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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
 Mean0.302
 SD0.767
 Sharpe ratio (Glass type estimate) 0.394
 Sharpe ratio (Hedges UMVUE)0.383
 df26.000
 t0.591
 p0.280
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.920
 Upperbound of 95% confidence interval for Sharpe Ratio1.702
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.928
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.694
Statistics related to Sortino ratio
 Sortino ratio0.668
 Upside Potential Ratio2.596
 Upside part of mean1.175
 Downside part of mean-0.873
 Upside SD0.607
 Downside SD0.453
 N nonnegative terms16.000
 N negative terms11.000
Statistics related to linear regression on benchmark
 N of observations27.000
 Mean of predictor0.125
 Mean of criterion0.302
 SD of predictor0.103
 SD of criterion0.767
 Covariance0.002
 r0.031
 b (slope, estimate of beta)0.228
 a (intercept, estimate of alpha)0.274
 Mean Square Error0.611
 DF error25.000
 t(b)0.153
 p(b)0.440
 t(a)0.495
 p(a)0.313
 Lowerbound of 95% confidence interval for beta-2.838
 Upperbound of 95% confidence interval for beta3.294
 Lowerbound of 95% confidence interval for alpha-0.866
 Upperbound of 95% confidence interval for alpha1.413
 Treynor index (mean / b)1.325
 Jensen alpha (a)0.274
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.031
 SD0.747
 Sharpe ratio (Glass type estimate) 0.042
 Sharpe ratio (Hedges UMVUE)0.041
 df26.000
 t0.063
 p0.475
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.265
 Upperbound of 95% confidence interval for Sharpe Ratio1.348
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.266
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.348
Statistics related to Sortino ratio
 Sortino ratio0.059
 Upside Potential Ratio1.935
 Upside part of mean1.028
 Downside part of mean-0.996
 Upside SD0.505
 Downside SD0.531
 N nonnegative terms16.000
 N negative terms11.000
Statistics related to linear regression on benchmark
 N of observations27.000
 Mean of predictor0.119
 Mean of criterion0.031
 SD of predictor0.103
 SD of criterion0.747
 Covariance0.001
 r0.007
 b (slope, estimate of beta)0.051
 a (intercept, estimate of alpha)0.025
 Mean Square Error0.580
 DF error25.000
 t(b)0.035
 p(b)0.486
 t(a)0.047
 p(a)0.481
 Lowerbound of 95% confidence interval for beta-2.948
 Upperbound of 95% confidence interval for beta3.050
 Lowerbound of 95% confidence interval for alpha-1.080
 Upperbound of 95% confidence interval for alpha1.131
 Treynor index (mean / b)0.615
 Jensen alpha (a)0.025
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.297
 Expected Shortfall on VaR0.355
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.150
 Expected Shortfall on VaR0.279
ORDER STATISTICS
Quartiles of return rates
 Number of observations27.000
 Minimum0.633
 Quartile 10.848
 Median1.015
 Quartile 31.171
 Maximum1.667
 Mean of quarter 10.778
 Mean of quarter 20.953
 Mean of quarter 31.100
 Mean of quarter 41.294
 Inter Quartile Range0.323
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.037
 Mean of outliers high1.667
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.336
 VaR(95%) (moments method)0.260
 Expected Shortfall (moments method)0.397
 Extreme Value Index (regression method)0.629
 VaR(95%) (regression method)0.222
 Expected Shortfall (regression method)0.409
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)0.082
 Compounded annual return (geometric extrapolation)0.078
 Calmar ratio (compounded annual return / max draw down)0.102
 Compounded annual return / average of 25% largest draw downs0.102
 Compounded annual return / Expected Shortfall lognormal0.220
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.202
 SD0.641
 Sharpe ratio (Glass type estimate) 0.315
 Sharpe ratio (Hedges UMVUE)0.315
 df777.000
 t0.474
 p0.318
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.988
 Upperbound of 95% confidence interval for Sharpe Ratio1.619
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.988
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.618
Statistics related to Sortino ratio
 Sortino ratio0.515
 Upside Potential Ratio7.643
 Upside part of mean2.998
 Downside part of mean-2.796
 Upside SD0.507
 Downside SD0.392
 N nonnegative terms369.000
 N negative terms409.000
Statistics related to linear regression on benchmark
 N of observations778.000
 Mean of predictor0.137
 Mean of criterion0.202
 SD of predictor0.119
 SD of criterion0.641
 Covariance0.008
 r0.110
 b (slope, estimate of beta)0.592
 a (intercept, estimate of alpha)0.121
 Mean Square Error0.407
 DF error776.000
 t(b)3.071
 p(b)0.001
 t(a)0.285
 p(a)0.388
 Lowerbound of 95% confidence interval for beta0.214
 Upperbound of 95% confidence interval for beta0.970
 Lowerbound of 95% confidence interval for alpha-0.713
 Upperbound of 95% confidence interval for alpha0.955
 Treynor index (mean / b)0.342
 Jensen alpha (a)0.121
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.014
 SD0.604
 Sharpe ratio (Glass type estimate) 0.023
 Sharpe ratio (Hedges UMVUE)0.023
 df777.000
 t0.035
 p0.486
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.280
 Upperbound of 95% confidence interval for Sharpe Ratio1.326
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.280
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.326
Statistics related to Sortino ratio
 Sortino ratio0.033
 Upside Potential Ratio6.962
 Upside part of mean2.893
 Downside part of mean-2.879
 Upside SD0.438
 Downside SD0.415
 N nonnegative terms369.000
 N negative terms409.000
Statistics related to linear regression on benchmark
 N of observations778.000
 Mean of predictor0.130
 Mean of criterion0.014
 SD of predictor0.119
 SD of criterion0.604
 Covariance0.008
 r0.109
 b (slope, estimate of beta)0.557
 a (intercept, estimate of alpha)-0.058
 Mean Square Error0.361
 DF error776.000
 t(b)3.064
 p(b)0.001
 t(a)-0.146
 p(a)0.558
 Lowerbound of 95% confidence interval for beta0.200
 Upperbound of 95% confidence interval for beta0.913
 Lowerbound of 95% confidence interval for alpha-0.844
 Upperbound of 95% confidence interval for alpha0.727
 Treynor index (mean / b)0.025
 Jensen alpha (a)-0.058
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.052
 Expected Shortfall on VaR0.065
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 observations778.000
 Minimum0.762
 Quartile 10.993
 Median1.000
 Quartile 31.011
 Maximum1.591
 Mean of quarter 10.970
 Mean of quarter 20.998
 Mean of quarter 31.004
 Mean of quarter 41.031
 Inter Quartile Range0.017
 Number outliers low60.000
 Percentage of outliers low0.077
 Mean of outliers low0.939
 Number of outliers high45.000
 Percentage of outliers high0.058
 Mean of outliers high1.068
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.274
 VaR(95%) (moments method)0.023
 Expected Shortfall (moments method)0.040
 Extreme Value Index (regression method)0.237
 VaR(95%) (regression method)0.028
 Expected Shortfall (regression method)0.049
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)0.062
 Compounded annual return (geometric extrapolation)0.060
 Calmar ratio (compounded annual return / max draw down)0.076
 Compounded annual return / average of 25% largest draw downs0.294
 Compounded annual return / Expected Shortfall lognormal0.919
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.732
 SD1.079
 Sharpe ratio (Glass type estimate) -0.679
 Sharpe ratio (Hedges UMVUE)-0.676
 df171.000
 t-0.480
 p0.523
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.450
 Upperbound of 95% confidence interval for Sharpe Ratio2.095
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.448
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.097
Statistics related to Sortino ratio
 Sortino ratio-1.183
 Upside Potential Ratio5.643
 Upside part of mean3.495
 Downside part of mean-4.227
 Upside SD0.881
 Downside SD0.619
 N nonnegative terms85.000
 N negative terms87.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.150
 Mean of criterion-0.732
 SD of predictor0.116
 SD of criterion1.079
 Covariance0.016
 r0.128
 b (slope, estimate of beta)1.191
 a (intercept, estimate of alpha)-0.911
 Mean Square Error1.152
 DF error170.000
 t(b)1.687
 p(b)0.436
 t(a)-0.599
 p(a)0.523
 Lowerbound of 95% confidence interval for beta-0.203
 Upperbound of 95% confidence interval for beta2.584
 Lowerbound of 95% confidence interval for alpha-3.915
 Upperbound of 95% confidence interval for alpha2.092
 Treynor index (mean / b)-0.615
 Jensen alpha (a)-0.911
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.236
 SD0.977
 Sharpe ratio (Glass type estimate) -1.264
 Sharpe ratio (Hedges UMVUE)-1.259
 df171.000
 t-0.894
 p0.543
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.038
 Upperbound of 95% confidence interval for Sharpe Ratio1.513
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.034
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.516
Statistics related to Sortino ratio
 Sortino ratio-1.843
 Upside Potential Ratio4.778
 Upside part of mean3.204
 Downside part of mean-4.440
 Upside SD0.710
 Downside SD0.670
 N nonnegative terms85.000
 N negative terms87.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.144
 Mean of criterion-1.236
 SD of predictor0.116
 SD of criterion0.977
 Covariance0.014
 r0.124
 b (slope, estimate of beta)1.043
 a (intercept, estimate of alpha)-1.386
 Mean Square Error0.946
 DF error170.000
 t(b)1.632
 p(b)0.438
 t(a)-1.005
 p(a)0.538
 Lowerbound of 95% confidence interval for beta-0.219
 Upperbound of 95% confidence interval for beta2.306
 Lowerbound of 95% confidence interval for alpha-4.107
 Upperbound of 95% confidence interval for alpha1.336
 Treynor index (mean / b)-1.184
 Jensen alpha (a)-1.386
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.086
 Expected Shortfall on VaR0.106
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.028
 Expected Shortfall on VaR0.060
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.762
 Quartile 10.994
 Median1.000
 Quartile 31.007
 Maximum1.591
 Mean of quarter 10.952
 Mean of quarter 20.999
 Mean of quarter 31.003
 Mean of quarter 41.038
 Inter Quartile Range0.013
 Number outliers low28.000
 Percentage of outliers low0.163
 Mean of outliers low0.934
 Number of outliers high16.000
 Percentage of outliers high0.093
 Mean of outliers high1.076
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.025
 VaR(95%) (moments method)0.024
 Expected Shortfall (moments method)0.036
 Extreme Value Index (regression method)0.091
 VaR(95%) (regression method)0.046
 Expected Shortfall (regression method)0.075
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.625
 Quartile 10.625
 Median0.625
 Quartile 30.625
 Maximum0.625
 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)-0.898
 Compounded annual return (geometric extrapolation)-0.696
 Calmar ratio (compounded annual return / max draw down)-1.114
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-6.566