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
 Mean0.382
 SD0.737
 Sharpe ratio (Glass type estimate) 0.518
 Sharpe ratio (Hedges UMVUE)0.505
 df30.000
 t0.832
 p0.206
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.713
 Upperbound of 95% confidence interval for Sharpe Ratio1.740
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.722
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.731
Statistics related to Sortino ratio
 Sortino ratio0.903
 Upside Potential Ratio2.713
 Upside part of mean1.146
 Downside part of mean-0.765
 Upside SD0.600
 Downside SD0.423
 N nonnegative terms17.000
 N negative terms14.000
Statistics related to linear regression on benchmark
 N of observations31.000
 Mean of predictor0.154
 Mean of criterion0.382
 SD of predictor0.108
 SD of criterion0.737
 Covariance0.010
 r0.130
 b (slope, estimate of beta)0.891
 a (intercept, estimate of alpha)0.245
 Mean Square Error0.553
 DF error29.000
 t(b)0.707
 p(b)0.243
 t(a)0.488
 p(a)0.314
 Lowerbound of 95% confidence interval for beta-1.687
 Upperbound of 95% confidence interval for beta3.469
 Lowerbound of 95% confidence interval for alpha-0.781
 Upperbound of 95% confidence interval for alpha1.271
 Treynor index (mean / b)0.428
 Jensen alpha (a)0.245
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.129
 SD0.716
 Sharpe ratio (Glass type estimate) 0.181
 Sharpe ratio (Hedges UMVUE)0.176
 df30.000
 t0.290
 p0.387
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.041
 Upperbound of 95% confidence interval for Sharpe Ratio1.400
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.044
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.396
Statistics related to Sortino ratio
 Sortino ratio0.261
 Upside Potential Ratio2.020
 Upside part of mean1.001
 Downside part of mean-0.872
 Upside SD0.501
 Downside SD0.496
 N nonnegative terms17.000
 N negative terms14.000
Statistics related to linear regression on benchmark
 N of observations31.000
 Mean of predictor0.147
 Mean of criterion0.129
 SD of predictor0.107
 SD of criterion0.716
 Covariance0.008
 r0.102
 b (slope, estimate of beta)0.684
 a (intercept, estimate of alpha)0.029
 Mean Square Error0.525
 DF error29.000
 t(b)0.551
 p(b)0.293
 t(a)0.060
 p(a)0.476
 Lowerbound of 95% confidence interval for beta-1.853
 Upperbound of 95% confidence interval for beta3.221
 Lowerbound of 95% confidence interval for alpha-0.965
 Upperbound of 95% confidence interval for alpha1.023
 Treynor index (mean / b)0.189
 Jensen alpha (a)0.029
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.280
 Expected Shortfall on VaR0.338
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.139
 Expected Shortfall on VaR0.265
ORDER STATISTICS
Quartiles of return rates
 Number of observations31.000
 Minimum0.633
 Quartile 10.849
 Median1.014
 Quartile 31.171
 Maximum1.667
 Mean of quarter 10.786
 Mean of quarter 20.976
 Mean of quarter 31.088
 Mean of quarter 41.298
 Inter Quartile Range0.322
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.032
 Mean of outliers high1.667
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.414
 VaR(95%) (moments method)0.252
 Expected Shortfall (moments method)0.404
 Extreme Value Index (regression method)1.149
 VaR(95%) (regression method)0.204
 Expected Shortfall (regression method)NA
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)0.219
 Compounded annual return (geometric extrapolation)0.189
 Calmar ratio (compounded annual return / max draw down)0.246
 Compounded annual return / average of 25% largest draw downs0.246
 Compounded annual return / Expected Shortfall lognormal0.560
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.305
 SD0.633
 Sharpe ratio (Glass type estimate) 0.481
 Sharpe ratio (Hedges UMVUE)0.481
 df916.000
 t0.786
 p0.216
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.719
 Upperbound of 95% confidence interval for Sharpe Ratio1.682
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.720
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.682
Statistics related to Sortino ratio
 Sortino ratio0.843
 Upside Potential Ratio7.431
 Upside part of mean2.685
 Downside part of mean-2.380
 Upside SD0.520
 Downside SD0.361
 N nonnegative terms371.000
 N negative terms546.000
Statistics related to linear regression on benchmark
 N of observations917.000
 Mean of predictor0.157
 Mean of criterion0.305
 SD of predictor0.127
 SD of criterion0.633
 Covariance0.008
 r0.101
 b (slope, estimate of beta)0.500
 a (intercept, estimate of alpha)0.226
 Mean Square Error0.397
 DF error915.000
 t(b)3.057
 p(b)0.001
 t(a)0.585
 p(a)0.279
 Lowerbound of 95% confidence interval for beta0.179
 Upperbound of 95% confidence interval for beta0.821
 Lowerbound of 95% confidence interval for alpha-0.533
 Upperbound of 95% confidence interval for alpha0.985
 Treynor index (mean / b)0.609
 Jensen alpha (a)0.226
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.124
 SD0.589
 Sharpe ratio (Glass type estimate) 0.210
 Sharpe ratio (Hedges UMVUE)0.210
 df916.000
 t0.344
 p0.366
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.990
 Upperbound of 95% confidence interval for Sharpe Ratio1.411
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.990
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.411
Statistics related to Sortino ratio
 Sortino ratio0.324
 Upside Potential Ratio6.727
 Upside part of mean2.574
 Downside part of mean-2.450
 Upside SD0.448
 Downside SD0.383
 N nonnegative terms371.000
 N negative terms546.000
Statistics related to linear regression on benchmark
 N of observations917.000
 Mean of predictor0.149
 Mean of criterion0.124
 SD of predictor0.127
 SD of criterion0.589
 Covariance0.008
 r0.101
 b (slope, estimate of beta)0.466
 a (intercept, estimate of alpha)0.055
 Mean Square Error0.344
 DF error915.000
 t(b)3.056
 p(b)0.001
 t(a)0.152
 p(a)0.440
 Lowerbound of 95% confidence interval for beta0.167
 Upperbound of 95% confidence interval for beta0.765
 Lowerbound of 95% confidence interval for alpha-0.652
 Upperbound of 95% confidence interval for alpha0.761
 Treynor index (mean / b)0.266
 Jensen alpha (a)0.055
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.051
 Expected Shortfall on VaR0.063
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.017
 Expected Shortfall on VaR0.037
ORDER STATISTICS
Quartiles of return rates
 Number of observations917.000
 Minimum0.762
 Quartile 10.996
 Median1.000
 Quartile 31.008
 Maximum1.591
 Mean of quarter 10.973
 Mean of quarter 20.999
 Mean of quarter 31.002
 Mean of quarter 41.029
 Inter Quartile Range0.012
 Number outliers low99.000
 Percentage of outliers low0.108
 Mean of outliers low0.953
 Number of outliers high80.000
 Percentage of outliers high0.087
 Mean of outliers high1.056
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.474
 VaR(95%) (moments method)0.019
 Expected Shortfall (moments method)0.045
 Extreme Value Index (regression method)0.290
 VaR(95%) (regression method)0.024
 Expected Shortfall (regression method)0.045
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)0.212
 Compounded annual return (geometric extrapolation)0.183
 Calmar ratio (compounded annual return / max draw down)0.232
 Compounded annual return / average of 25% largest draw downs0.903
 Compounded annual return / Expected Shortfall lognormal2.902
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.305
 SD0.562
 Sharpe ratio (Glass type estimate) 0.542
 Sharpe ratio (Hedges UMVUE)0.540
 df171.000
 t0.383
 p0.481
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.231
 Upperbound of 95% confidence interval for Sharpe Ratio3.314
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.232
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.312
Statistics related to Sortino ratio
 Sortino ratio1.631
 Upside Potential Ratio4.883
 Upside part of mean0.912
 Downside part of mean-0.607
 Upside SD0.529
 Downside SD0.187
 N nonnegative terms18.000
 N negative terms154.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.201
 Mean of criterion0.305
 SD of predictor0.162
 SD of criterion0.562
 Covariance0.009
 r0.101
 b (slope, estimate of beta)0.350
 a (intercept, estimate of alpha)0.235
 Mean Square Error0.314
 DF error170.000
 t(b)1.323
 p(b)0.450
 t(a)0.295
 p(a)0.489
 Lowerbound of 95% confidence interval for beta-0.172
 Upperbound of 95% confidence interval for beta0.872
 Lowerbound of 95% confidence interval for alpha-1.334
 Upperbound of 95% confidence interval for alpha1.804
 Treynor index (mean / b)0.871
 Jensen alpha (a)0.235
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.174
 SD0.492
 Sharpe ratio (Glass type estimate) 0.353
 Sharpe ratio (Hedges UMVUE)0.351
 df171.000
 t0.249
 p0.488
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.420
 Upperbound of 95% confidence interval for Sharpe Ratio3.124
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.421
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.123
Statistics related to Sortino ratio
 Sortino ratio0.885
 Upside Potential Ratio4.079
 Upside part of mean0.799
 Downside part of mean-0.626
 Upside SD0.450
 Downside SD0.196
 N nonnegative terms18.000
 N negative terms154.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.188
 Mean of criterion0.174
 SD of predictor0.162
 SD of criterion0.492
 Covariance0.009
 r0.107
 b (slope, estimate of beta)0.326
 a (intercept, estimate of alpha)0.112
 Mean Square Error0.241
 DF error170.000
 t(b)1.406
 p(b)0.446
 t(a)0.162
 p(a)0.494
 Lowerbound of 95% confidence interval for beta-0.132
 Upperbound of 95% confidence interval for beta0.785
 Lowerbound of 95% confidence interval for alpha-1.260
 Upperbound of 95% confidence interval for alpha1.484
 Treynor index (mean / b)0.532
 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%)0.042
 Expected Shortfall on VaR0.053
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.013
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.373
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.011
 Inter Quartile Range0.000
 Number outliers low12.000
 Percentage of outliers low0.070
 Mean of outliers low0.976
 Number of outliers high19.000
 Percentage of outliers high0.110
 Mean of outliers high1.024
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)0.463
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.029
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.019
 Quartile 10.069
 Median0.119
 Quartile 30.169
 Maximum0.219
 Mean of quarter 10.019
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.219
 Inter Quartile Range0.100
 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)0.230
 Compounded annual return (geometric extrapolation)0.243
 Calmar ratio (compounded annual return / max draw down)1.111
 Compounded annual return / average of 25% largest draw downs1.111
 Compounded annual return / Expected Shortfall lognormal4.611