0.177
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.089
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.243
 Upperbound of 95% confidence interval for alpha0.203
 Treynor index (mean / b)0.888
 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 observations1772.000
 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 low256.000
 Percentage of outliers low0.144
 Mean of outliers low0.986
 Number of outliers high284.000
 Percentage of outliers high0.160
 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)0.036
 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 downs0.204
 Compounded annual return / Expected Shortfall lognormal0.670
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 predictor0.032
 Mean of criterion-0.044
 SD of predictor0.255
 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 predictor-0.001
 Mean of criterion-0.044
 SD of predictor0.255
 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)-5595544523252211.000
 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)104999831513832529369115515682816.000
 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
 Mean0.059
 SD0.352
 Sharpe ratio (Glass type estimate) 0.169
 Sharpe ratio (Hedges UMVUE)0.167
 df60.000
 t0.380
 p0.353
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.702
 Upperbound of 95% confidence interval for Sharpe Ratio1.038
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.703
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.036
Statistics related to Sortino ratio
 Sortino ratio0.200
 Upside Potential Ratio1.089
 Upside part of mean0.322
 Downside part of mean-0.263
 Upside SD0.186
 Downside SD0.296
 N nonnegative terms33.000
 N negative terms28.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.193
 Mean of criterion0.059
 SD of predictor0.180
 SD of criterion0.352
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.035
 a (intercept, estimate of alpha)0.053
 Mean Square Error0.126
 DF error59.000
 t(b)0.139
 p(b)0.445
 t(a)0.319
 p(a)0.376
 Lowerbound of 95% confidence interval for beta-0.475
 Upperbound of 95% confidence interval for beta0.546
 Lowerbound of 95% confidence interval for alpha-0.277
 Upperbound of 95% confidence interval for alpha0.383
 Treynor index (mean / b)1.678
 Jensen alpha (a)0.053
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.454
 Sharpe ratio (Glass type estimate) -0.055
 Sharpe ratio (Hedges UMVUE)-0.054
 df60.000
 t-0.124
 p0.549
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.924
 Upperbound of 95% confidence interval for Sharpe Ratio0.815
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.924
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.815
Statistics related to Sortino ratio
 Sortino ratio-0.060
 Upside Potential Ratio0.734
 Upside part of mean0.306
 Downside part of mean-0.331
 Upside SD0.172
 Downside SD0.416
 N nonnegative terms33.000
 N negative terms28.000
Statistics related to linear regression on benchmark
 N of observations61.000
 Mean of predictor0.175
 Mean of criterion-0.025
 SD of predictor0.176
 SD of criterion0.454
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.054
 a (intercept, estimate of alpha)-0.015
 Mean Square Error0.210
 DF error59.000
 t(b)-0.161
 p(b)0.564
 t(a)-0.073
 p(a)0.529
 Lowerbound of 95% confidence interval for beta-0.727
 Upperbound of 95% confidence interval for beta0.619
 Lowerbound of 95% confidence interval for alpha-0.439
 Upperbound of 95% confidence interval for alpha0.408
 Treynor index (mean / b)0.461
 Jensen alpha (a)-0.015
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.196
 Expected Shortfall on VaR0.238
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 observations61.000
 Minimum0.429
 Quartile 11.000
 Median1.012
 Quartile 31.034
 Maximum1.250
 Mean of quarter 10.923
 Mean of quarter 21.002
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.034
 Number outliers low3.000
 Percentage of outliers low0.049
 Mean of outliers low0.681
 Number of outliers high7.000
 Percentage of outliers high0.115
 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)0.053
 Expected Shortfall (regression method)0.323
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 downs0.070
 Compounded annual return / Expected Shortfall lognormal0.081
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.007
 SD0.249
 Sharpe ratio (Glass type estimate) 0.029
 Sharpe ratio (Hedges UMVUE)0.029
 df1771.000
 t0.066
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.834
 Upperbound of 95% confidence interval for Sharpe Ratio0.893
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.834
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.893
Statistics related to Sortino ratio
 Sortino ratio0.037
 Upside Potential Ratio4.105
 Upside part of mean0.817
 Downside part of mean-0.810
 Upside SD0.150
 Downside SD0.199
 N nonnegative terms522.000
 N negative terms1250.000
Statistics related to linear regression on benchmark
 N of observations1772.000
 Mean of predictor0.198
 Mean of criterion0.007
 SD of predictor0.200
 SD of criterion0.249
 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 error1770.000
 t(b)-0.840
 p(b)0.510
 t(a)0.111
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.083
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.204
 Upperbound of 95% confidence interval for alpha0.228
 Treynor index (mean / b)-0.292
 Jensen alpha (a)0.012
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.258
 Sharpe ratio (Glass type estimate) -0.098
 Sharpe ratio (Hedges UMVUE)-0.098
 df1771.000
 t-0.222
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.961
 Upperbound of 95% confidence interval for Sharpe Ratio0.766
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.961
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.766
Statistics related to Sortino ratio
 Sortino ratio-0.118
 Upside Potential Ratio3.787
 Upside part of mean0.806
 Downside part of mean-0.831
 Upside SD0.146
 Downside SD0.213
 N nonnegative terms522.000
 N negative terms1250.000
Statistics related to linear regression on benchmark
 N of observations1772.000
 Mean of predictor0.178
 Mean of criterion-0.025
 SD of predictor0.200
 SD of criterion0.258
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.067
 DF error1770.000
 t(b)-0.924
 p(b)0.511
 t(a)-0.177
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.089
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.243
 Upperbound of 95% confidence interval for alpha0.203
 Treynor index (mean / b)0.888
 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 observations1772.000
 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 low256.000
 Percentage of outliers low0.144
 Mean of outliers low0.986
 Number of outliers high284.000
 Percentage of outliers high0.160
 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)0.036
 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 downs0.204
 Compounded annual return / Expected Shortfall lognormal0.670
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 predictor0.032
 Mean of criterion-0.044
 SD of predictor0.255
 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 predictor-0.001
 Mean of criterion-0.044
 SD of predictor0.255
 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)-5595544523252211.000
 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)104999831513832529369115515682816.000
 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