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Advanced Statistics: GSystem

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-0.207
 SD0.229
 Sharpe ratio (Glass type estimate) -0.904
 Sharpe ratio (Hedges UMVUE)-0.869
 df20.000
 t-1.195
 p0.629
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.400
 Upperbound of 95% confidence interval for Sharpe Ratio0.615
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.375
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.637
Statistics related to Sortino ratio
 Sortino ratio-0.895
 Upside Potential Ratio0.032
 Upside part of mean0.007
 Downside part of mean-0.214
 Upside SD0.010
 Downside SD0.231
 N nonnegative terms1.000
 N negative terms20.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.114
 Mean of criterion-0.207
 SD of predictor0.200
 SD of criterion0.229
 Covariance0.012
 r0.264
 b (slope, estimate of beta)0.302
 a (intercept, estimate of alpha)-0.241
 Mean Square Error0.051
 DF error19.000
 t(b)1.192
 p(b)0.334
 t(a)-1.389
 p(a)0.690
 Lowerbound of 95% confidence interval for beta-0.228
 Upperbound of 95% confidence interval for beta0.833
 Lowerbound of 95% confidence interval for alpha-0.604
 Upperbound of 95% confidence interval for alpha0.122
 Treynor index (mean / b)-0.683
 Jensen alpha (a)-0.241
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.239
 SD0.272
 Sharpe ratio (Glass type estimate) -0.880
 Sharpe ratio (Hedges UMVUE)-0.847
 df20.000
 t-1.164
 p0.626
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.376
 Upperbound of 95% confidence interval for Sharpe Ratio0.636
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.351
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.658
Statistics related to Sortino ratio
 Sortino ratio-0.873
 Upside Potential Ratio0.027
 Upside part of mean0.007
 Downside part of mean-0.247
 Upside SD0.010
 Downside SD0.274
 N nonnegative terms1.000
 N negative terms20.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.093
 Mean of criterion-0.239
 SD of predictor0.206
 SD of criterion0.272
 Covariance0.014
 r0.254
 b (slope, estimate of beta)0.335
 a (intercept, estimate of alpha)-0.270
 Mean Square Error0.073
 DF error19.000
 t(b)1.146
 p(b)0.340
 t(a)-1.315
 p(a)0.681
 Lowerbound of 95% confidence interval for beta-0.277
 Upperbound of 95% confidence interval for beta0.947
 Lowerbound of 95% confidence interval for alpha-0.701
 Upperbound of 95% confidence interval for alpha0.160
 Treynor index (mean / b)-0.714
 Jensen alpha (a)-0.270
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.138
 Expected Shortfall on VaR0.166
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.060
 Expected Shortfall on VaR0.130
ORDER STATISTICS
Quartiles of return rates
 Number of observations21.000
 Minimum0.699
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.017
 Mean of quarter 10.950
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.003
 Inter Quartile Range0.000
 Number outliers low2.000
 Percentage of outliers low0.095
 Mean of outliers low0.849
 Number of outliers high3.000
 Percentage of outliers high0.143
 Mean of outliers high1.006
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
 Minimum0.301
 Quartile 10.301
 Median0.301
 Quartile 30.301
 Maximum0.301
 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)-0.165
 Compounded annual return (geometric extrapolation)-0.177
 Calmar ratio (compounded annual return / max draw down)-0.589
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.069
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.216
 SD0.176
 Sharpe ratio (Glass type estimate) -1.227
 Sharpe ratio (Hedges UMVUE)-1.226
 df621.000
 t-1.650
 p0.950
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.686
 Upperbound of 95% confidence interval for Sharpe Ratio0.232
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.685
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.233
Statistics related to Sortino ratio
 Sortino ratio-1.327
 Upside Potential Ratio0.673
 Upside part of mean0.110
 Downside part of mean-0.326
 Upside SD0.068
 Downside SD0.163
 N nonnegative terms10.000
 N negative terms612.000
Statistics related to linear regression on benchmark
 N of observations622.000
 Mean of predictor0.207
 Mean of criterion-0.216
 SD of predictor0.235
 SD of criterion0.176
 Covariance0.002
 r0.039
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)-0.222
 Mean Square Error0.031
 DF error620.000
 t(b)0.968
 p(b)0.167
 t(a)-1.694
 p(a)0.955
 Lowerbound of 95% confidence interval for beta-0.030
 Upperbound of 95% confidence interval for beta0.088
 Lowerbound of 95% confidence interval for alpha-0.480
 Upperbound of 95% confidence interval for alpha0.035
 Treynor index (mean / b)-7.425
 Jensen alpha (a)-0.222
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.233
 SD0.187
 Sharpe ratio (Glass type estimate) -1.249
 Sharpe ratio (Hedges UMVUE)-1.247
 df621.000
 t-1.679
 p0.953
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.708
 Upperbound of 95% confidence interval for Sharpe Ratio0.211
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.707
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.212
Statistics related to Sortino ratio
 Sortino ratio-1.333
 Upside Potential Ratio0.614
 Upside part of mean0.107
 Downside part of mean-0.340
 Upside SD0.066
 Downside SD0.175
 N nonnegative terms10.000
 N negative terms612.000
Statistics related to linear regression on benchmark
 N of observations622.000
 Mean of predictor0.179
 Mean of criterion-0.233
 SD of predictor0.235
 SD of criterion0.187
 Covariance0.002
 r0.040
 b (slope, estimate of beta)0.032
 a (intercept, estimate of alpha)-0.239
 Mean Square Error0.035
 DF error620.000
 t(b)0.993
 p(b)0.161
 t(a)-1.719
 p(a)0.957
 Lowerbound of 95% confidence interval for beta-0.031
 Upperbound of 95% confidence interval for beta0.094
 Lowerbound of 95% confidence interval for alpha-0.511
 Upperbound of 95% confidence interval for alpha0.034
 Treynor index (mean / b)-7.374
 Jensen alpha (a)-0.239
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.017
 Expected Shortfall on VaR0.021
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 observations622.000
 Minimum0.846
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.068
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.001
 Inter Quartile Range0.000
 Number outliers low19.000
 Percentage of outliers low0.031
 Mean of outliers low0.973
 Number of outliers high15.000
 Percentage of outliers high0.024
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-2.290
 VaR(95%) (moments method)-0.014
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.402
 VaR(95%) (regression method)-0.008
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.026
 Quartile 10.040
 Median0.055
 Quartile 30.195
 Maximum0.335
 Mean of quarter 10.026
 Mean of quarter 20.055
 Mean of quarter 3NA
 Mean of quarter 40.335
 Inter Quartile Range0.155
 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)-0.160
 Compounded annual return (geometric extrapolation)-0.172
 Calmar ratio (compounded annual return / max draw down)-0.513
 Compounded annual return / average of 25% largest draw downs-0.513
 Compounded annual return / Expected Shortfall lognormal-8.126
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 predictor0.691
 Mean of criterion-0.044
 SD of predictor0.293
 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 predictor0.648
 Mean of criterion-0.044
 SD of predictor0.292
 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)-5555758831844097.000
 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)65293025186600569238916937285632.000
 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