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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
 Mean0.343
 SD0.667
 Sharpe ratio (Glass type estimate) 0.514
 Sharpe ratio (Hedges UMVUE)0.514
 df826.000
 t0.797
 p0.213
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.750
 Upperbound of 95% confidence interval for Sharpe Ratio1.778
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.751
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.778
Statistics related to Sortino ratio
 Sortino ratio0.901
 Upside Potential Ratio7.825
 Upside part of mean2.977
 Downside part of mean-2.635
 Upside SD0.547
 Downside SD0.380
 N nonnegative terms371.000
 N negative terms456.000
Statistics related to linear regression on benchmark
 N of observations827.000
 Mean of predictor0.150
 Mean of criterion0.343
 SD of predictor0.119
 SD of criterion0.667
 Covariance0.009
 r0.114
 b (slope, estimate of beta)0.640
 a (intercept, estimate of alpha)0.247
 Mean Square Error0.439
 DF error825.000
 t(b)3.292
 p(b)0.001
 t(a)0.576
 p(a)0.283
 Lowerbound of 95% confidence interval for beta0.259
 Upperbound of 95% confidence interval for beta1.022
 Lowerbound of 95% confidence interval for alpha-0.594
 Upperbound of 95% confidence interval for alpha1.087
 Treynor index (mean / b)0.535
 Jensen alpha (a)0.247
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.142
 SD0.621
 Sharpe ratio (Glass type estimate) 0.229
 Sharpe ratio (Hedges UMVUE)0.229
 df826.000
 t0.355
 p0.361
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.035
 Upperbound of 95% confidence interval for Sharpe Ratio1.493
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.035
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.493
Statistics related to Sortino ratio
 Sortino ratio0.353
 Upside Potential Ratio7.083
 Upside part of mean2.855
 Downside part of mean-2.712
 Upside SD0.471
 Downside SD0.403
 N nonnegative terms371.000
 N negative terms456.000
Statistics related to linear regression on benchmark
 N of observations827.000
 Mean of predictor0.143
 Mean of criterion0.142
 SD of predictor0.119
 SD of criterion0.621
 Covariance0.008
 r0.114
 b (slope, estimate of beta)0.595
 a (intercept, estimate of alpha)0.057
 Mean Square Error0.381
 DF error825.000
 t(b)3.285
 p(b)0.001
 t(a)0.144
 p(a)0.443
 Lowerbound of 95% confidence interval for beta0.239
 Upperbound of 95% confidence interval for beta0.951
 Lowerbound of 95% confidence interval for alpha-0.725
 Upperbound of 95% confidence interval for alpha0.840
 Treynor index (mean / b)0.239
 Jensen alpha (a)0.057
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 VaR0.066
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.039
ORDER STATISTICS
Quartiles of return rates
 Number of observations827.000
 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 low0.083
 Mean of outliers low0.943
 Number of outliers high54.000
 Percentage of outliers high0.065
 Mean of outliers high1.069
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.380
 VaR(95%) (moments method)0.022
 Expected Shortfall (moments method)0.045
 Extreme Value Index (regression method)0.269
 VaR(95%) (regression method)0.026
 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)0.235
 Compounded annual return (geometric extrapolation)0.205
 Calmar ratio (compounded annual return / max draw down)0.260
 Compounded annual return / average of 25% largest draw downs1.011
 Compounded annual return / Expected Shortfall lognormal3.092
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean1.149
 SD1.073
 Sharpe ratio (Glass type estimate) 1.070
 Sharpe ratio (Hedges UMVUE)1.065
 df171.000
 t0.757
 p0.463
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.706
 Upperbound of 95% confidence interval for Sharpe Ratio3.843
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.709
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.840
Statistics related to Sortino ratio
 Sortino ratio3.313
 Upside Potential Ratio9.654
 Upside part of mean3.347
 Downside part of mean-2.199
 Upside SD1.014
 Downside SD0.347
 N nonnegative terms60.000
 N negative terms112.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.181
 Mean of criterion1.149
 SD of predictor0.117
 SD of criterion1.073
 Covariance0.019
 r0.147
 b (slope, estimate of beta)1.345
 a (intercept, estimate of alpha)0.905
 Mean Square Error1.134
 DF error170.000
 t(b)1.939
 p(b)0.426
 t(a)0.599
 p(a)0.477
 Lowerbound of 95% confidence interval for beta-0.024
 Upperbound of 95% confidence interval for beta2.714
 Lowerbound of 95% confidence interval for alpha-2.078
 Upperbound of 95% confidence interval for alpha3.888
 Treynor index (mean / b)0.854
 Jensen alpha (a)0.905
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.695
 SD0.903
 Sharpe ratio (Glass type estimate) 0.769
 Sharpe ratio (Hedges UMVUE)0.766
 df171.000
 t0.544
 p0.474
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.005
 Upperbound of 95% confidence interval for Sharpe Ratio3.541
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.007
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.539
Statistics related to Sortino ratio
 Sortino ratio1.926
 Upside Potential Ratio8.198
 Upside part of mean2.957
 Downside part of mean-2.262
 Upside SD0.826
 Downside SD0.361
 N nonnegative terms60.000
 N negative terms112.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.174
 Mean of criterion0.695
 SD of predictor0.118
 SD of criterion0.903
 Covariance0.016
 r0.148
 b (slope, estimate of beta)1.135
 a (intercept, estimate of alpha)0.497
 Mean Square Error0.802
 DF error170.000
 t(b)1.949
 p(b)0.426
 t(a)0.391
 p(a)0.485
 Lowerbound of 95% confidence interval for beta-0.014
 Upperbound of 95% confidence interval for beta2.285
 Lowerbound of 95% confidence interval for alpha-2.012
 Upperbound of 95% confidence interval for alpha3.005
 Treynor index (mean / b)0.612
 Jensen alpha (a)0.497
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.075
 Expected Shortfall on VaR0.094
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 observations172.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.002
 Maximum1.591
 Mean of quarter 10.975
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.039
 Inter Quartile Range0.002
 Number outliers low34.000
 Percentage of outliers low0.198
 Mean of outliers low0.968
 Number of outliers high32.000
 Percentage of outliers high0.186
 Mean of outliers high1.051
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.190
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.092
 VaR(95%) (regression method)0.026
 Expected Shortfall (regression method)0.046
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.014
 Quartile 10.128
 Median0.242
 Quartile 30.273
 Maximum0.304
 Mean of quarter 10.014
 Mean of quarter 20.242
 Mean of quarter 3NA
 Mean of quarter 40.304
 Inter Quartile Range0.145
 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)0.894
 Compounded annual return (geometric extrapolation)1.093
 Calmar ratio (compounded annual return / max draw down)3.601
 Compounded annual return / average of 25% largest draw downs3.601
 Compounded annual return / Expected Shortfall lognormal11.684