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Advanced Statistics: gdes

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
 Mean-0.078
 SD0.146
 Sharpe ratio (Glass type estimate) -0.537
 Sharpe ratio (Hedges UMVUE)-0.523
 df29.000
 t-0.849
 p0.799
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.780
 Upperbound of 95% confidence interval for Sharpe Ratio0.715
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.770
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.724
Statistics related to Sortino ratio
 Sortino ratio-0.612
 Upside Potential Ratio0.339
 Upside part of mean0.043
 Downside part of mean-0.122
 Upside SD0.069
 Downside SD0.128
 N nonnegative terms1.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations30.000
 Mean of predictor0.105
 Mean of criterion-0.078
 SD of predictor0.152
 SD of criterion0.146
 Covariance0.008
 r0.373
 b (slope, estimate of beta)0.358
 a (intercept, estimate of alpha)-0.116
 Mean Square Error0.019
 DF error28.000
 t(b)2.127
 p(b)0.021
 t(a)-1.304
 p(a)0.899
 Lowerbound of 95% confidence interval for beta0.013
 Upperbound of 95% confidence interval for beta0.703
 Lowerbound of 95% confidence interval for alpha-0.298
 Upperbound of 95% confidence interval for alpha0.066
 Treynor index (mean / b)-0.219
 Jensen alpha (a)-0.116
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.090
 SD0.157
 Sharpe ratio (Glass type estimate) -0.572
 Sharpe ratio (Hedges UMVUE)-0.557
 df29.000
 t-0.904
 p0.813
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.815
 Upperbound of 95% confidence interval for Sharpe Ratio0.681
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.805
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.691
Statistics related to Sortino ratio
 Sortino ratio-0.631
 Upside Potential Ratio0.289
 Upside part of mean0.041
 Downside part of mean-0.131
 Upside SD0.065
 Downside SD0.142
 N nonnegative terms1.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations30.000
 Mean of predictor0.093
 Mean of criterion-0.090
 SD of predictor0.153
 SD of criterion0.157
 Covariance0.009
 r0.393
 b (slope, estimate of beta)0.402
 a (intercept, estimate of alpha)-0.127
 Mean Square Error0.021
 DF error28.000
 t(b)2.264
 p(b)0.016
 t(a)-1.348
 p(a)0.906
 Lowerbound of 95% confidence interval for beta0.038
 Upperbound of 95% confidence interval for beta0.766
 Lowerbound of 95% confidence interval for alpha-0.319
 Upperbound of 95% confidence interval for alpha0.066
 Treynor index (mean / b)-0.223
 Jensen alpha (a)-0.127
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.079
 Expected Shortfall on VaR0.096
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.035
 Expected Shortfall on VaR0.074
ORDER STATISTICS
Quartiles of return rates
 Number of observations30.000
 Minimum0.803
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.112
 Mean of quarter 10.975
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.014
 Inter Quartile Range0.000
 Number outliers low1.000
 Percentage of outliers low0.033
 Mean of outliers low0.803
 Number of outliers high1.000
 Percentage of outliers high0.033
 Mean of outliers high1.112
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 observations1.000
 Minimum0.197
 Quartile 10.197
 Median0.197
 Quartile 30.197
 Maximum0.197
 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 low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 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)-0.043
 Compounded annual return (geometric extrapolation)-0.044
 Calmar ratio (compounded annual return / max draw down)-0.225
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.465
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.073
 SD0.175
 Sharpe ratio (Glass type estimate) -0.421
 Sharpe ratio (Hedges UMVUE)-0.420
 df866.000
 t-0.668
 p0.748
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.655
 Upperbound of 95% confidence interval for Sharpe Ratio0.814
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.655
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.815
Statistics related to Sortino ratio
 Sortino ratio-0.515
 Upside Potential Ratio1.502
 Upside part of mean0.214
 Downside part of mean-0.288
 Upside SD0.101
 Downside SD0.143
 N nonnegative terms16.000
 N negative terms851.000
Statistics related to linear regression on benchmark
 N of observations867.000
 Mean of predictor0.122
 Mean of criterion-0.073
 SD of predictor0.197
 SD of criterion0.175
 Covariance0.008
 r0.239
 b (slope, estimate of beta)0.211
 a (intercept, estimate of alpha)-0.099
 Mean Square Error0.029
 DF error865.000
 t(b)7.224
 p(b)-0.000
 t(a)-0.927
 p(a)0.823
 Lowerbound of 95% confidence interval for beta0.154
 Upperbound of 95% confidence interval for beta0.268
 Lowerbound of 95% confidence interval for alpha-0.309
 Upperbound of 95% confidence interval for alpha0.111
 Treynor index (mean / b)-0.348
 Jensen alpha (a)-0.099
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.089
 SD0.179
 Sharpe ratio (Glass type estimate) -0.498
 Sharpe ratio (Hedges UMVUE)-0.498
 df866.000
 t-0.791
 p0.785
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.733
 Upperbound of 95% confidence interval for Sharpe Ratio0.737
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.732
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.737
Statistics related to Sortino ratio
 Sortino ratio-0.595
 Upside Potential Ratio1.397
 Upside part of mean0.209
 Downside part of mean-0.299
 Upside SD0.098
 Downside SD0.150
 N nonnegative terms16.000
 N negative terms851.000
Statistics related to linear regression on benchmark
 N of observations867.000
 Mean of predictor0.102
 Mean of criterion-0.089
 SD of predictor0.197
 SD of criterion0.179
 Covariance0.009
 r0.246
 b (slope, estimate of beta)0.223
 a (intercept, estimate of alpha)-0.112
 Mean Square Error0.030
 DF error865.000
 t(b)7.471
 p(b)-0.000
 t(a)-1.024
 p(a)0.847
 Lowerbound of 95% confidence interval for beta0.165
 Upperbound of 95% confidence interval for beta0.282
 Lowerbound of 95% confidence interval for alpha-0.327
 Upperbound of 95% confidence interval for alpha0.103
 Treynor index (mean / b)-0.399
 Jensen alpha (a)-0.112
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.016
 Expected Shortfall on VaR0.020
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.007
ORDER STATISTICS
Quartiles of return rates
 Number of observations867.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.080
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.002
 Inter Quartile Range0.000
 Number outliers low11.000
 Percentage of outliers low0.013
 Mean of outliers low0.944
 Number of outliers high16.000
 Percentage of outliers high0.018
 Mean of outliers high1.034
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)-1.335
 VaR(95%) (regression method)-0.375
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.369
 Quartile 10.369
 Median0.369
 Quartile 30.369
 Maximum0.369
 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 low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 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)-0.043
 Compounded annual return (geometric extrapolation)-0.044
 Calmar ratio (compounded annual return / max draw down)-0.119
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-2.210
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 predictor0.389
 Mean of criterion-0.044
 SD of predictor0.158
 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 predictor0.376
 Mean of criterion-0.044
 SD of predictor0.157
 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)-5549382945632657.000
 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)20322996447121615314362002571264.000
 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