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
 Mean0.067
 SD0.364
 Sharpe ratio (Glass type estimate) 0.183
 Sharpe ratio (Hedges UMVUE)0.180
 df56.000
 t0.399
 p0.346
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.718
 Upperbound of 95% confidence interval for Sharpe Ratio1.082
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.719
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.080
Statistics related to Sortino ratio
 Sortino ratio0.217
 Upside Potential Ratio1.126
 Upside part of mean0.345
 Downside part of mean-0.278
 Upside SD0.192
 Downside SD0.306
 N nonnegative terms33.000
 N negative terms24.000
Statistics related to linear regression on benchmark
 N of observations57.000
 Mean of predictor0.210
 Mean of criterion0.067
 SD of predictor0.181
 SD of criterion0.364
 Covariance0.001
 r0.016
 b (slope, estimate of beta)0.032
 a (intercept, estimate of alpha)0.060
 Mean Square Error0.135
 DF error55.000
 t(b)0.119
 p(b)0.453
 t(a)0.336
 p(a)0.369
 Lowerbound of 95% confidence interval for beta-0.511
 Upperbound of 95% confidence interval for beta0.576
 Lowerbound of 95% confidence interval for alpha-0.297
 Upperbound of 95% confidence interval for alpha0.417
 Treynor index (mean / b)2.062
 Jensen alpha (a)0.060
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.470
 Sharpe ratio (Glass type estimate) -0.050
 Sharpe ratio (Hedges UMVUE)-0.050
 df56.000
 t-0.109
 p0.543
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.949
 Upperbound of 95% confidence interval for Sharpe Ratio0.849
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.949
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.850
Statistics related to Sortino ratio
 Sortino ratio-0.055
 Upside Potential Ratio0.759
 Upside part of mean0.327
 Downside part of mean-0.351
 Upside SD0.178
 Downside SD0.431
 N nonnegative terms33.000
 N negative terms24.000
Statistics related to linear regression on benchmark
 N of observations57.000
 Mean of predictor0.192
 Mean of criterion-0.024
 SD of predictor0.177
 SD of criterion0.470
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.058
 a (intercept, estimate of alpha)-0.012
 Mean Square Error0.225
 DF error55.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.054
 p(a)0.522
 Lowerbound of 95% confidence interval for beta-0.776
 Upperbound of 95% confidence interval for beta0.660
 Lowerbound of 95% confidence interval for alpha-0.470
 Upperbound of 95% confidence interval for alpha0.445
 Treynor index (mean / b)0.406
 Jensen alpha (a)-0.012
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.202
 Expected Shortfall on VaR0.245
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 observations57.000
 Minimum0.429
 Quartile 10.994
 Median1.013
 Quartile 31.037
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.004
 Mean of quarter 31.024
 Mean of quarter 41.098
 Inter Quartile Range0.043
 Number outliers low3.000
 Percentage of outliers low0.053
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.088
 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)0.057
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.057
 Expected Shortfall (regression method)4.921
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)0.021
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.075
 Compounded annual return / Expected Shortfall lognormal0.084
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.011
 SD0.259
 Sharpe ratio (Glass type estimate) 0.044
 Sharpe ratio (Hedges UMVUE)0.044
 df1637.000
 t0.096
 p0.498
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.854
 Upperbound of 95% confidence interval for Sharpe Ratio0.942
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.854
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.942
Statistics related to Sortino ratio
 Sortino ratio0.055
 Upside Potential Ratio4.270
 Upside part of mean0.884
 Downside part of mean-0.872
 Upside SD0.156
 Downside SD0.207
 N nonnegative terms522.000
 N negative terms1116.000
Statistics related to linear regression on benchmark
 N of observations1638.000
 Mean of predictor0.213
 Mean of criterion0.011
 SD of predictor0.192
 SD of criterion0.259
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.029
 a (intercept, estimate of alpha)0.018
 Mean Square Error0.067
 DF error1636.000
 t(b)-0.876
 p(b)0.511
 t(a)0.149
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.095
 Upperbound of 95% confidence interval for beta0.036
 Lowerbound of 95% confidence interval for alpha-0.216
 Upperbound of 95% confidence interval for alpha0.251
 Treynor index (mean / b)-0.392
 Jensen alpha (a)0.018
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.268
 Sharpe ratio (Glass type estimate) -0.088
 Sharpe ratio (Hedges UMVUE)-0.088
 df1637.000
 t-0.192
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.986
 Upperbound of 95% confidence interval for Sharpe Ratio0.810
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.986
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.810
Statistics related to Sortino ratio
 Sortino ratio-0.107
 Upside Potential Ratio3.939
 Upside part of mean0.872
 Downside part of mean-0.896
 Upside SD0.151
 Downside SD0.221
 N nonnegative terms522.000
 N negative terms1116.000
Statistics related to linear regression on benchmark
 N of observations1638.000
 Mean of predictor0.195
 Mean of criterion-0.024
 SD of predictor0.192
 SD of criterion0.268
 Covariance-0.001
 r-0.024
 b (slope, estimate of beta)-0.033
 a (intercept, estimate of alpha)-0.017
 Mean Square Error0.072
 DF error1636.000
 t(b)-0.962
 p(b)0.512
 t(a)-0.140
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.101
 Upperbound of 95% confidence interval for beta0.035
 Lowerbound of 95% confidence interval for alpha-0.259
 Upperbound of 95% confidence interval for alpha0.224
 Treynor index (mean / b)0.712
 Jensen alpha (a)-0.017
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.024
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations1638.000
 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 low177.000
 Percentage of outliers low0.108
 Mean of outliers low0.981
 Number of outliers high212.000
 Percentage of outliers high0.129
 Mean of outliers high1.017
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.839
 VaR(95%) (moments method)0.007
 Expected Shortfall (moments method)0.047
 Extreme Value Index (regression method)0.560
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.018
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)0.021
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.221
 Compounded annual return / Expected Shortfall lognormal0.698
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 predictor0.233
 Mean of criterion-0.044
 SD of predictor0.162
 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 predictor0.219
 Mean of criterion-0.044
 SD of predictor0.162
 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)-5580569775573173.000
 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)-33584381937439336491119751987200.000
 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
 Mean0.067
 SD0.364
 Sharpe ratio (Glass type estimate) 0.183
 Sharpe ratio (Hedges UMVUE)0.180
 df56.000
 t0.399
 p0.346
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.718
 Upperbound of 95% confidence interval for Sharpe Ratio1.082
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.719
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.080
Statistics related to Sortino ratio
 Sortino ratio0.217
 Upside Potential Ratio1.126
 Upside part of mean0.345
 Downside part of mean-0.278
 Upside SD0.192
 Downside SD0.306
 N nonnegative terms33.000
 N negative terms24.000
Statistics related to linear regression on benchmark
 N of observations57.000
 Mean of predictor0.210
 Mean of criterion0.067
 SD of predictor0.181
 SD of criterion0.364
 Covariance0.001
 r0.016
 b (slope, estimate of beta)0.032
 a (intercept, estimate of alpha)0.060
 Mean Square Error0.135
 DF error55.000
 t(b)0.119
 p(b)0.453
 t(a)0.336
 p(a)0.369
 Lowerbound of 95% confidence interval for beta-0.511
 Upperbound of 95% confidence interval for beta0.576
 Lowerbound of 95% confidence interval for alpha-0.297
 Upperbound of 95% confidence interval for alpha0.417
 Treynor index (mean / b)2.062
 Jensen alpha (a)0.060
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.470
 Sharpe ratio (Glass type estimate) -0.050
 Sharpe ratio (Hedges UMVUE)-0.050
 df56.000
 t-0.109
 p0.543
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.949
 Upperbound of 95% confidence interval for Sharpe Ratio0.849
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.949
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.850
Statistics related to Sortino ratio
 Sortino ratio-0.055
 Upside Potential Ratio0.759
 Upside part of mean0.327
 Downside part of mean-0.351
 Upside SD0.178
 Downside SD0.431
 N nonnegative terms33.000
 N negative terms24.000
Statistics related to linear regression on benchmark
 N of observations57.000
 Mean of predictor0.192
 Mean of criterion-0.024
 SD of predictor0.177
 SD of criterion0.470
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.058
 a (intercept, estimate of alpha)-0.012
 Mean Square Error0.225
 DF error55.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.054
 p(a)0.522
 Lowerbound of 95% confidence interval for beta-0.776
 Upperbound of 95% confidence interval for beta0.660
 Lowerbound of 95% confidence interval for alpha-0.470
 Upperbound of 95% confidence interval for alpha0.445
 Treynor index (mean / b)0.406
 Jensen alpha (a)-0.012
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.202
 Expected Shortfall on VaR0.245
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 observations57.000
 Minimum0.429
 Quartile 10.994
 Median1.013
 Quartile 31.037
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.004
 Mean of quarter 31.024
 Mean of quarter 41.098
 Inter Quartile Range0.043
 Number outliers low3.000
 Percentage of outliers low0.053
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.088
 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)0.057
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.057
 Expected Shortfall (regression method)4.921
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)0.021
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.075
 Compounded annual return / Expected Shortfall lognormal0.084
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.011
 SD0.259
 Sharpe ratio (Glass type estimate) 0.044
 Sharpe ratio (Hedges UMVUE)0.044
 df1637.000
 t0.096
 p0.498
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.854
 Upperbound of 95% confidence interval for Sharpe Ratio0.942
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.854
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.942
Statistics related to Sortino ratio
 Sortino ratio0.055
 Upside Potential Ratio4.270
 Upside part of mean0.884
 Downside part of mean-0.872
 Upside SD0.156
 Downside SD0.207
 N nonnegative terms522.000
 N negative terms1116.000
Statistics related to linear regression on benchmark
 N of observations1638.000
 Mean of predictor0.213
 Mean of criterion0.011
 SD of predictor0.192
 SD of criterion0.259
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.029
 a (intercept, estimate of alpha)0.018
 Mean Square Error0.067
 DF error1636.000
 t(b)-0.876
 p(b)0.511
 t(a)0.149
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.095
 Upperbound of 95% confidence interval for beta0.036
 Lowerbound of 95% confidence interval for alpha-0.216
 Upperbound of 95% confidence interval for alpha0.251
 Treynor index (mean / b)-0.392
 Jensen alpha (a)0.018
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.268
 Sharpe ratio (Glass type estimate) -0.088
 Sharpe ratio (Hedges UMVUE)-0.088
 df1637.000
 t-0.192
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.986
 Upperbound of 95% confidence interval for Sharpe Ratio0.810
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.986
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.810
Statistics related to Sortino ratio
 Sortino ratio-0.107
 Upside Potential Ratio3.939
 Upside part of mean0.872
 Downside part of mean-0.896
 Upside SD0.151
 Downside SD0.221
 N nonnegative terms522.000
 N negative terms1116.000
Statistics related to linear regression on benchmark
 N of observations1638.000
 Mean of predictor0.195
 Mean of criterion-0.024
 SD of predictor0.192
 SD of criterion0.268
 Covariance-0.001
 r-0.024
 b (slope, estimate of beta)-0.033
 a (intercept, estimate of alpha)-0.017
 Mean Square Error0.072
 DF error1636.000
 t(b)-0.962
 p(b)0.512
 t(a)-0.140
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.101
 Upperbound of 95% confidence interval for beta0.035
 Lowerbound of 95% confidence interval for alpha-0.259
 Upperbound of 95% confidence interval for alpha0.224
 Treynor index (mean / b)0.712
 Jensen alpha (a)-0.017
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.024
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations1638.000
 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 low177.000
 Percentage of outliers low0.108
 Mean of outliers low0.981
 Number of outliers high212.000
 Percentage of outliers high0.129
 Mean of outliers high1.017
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.839
 VaR(95%) (moments method)0.007
 Expected Shortfall (moments method)0.047
 Extreme Value Index (regression method)0.560
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.018
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)0.021
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.221
 Compounded annual return / Expected Shortfall lognormal0.698
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 predictor0.233
 Mean of criterion-0.044
 SD of predictor0.162
 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 predictor0.219
 Mean of criterion-0.044
 SD of predictor0.162
 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)-5580569775573173.000
 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)-33584381937439336491119751987200.000
 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