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Advanced Statistics: Green Dog

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
 Mean0.427
 SD0.776
 Sharpe ratio (Glass type estimate) 0.551
 Sharpe ratio (Hedges UMVUE)0.535
 df27.000
 t0.841
 p0.204
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.746
 Upperbound of 95% confidence interval for Sharpe Ratio1.837
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.756
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.826
Statistics related to Sortino ratio
 Sortino ratio0.961
 Upside Potential Ratio2.855
 Upside part of mean1.269
 Downside part of mean-0.842
 Upside SD0.631
 Downside SD0.445
 N nonnegative terms17.000
 N negative terms11.000
Statistics related to linear regression on benchmark
 N of observations28.000
 Mean of predictor0.156
 Mean of criterion0.427
 SD of predictor0.112
 SD of criterion0.776
 Covariance0.011
 r0.131
 b (slope, estimate of beta)0.914
 a (intercept, estimate of alpha)0.285
 Mean Square Error0.615
 DF error26.000
 t(b)0.676
 p(b)0.253
 t(a)0.513
 p(a)0.306
 Lowerbound of 95% confidence interval for beta-1.866
 Upperbound of 95% confidence interval for beta3.694
 Lowerbound of 95% confidence interval for alpha-0.857
 Upperbound of 95% confidence interval for alpha1.426
 Treynor index (mean / b)0.468
 Jensen alpha (a)0.285
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.148
 SD0.754
 Sharpe ratio (Glass type estimate) 0.196
 Sharpe ratio (Hedges UMVUE)0.191
 df27.000
 t0.300
 p0.383
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.090
 Upperbound of 95% confidence interval for Sharpe Ratio1.478
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.093
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.475
Statistics related to Sortino ratio
 Sortino ratio0.284
 Upside Potential Ratio2.125
 Upside part of mean1.109
 Downside part of mean-0.961
 Upside SD0.528
 Downside SD0.522
 N nonnegative terms17.000
 N negative terms11.000
Statistics related to linear regression on benchmark
 N of observations28.000
 Mean of predictor0.149
 Mean of criterion0.148
 SD of predictor0.110
 SD of criterion0.754
 Covariance0.009
 r0.103
 b (slope, estimate of beta)0.705
 a (intercept, estimate of alpha)0.043
 Mean Square Error0.585
 DF error26.000
 t(b)0.529
 p(b)0.301
 t(a)0.080
 p(a)0.468
 Lowerbound of 95% confidence interval for beta-2.034
 Upperbound of 95% confidence interval for beta3.444
 Lowerbound of 95% confidence interval for alpha-1.064
 Upperbound of 95% confidence interval for alpha1.150
 Treynor index (mean / b)0.210
 Jensen alpha (a)0.043
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.292
 Expected Shortfall on VaR0.352
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.141
 Expected Shortfall on VaR0.267
ORDER STATISTICS
Quartiles of return rates
 Number of observations28.000
 Minimum0.633
 Quartile 10.848
 Median1.027
 Quartile 31.194
 Maximum1.667
 Mean of quarter 10.778
 Mean of quarter 20.953
 Mean of quarter 31.113
 Mean of quarter 41.313
 Inter Quartile Range0.346
 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)0.336
 VaR(95%) (moments method)0.256
 Expected Shortfall (moments method)0.392
 Extreme Value Index (regression method)0.629
 VaR(95%) (regression method)0.220
 Expected Shortfall (regression method)0.403
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.006
 Quartile 10.143
 Median0.279
 Quartile 30.525
 Maximum0.771
 Mean of quarter 10.006
 Mean of quarter 20.279
 Mean of quarter 3NA
 Mean of quarter 40.771
 Inter Quartile Range0.382
 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)0.242
 Compounded annual return (geometric extrapolation)0.212
 Calmar ratio (compounded annual return / max draw down)0.275
 Compounded annual return / average of 25% largest draw downs0.275
 Compounded annual return / Expected Shortfall lognormal0.601
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.347
 SD0.671
 Sharpe ratio (Glass type estimate) 0.518
 Sharpe ratio (Hedges UMVUE)0.518
 df816.000
 t0.798
 p0.212
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.754
 Upperbound of 95% confidence interval for Sharpe Ratio1.790
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.755
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.790
Statistics related to Sortino ratio
 Sortino ratio0.908
 Upside Potential Ratio7.873
 Upside part of mean3.014
 Downside part of mean-2.666
 Upside SD0.550
 Downside SD0.383
 N nonnegative terms371.000
 N negative terms446.000
Statistics related to linear regression on benchmark
 N of observations817.000
 Mean of predictor0.152
 Mean of criterion0.347
 SD of predictor0.118
 SD of criterion0.671
 Covariance0.009
 r0.115
 b (slope, estimate of beta)0.656
 a (intercept, estimate of alpha)0.248
 Mean Square Error0.444
 DF error815.000
 t(b)3.310
 p(b)0.000
 t(a)0.572
 p(a)0.284
 Lowerbound of 95% confidence interval for beta0.267
 Upperbound of 95% confidence interval for beta1.044
 Lowerbound of 95% confidence interval for alpha-0.603
 Upperbound of 95% confidence interval for alpha1.099
 Treynor index (mean / b)0.530
 Jensen alpha (a)0.248
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.145
 SD0.624
 Sharpe ratio (Glass type estimate) 0.232
 Sharpe ratio (Hedges UMVUE)0.231
 df816.000
 t0.357
 p0.361
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.040
 Upperbound of 95% confidence interval for Sharpe Ratio1.503
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.041
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.503
Statistics related to Sortino ratio
 Sortino ratio0.357
 Upside Potential Ratio7.127
 Upside part of mean2.890
 Downside part of mean-2.745
 Upside SD0.474
 Downside SD0.405
 N nonnegative terms371.000
 N negative terms446.000
Statistics related to linear regression on benchmark
 N of observations817.000
 Mean of predictor0.145
 Mean of criterion0.145
 SD of predictor0.118
 SD of criterion0.624
 Covariance0.008
 r0.115
 b (slope, estimate of beta)0.609
 a (intercept, estimate of alpha)0.056
 Mean Square Error0.385
 DF error815.000
 t(b)3.304
 p(b)0.000
 t(a)0.140
 p(a)0.445
 Lowerbound of 95% confidence interval for beta0.247
 Upperbound of 95% confidence interval for beta0.971
 Lowerbound of 95% confidence interval for alpha-0.736
 Upperbound of 95% confidence interval for alpha0.849
 Treynor index (mean / b)0.237
 Jensen alpha (a)0.056
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.053
 Expected Shortfall on VaR0.067
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.019
 Expected Shortfall on VaR0.040
ORDER STATISTICS
Quartiles of return rates
 Number of observations817.000
 Minimum0.762
 Quartile 10.994
 Median1.000
 Quartile 31.010
 Maximum1.591
 Mean of quarter 10.971
 Mean of quarter 20.999
 Mean of quarter 31.003
 Mean of quarter 41.032
 Inter Quartile Range0.016
 Number outliers low69.000
 Percentage of outliers low0.084
 Mean of outliers low0.943
 Number of outliers high52.000
 Percentage of outliers high0.064
 Mean of outliers high1.070
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.394
 VaR(95%) (moments method)0.023
 Expected Shortfall (moments method)0.047
 Extreme Value Index (regression method)0.276
 VaR(95%) (regression method)0.027
 Expected Shortfall (regression method)0.048
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations32.000
 Minimum0.000
 Quartile 10.007
 Median0.026
 Quartile 30.049
 Maximum0.788
 Mean of quarter 10.002
 Mean of quarter 20.018
 Mean of quarter 30.035
 Mean of quarter 40.203
 Inter Quartile Range0.042
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.094
 Mean of outliers high0.427
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.868
 VaR(95%) (moments method)0.204
 Expected Shortfall (moments method)1.609
 Extreme Value Index (regression method)1.426
 VaR(95%) (regression method)0.192
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.238
 Compounded annual return (geometric extrapolation)0.208
 Calmar ratio (compounded annual return / max draw down)0.263
 Compounded annual return / average of 25% largest draw downs1.025
 Compounded annual return / Expected Shortfall lognormal3.115
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.544
 SD1.133
 Sharpe ratio (Glass type estimate) 0.480
 Sharpe ratio (Hedges UMVUE)0.478
 df171.000
 t0.339
 p0.483
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.293
 Upperbound of 95% confidence interval for Sharpe Ratio3.252
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.294
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.250
Statistics related to Sortino ratio
 Sortino ratio1.100
 Upside Potential Ratio6.988
 Upside part of mean3.455
 Downside part of mean-2.911
 Upside SD1.016
 Downside SD0.494
 N nonnegative terms64.000
 N negative terms108.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.188
 Mean of criterion0.544
 SD of predictor0.111
 SD of criterion1.133
 Covariance0.017
 r0.138
 b (slope, estimate of beta)1.409
 a (intercept, estimate of alpha)0.279
 Mean Square Error1.266
 DF error170.000
 t(b)1.822
 p(b)0.431
 t(a)0.175
 p(a)0.493
 Lowerbound of 95% confidence interval for beta-0.117
 Upperbound of 95% confidence interval for beta2.935
 Lowerbound of 95% confidence interval for alpha-2.875
 Upperbound of 95% confidence interval for alpha3.433
 Treynor index (mean / b)0.386
 Jensen alpha (a)0.279
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.015
 SD0.990
 Sharpe ratio (Glass type estimate) 0.015
 Sharpe ratio (Hedges UMVUE)0.015
 df171.000
 t0.011
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.757
 Upperbound of 95% confidence interval for Sharpe Ratio2.787
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.757
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.787
Statistics related to Sortino ratio
 Sortino ratio0.028
 Upside Potential Ratio5.695
 Upside part of mean3.062
 Downside part of mean-3.047
 Upside SD0.827
 Downside SD0.538
 N nonnegative terms64.000
 N negative terms108.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.181
 Mean of criterion0.015
 SD of predictor0.111
 SD of criterion0.990
 Covariance0.014
 r0.131
 b (slope, estimate of beta)1.161
 a (intercept, estimate of alpha)-0.195
 Mean Square Error0.968
 DF error170.000
 t(b)1.718
 p(b)0.435
 t(a)-0.140
 p(a)0.505
 Lowerbound of 95% confidence interval for beta-0.173
 Upperbound of 95% confidence interval for beta2.494
 Lowerbound of 95% confidence interval for alpha-2.953
 Upperbound of 95% confidence interval for alpha2.562
 Treynor index (mean / b)0.013
 Jensen alpha (a)-0.195
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.084
 Expected Shortfall on VaR0.104
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.048
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.762
 Quartile 10.999
 Median1.000
 Quartile 31.002
 Maximum1.591
 Mean of quarter 10.966
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.040
 Inter Quartile Range0.003
 Number outliers low34.000
 Percentage of outliers low0.198
 Mean of outliers low0.958
 Number of outliers high28.000
 Percentage of outliers high0.163
 Mean of outliers high1.059
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.561
 VaR(95%) (moments method)0.010
 Expected Shortfall (moments method)0.030
 Extreme Value Index (regression method)0.350
 VaR(95%) (regression method)0.031
 Expected Shortfall (regression method)0.067
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.516
 Quartile 10.516
 Median0.516
 Quartile 30.516
 Maximum0.516
 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)0.060
 Compounded annual return (geometric extrapolation)0.061
 Calmar ratio (compounded annual return / max draw down)0.118
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.586