Advanced Statistics: Buzo Principle

Advanced Statistics module contributed by Jules Ellis, C2 Member.

Jules has written a very helpful guide for these statistics.

MonthlyDaily (all)Daily (last 6 mo.)
ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.065
 SD0.361
 Sharpe ratio (Glass type estimate) 0.179
 Sharpe ratio (Hedges UMVUE)0.177
 df57.000
 t0.394
 p0.348
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.714
 Upperbound of 95% confidence interval for Sharpe Ratio1.071
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.715
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.069
Statistics related to Sortino ratio
 Sortino ratio0.213
 Upside Potential Ratio1.116
 Upside part of mean0.339
 Downside part of mean-0.274
 Upside SD0.190
 Downside SD0.304
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.204
 Mean of criterion0.065
 SD of predictor0.180
 SD of criterion0.361
 Covariance0.001
 r0.017
 b (slope, estimate of beta)0.034
 a (intercept, estimate of alpha)0.058
 Mean Square Error0.133
 DF error56.000
 t(b)0.126
 p(b)0.450
 t(a)0.331
 p(a)0.371
 Lowerbound of 95% confidence interval for beta-0.503
 Upperbound of 95% confidence interval for beta0.571
 Lowerbound of 95% confidence interval for alpha-0.292
 Upperbound of 95% confidence interval for alpha0.407
 Treynor index (mean / b)1.908
 Jensen alpha (a)0.058
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.466
 Sharpe ratio (Glass type estimate) -0.051
 Sharpe ratio (Hedges UMVUE)-0.051
 df57.000
 t-0.113
 p0.545
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.943
 Upperbound of 95% confidence interval for Sharpe Ratio0.840
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.942
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.841
Statistics related to Sortino ratio
 Sortino ratio-0.056
 Upside Potential Ratio0.753
 Upside part of mean0.321
 Downside part of mean-0.345
 Upside SD0.177
 Downside SD0.427
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.186
 Mean of criterion-0.024
 SD of predictor0.176
 SD of criterion0.466
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.057
 a (intercept, estimate of alpha)-0.013
 Mean Square Error0.221
 DF error56.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.059
 p(a)0.524
 Lowerbound of 95% confidence interval for beta-0.766
 Upperbound of 95% confidence interval for beta0.652
 Lowerbound of 95% confidence interval for alpha-0.461
 Upperbound of 95% confidence interval for alpha0.435
 Treynor index (mean / b)0.417
 Jensen alpha (a)-0.013
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.200
 Expected Shortfall on VaR0.243
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations58.000
 Minimum0.429
 Quartile 10.995
 Median1.013
 Quartile 31.036
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.003
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.041
 Number outliers low3.000
 Percentage of outliers low0.052
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.086
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.182
 VaR(95%) (moments method)0.056
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.055
 Expected Shortfall (regression method)4.839
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.006
 Quartile 10.018
 Median0.040
 Quartile 30.044
 Maximum0.703
 Mean of quarter 10.010
 Mean of quarter 20.030
 Mean of quarter 30.042
 Mean of quarter 40.276
 Inter Quartile Range0.026
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.091
 Mean of outliers high0.703
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.030
 VaR(95%) (moments method)0.248
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)3.283
 VaR(95%) (regression method)1.059
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.073
 Compounded annual return / Expected Shortfall lognormal0.083
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.010
 SD0.257
 Sharpe ratio (Glass type estimate) 0.040
 Sharpe ratio (Hedges UMVUE)0.040
 df1673.000
 t0.088
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.848
 Upperbound of 95% confidence interval for Sharpe Ratio0.928
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.848
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.928
Statistics related to Sortino ratio
 Sortino ratio0.050
 Upside Potential Ratio4.224
 Upside part of mean0.865
 Downside part of mean-0.854
 Upside SD0.155
 Downside SD0.205
 N nonnegative terms522.000
 N negative terms1152.000
Statistics related to linear regression on benchmark
 N of observations1674.000
 Mean of predictor0.194
 Mean of criterion0.010
 SD of predictor0.193
 SD of criterion0.257
 Covariance-0.001
 r-0.021
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)0.016
 Mean Square Error0.066
 DF error1672.000
 t(b)-0.871
 p(b)0.511
 t(a)0.135
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.092
 Upperbound of 95% confidence interval for beta0.035
 Lowerbound of 95% confidence interval for alpha-0.213
 Upperbound of 95% confidence interval for alpha0.244
 Treynor index (mean / b)-0.362
 Jensen alpha (a)0.016
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.265
 Sharpe ratio (Glass type estimate) -0.091
 Sharpe ratio (Hedges UMVUE)-0.091
 df1673.000
 t-0.200
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.979
 Upperbound of 95% confidence interval for Sharpe Ratio0.798
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.979
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.798
Statistics related to Sortino ratio
 Sortino ratio-0.110
 Upside Potential Ratio3.896
 Upside part of mean0.853
 Downside part of mean-0.877
 Upside SD0.150
 Downside SD0.219
 N nonnegative terms522.000
 N negative terms1152.000
Statistics related to linear regression on benchmark
 N of observations1674.000
 Mean of predictor0.176
 Mean of criterion-0.024
 SD of predictor0.193
 SD of criterion0.265
 Covariance-0.001
 r-0.023
 b (slope, estimate of beta)-0.032
 a (intercept, estimate of alpha)-0.018
 Mean Square Error0.070
 DF error1672.000
 t(b)-0.958
 p(b)0.512
 t(a)-0.153
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.098
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.255
 Upperbound of 95% confidence interval for alpha0.218
 Treynor index (mean / b)0.746
 Jensen alpha (a)-0.018
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1674.000
 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 low202.000
 Percentage of outliers low0.121
 Mean of outliers low0.983
 Number of outliers high223.000
 Percentage of outliers high0.133
 Mean of outliers high1.016
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)0.038
 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)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.216
 Compounded annual return / Expected Shortfall lognormal0.691
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 predictor-0.013
 Mean of criterion-0.044
 SD of predictor0.174
 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-0.028
 Mean of criterion-0.044
 SD of predictor0.174
 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)-5595335220898169.000
 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)-36760250152476066096761819627520.000
 Jensen alpha (a)-0.044
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 Mean of quarter 1NA
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 4NA
 Inter Quartile Range0.000
 Number outliers low0.000
 Percentage of outliers lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 Mean of outliers highNA
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.000
 Compounded annual return (geometric extrapolation)0.000
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.000

Advanced Statistics: Buzo Principle

Advanced Statistics module contributed by Jules Ellis, C2 Member.

Jules has written a very helpful guide for these statistics.

MonthlyDaily (all)Daily (last 6 mo.)
ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.065
 SD0.361
 Sharpe ratio (Glass type estimate) 0.179
 Sharpe ratio (Hedges UMVUE)0.177
 df57.000
 t0.394
 p0.348
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.714
 Upperbound of 95% confidence interval for Sharpe Ratio1.071
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.715
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.069
Statistics related to Sortino ratio
 Sortino ratio0.213
 Upside Potential Ratio1.116
 Upside part of mean0.339
 Downside part of mean-0.274
 Upside SD0.190
 Downside SD0.304
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.204
 Mean of criterion0.065
 SD of predictor0.180
 SD of criterion0.361
 Covariance0.001
 r0.017
 b (slope, estimate of beta)0.034
 a (intercept, estimate of alpha)0.058
 Mean Square Error0.133
 DF error56.000
 t(b)0.126
 p(b)0.450
 t(a)0.331
 p(a)0.371
 Lowerbound of 95% confidence interval for beta-0.503
 Upperbound of 95% confidence interval for beta0.571
 Lowerbound of 95% confidence interval for alpha-0.292
 Upperbound of 95% confidence interval for alpha0.407
 Treynor index (mean / b)1.908
 Jensen alpha (a)0.058
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.466
 Sharpe ratio (Glass type estimate) -0.051
 Sharpe ratio (Hedges UMVUE)-0.051
 df57.000
 t-0.113
 p0.545
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.943
 Upperbound of 95% confidence interval for Sharpe Ratio0.840
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.942
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.841
Statistics related to Sortino ratio
 Sortino ratio-0.056
 Upside Potential Ratio0.753
 Upside part of mean0.321
 Downside part of mean-0.345
 Upside SD0.177
 Downside SD0.427
 N nonnegative terms33.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.186
 Mean of criterion-0.024
 SD of predictor0.176
 SD of criterion0.466
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.057
 a (intercept, estimate of alpha)-0.013
 Mean Square Error0.221
 DF error56.000
 t(b)-0.162
 p(b)0.564
 t(a)-0.059
 p(a)0.524
 Lowerbound of 95% confidence interval for beta-0.766
 Upperbound of 95% confidence interval for beta0.652
 Lowerbound of 95% confidence interval for alpha-0.461
 Upperbound of 95% confidence interval for alpha0.435
 Treynor index (mean / b)0.417
 Jensen alpha (a)-0.013
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.200
 Expected Shortfall on VaR0.243
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations58.000
 Minimum0.429
 Quartile 10.995
 Median1.013
 Quartile 31.036
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.003
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.041
 Number outliers low3.000
 Percentage of outliers low0.052
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.086
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.182
 VaR(95%) (moments method)0.056
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.055
 Expected Shortfall (regression method)4.839
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.006
 Quartile 10.018
 Median0.040
 Quartile 30.044
 Maximum0.703
 Mean of quarter 10.010
 Mean of quarter 20.030
 Mean of quarter 30.042
 Mean of quarter 40.276
 Inter Quartile Range0.026
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.091
 Mean of outliers high0.703
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.030
 VaR(95%) (moments method)0.248
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)3.283
 VaR(95%) (regression method)1.059
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.073
 Compounded annual return / Expected Shortfall lognormal0.083
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.010
 SD0.257
 Sharpe ratio (Glass type estimate) 0.040
 Sharpe ratio (Hedges UMVUE)0.040
 df1673.000
 t0.088
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.848
 Upperbound of 95% confidence interval for Sharpe Ratio0.928
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.848
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.928
Statistics related to Sortino ratio
 Sortino ratio0.050
 Upside Potential Ratio4.224
 Upside part of mean0.865
 Downside part of mean-0.854
 Upside SD0.155
 Downside SD0.205
 N nonnegative terms522.000
 N negative terms1152.000
Statistics related to linear regression on benchmark
 N of observations1674.000
 Mean of predictor0.194
 Mean of criterion0.010
 SD of predictor0.193
 SD of criterion0.257
 Covariance-0.001
 r-0.021
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)0.016
 Mean Square Error0.066
 DF error1672.000
 t(b)-0.871
 p(b)0.511
 t(a)0.135
 p(a)0.498
 Lowerbound of 95% confidence interval for beta-0.092
 Upperbound of 95% confidence interval for beta0.035
 Lowerbound of 95% confidence interval for alpha-0.213
 Upperbound of 95% confidence interval for alpha0.244
 Treynor index (mean / b)-0.362
 Jensen alpha (a)0.016
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.265
 Sharpe ratio (Glass type estimate) -0.091
 Sharpe ratio (Hedges UMVUE)-0.091
 df1673.000
 t-0.200
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.979
 Upperbound of 95% confidence interval for Sharpe Ratio0.798
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.979
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.798
Statistics related to Sortino ratio
 Sortino ratio-0.110
 Upside Potential Ratio3.896
 Upside part of mean0.853
 Downside part of mean-0.877
 Upside SD0.150
 Downside SD0.219
 N nonnegative terms522.000
 N negative terms1152.000
Statistics related to linear regression on benchmark
 N of observations1674.000
 Mean of predictor0.176
 Mean of criterion-0.024
 SD of predictor0.193
 SD of criterion0.265
 Covariance-0.001
 r-0.023
 b (slope, estimate of beta)-0.032
 a (intercept, estimate of alpha)-0.018
 Mean Square Error0.070
 DF error1672.000
 t(b)-0.958
 p(b)0.512
 t(a)-0.153
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.098
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.255
 Upperbound of 95% confidence interval for alpha0.218
 Treynor index (mean / b)0.746
 Jensen alpha (a)-0.018
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1674.000
 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 low202.000
 Percentage of outliers low0.121
 Mean of outliers low0.983
 Number of outliers high223.000
 Percentage of outliers high0.133
 Mean of outliers high1.016
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)0.038
 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)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.029
 Compounded annual return / average of 25% largest draw downs0.216
 Compounded annual return / Expected Shortfall lognormal0.691
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 predictor-0.013
 Mean of criterion-0.044
 SD of predictor0.174
 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-0.028
 Mean of criterion-0.044
 SD of predictor0.174
 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)-5595335220898169.000
 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)-36760250152476066096761819627520.000
 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