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
 Mean0.368
 SD0.726
 Sharpe ratio (Glass type estimate) 0.508
 Sharpe ratio (Hedges UMVUE)0.495
 df31.000
 t0.829
 p0.207
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.703
 Upperbound of 95% confidence interval for Sharpe Ratio1.710
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.711
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.702
Statistics related to Sortino ratio
 Sortino ratio0.886
 Upside Potential Ratio2.671
 Upside part of mean1.111
 Downside part of mean-0.742
 Upside SD0.591
 Downside SD0.416
 N nonnegative terms17.000
 N negative terms15.000
Statistics related to linear regression on benchmark
 N of observations32.000
 Mean of predictor0.156
 Mean of criterion0.368
 SD of predictor0.106
 SD of criterion0.726
 Covariance0.010
 r0.129
 b (slope, estimate of beta)0.883
 a (intercept, estimate of alpha)0.231
 Mean Square Error0.535
 DF error30.000
 t(b)0.713
 p(b)0.241
 t(a)0.473
 p(a)0.320
 Lowerbound of 95% confidence interval for beta-1.648
 Upperbound of 95% confidence interval for beta3.414
 Lowerbound of 95% confidence interval for alpha-0.765
 Upperbound of 95% confidence interval for alpha1.227
 Treynor index (mean / b)0.417
 Jensen alpha (a)0.231
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.124
 SD0.704
 Sharpe ratio (Glass type estimate) 0.176
 Sharpe ratio (Hedges UMVUE)0.172
 df31.000
 t0.287
 p0.388
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.026
 Upperbound of 95% confidence interval for Sharpe Ratio1.376
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.029
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.373
Statistics related to Sortino ratio
 Sortino ratio0.254
 Upside Potential Ratio1.988
 Upside part of mean0.970
 Downside part of mean-0.846
 Upside SD0.494
 Downside SD0.488
 N nonnegative terms17.000
 N negative terms15.000
Statistics related to linear regression on benchmark
 N of observations32.000
 Mean of predictor0.149
 Mean of criterion0.124
 SD of predictor0.105
 SD of criterion0.704
 Covariance0.007
 r0.101
 b (slope, estimate of beta)0.680
 a (intercept, estimate of alpha)0.023
 Mean Square Error0.507
 DF error30.000
 t(b)0.558
 p(b)0.291
 t(a)0.048
 p(a)0.481
 Lowerbound of 95% confidence interval for beta-1.810
 Upperbound of 95% confidence interval for beta3.170
 Lowerbound of 95% confidence interval for alpha-0.942
 Upperbound of 95% confidence interval for alpha0.987
 Treynor index (mean / b)0.182
 Jensen alpha (a)0.023
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.277
 Expected Shortfall on VaR0.334
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.138
 Expected Shortfall on VaR0.264
ORDER STATISTICS
Quartiles of return rates
 Number of observations32.000
 Minimum0.633
 Quartile 10.850
 Median1.013
 Quartile 31.162
 Maximum1.667
 Mean of quarter 10.786
 Mean of quarter 20.975
 Mean of quarter 31.079
 Mean of quarter 41.298
 Inter Quartile Range0.312
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.031
 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)0.249
 Expected Shortfall (moments method)0.399
 Extreme Value Index (regression method)1.149
 VaR(95%) (regression method)0.201
 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)0.212
 Compounded annual return (geometric extrapolation)0.183
 Calmar ratio (compounded annual return / max draw down)0.237
 Compounded annual return / average of 25% largest draw downs0.237
 Compounded annual return / Expected Shortfall lognormal0.548
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.301
 SD0.629
 Sharpe ratio (Glass type estimate) 0.478
 Sharpe ratio (Hedges UMVUE)0.477
 df927.000
 t0.785
 p0.216
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.716
 Upperbound of 95% confidence interval for Sharpe Ratio1.671
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.716
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.671
Statistics related to Sortino ratio
 Sortino ratio0.837
 Upside Potential Ratio7.387
 Upside part of mean2.653
 Downside part of mean-2.353
 Upside SD0.517
 Downside SD0.359
 N nonnegative terms371.000
 N negative terms557.000
Statistics related to linear regression on benchmark
 N of observations928.000
 Mean of predictor0.147
 Mean of criterion0.301
 SD of predictor0.128
 SD of criterion0.629
 Covariance0.008
 r0.100
 b (slope, estimate of beta)0.490
 a (intercept, estimate of alpha)0.228
 Mean Square Error0.392
 DF error926.000
 t(b)3.046
 p(b)0.001
 t(a)0.598
 p(a)0.275
 Lowerbound of 95% confidence interval for beta0.174
 Upperbound of 95% confidence interval for beta0.806
 Lowerbound of 95% confidence interval for alpha-0.522
 Upperbound of 95% confidence interval for alpha0.978
 Treynor index (mean / b)0.613
 Jensen alpha (a)0.228
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.122
 SD0.586
 Sharpe ratio (Glass type estimate) 0.208
 Sharpe ratio (Hedges UMVUE)0.208
 df927.000
 t0.342
 p0.366
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.985
 Upperbound of 95% confidence interval for Sharpe Ratio1.402
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.985
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.401
Statistics related to Sortino ratio
 Sortino ratio0.321
 Upside Potential Ratio6.687
 Upside part of mean2.544
 Downside part of mean-2.422
 Upside SD0.445
 Downside SD0.380
 N nonnegative terms371.000
 N negative terms557.000
Statistics related to linear regression on benchmark
 N of observations928.000
 Mean of predictor0.139
 Mean of criterion0.122
 SD of predictor0.128
 SD of criterion0.586
 Covariance0.007
 r0.099
 b (slope, estimate of beta)0.456
 a (intercept, estimate of alpha)0.059
 Mean Square Error0.340
 DF error926.000
 t(b)3.043
 p(b)0.001
 t(a)0.165
 p(a)0.435
 Lowerbound of 95% confidence interval for beta0.162
 Upperbound of 95% confidence interval for beta0.750
 Lowerbound of 95% confidence interval for alpha-0.639
 Upperbound of 95% confidence interval for alpha0.757
 Treynor index (mean / b)0.268
 Jensen alpha (a)0.059
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.050
 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 observations928.000
 Minimum0.762
 Quartile 10.996
 Median1.000
 Quartile 31.007
 Maximum1.591
 Mean of quarter 10.974
 Mean of quarter 20.999
 Mean of quarter 31.002
 Mean of quarter 41.029
 Inter Quartile Range0.011
 Number outliers low100.000
 Percentage of outliers low0.108
 Mean of outliers low0.953
 Number of outliers high87.000
 Percentage of outliers high0.094
 Mean of outliers high1.054
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.465
 VaR(95%) (moments method)0.019
 Expected Shortfall (moments method)0.043
 Extreme Value Index (regression method)0.285
 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)0.209
 Compounded annual return (geometric extrapolation)0.181
 Calmar ratio (compounded annual return / max draw down)0.229
 Compounded annual return / average of 25% largest draw downs0.892
 Compounded annual return / Expected Shortfall lognormal2.881
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.306
 SD0.562
 Sharpe ratio (Glass type estimate) 0.545
 Sharpe ratio (Hedges UMVUE)0.543
 df171.000
 t0.386
 p0.481
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.228
 Upperbound of 95% confidence interval for Sharpe Ratio3.317
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.229
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.315
Statistics related to Sortino ratio
 Sortino ratio1.648
 Upside Potential Ratio4.719
 Upside part of mean0.877
 Downside part of mean-0.571
 Upside SD0.528
 Downside SD0.186
 N nonnegative terms12.000
 N negative terms160.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.196
 Mean of criterion0.306
 SD of predictor0.167
 SD of criterion0.562
 Covariance0.009
 r0.098
 b (slope, estimate of beta)0.329
 a (intercept, estimate of alpha)0.242
 Mean Square Error0.314
 DF error170.000
 t(b)1.278
 p(b)0.451
 t(a)0.305
 p(a)0.488
 Lowerbound of 95% confidence interval for beta-0.179
 Upperbound of 95% confidence interval for beta0.837
 Lowerbound of 95% confidence interval for alpha-1.326
 Upperbound of 95% confidence interval for alpha1.810
 Treynor index (mean / b)0.931
 Jensen alpha (a)0.242
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.175
 SD0.491
 Sharpe ratio (Glass type estimate) 0.357
 Sharpe ratio (Hedges UMVUE)0.355
 df171.000
 t0.252
 p0.488
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.416
 Upperbound of 95% confidence interval for Sharpe Ratio3.128
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.417
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.127
Statistics related to Sortino ratio
 Sortino ratio0.899
 Upside Potential Ratio3.919
 Upside part of mean0.765
 Downside part of mean-0.589
 Upside SD0.449
 Downside SD0.195
 N nonnegative terms12.000
 N negative terms160.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.182
 Mean of criterion0.175
 SD of predictor0.166
 SD of criterion0.491
 Covariance0.008
 r0.104
 b (slope, estimate of beta)0.306
 a (intercept, estimate of alpha)0.120
 Mean Square Error0.240
 DF error170.000
 t(b)1.358
 p(b)0.448
 t(a)0.172
 p(a)0.493
 Lowerbound of 95% confidence interval for beta-0.139
 Upperbound of 95% confidence interval for beta0.751
 Lowerbound of 95% confidence interval for alpha-1.251
 Upperbound of 95% confidence interval for alpha1.490
 Treynor index (mean / b)0.573
 Jensen alpha (a)0.120
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 VaR0.012
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 10.994
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.010
 Inter Quartile Range0.000
 Number outliers low9.000
 Percentage of outliers low0.052
 Mean of outliers low0.971
 Number of outliers high13.000
 Percentage of outliers high0.076
 Mean of outliers high1.034
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)0.310
 VaR(95%) (regression method)0.002
 Expected Shortfall (regression method)0.026
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.219
 Quartile 10.219
 Median0.219
 Quartile 30.219
 Maximum0.219
 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)0.232
 Compounded annual return (geometric extrapolation)0.245
 Calmar ratio (compounded annual return / max draw down)1.121
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal4.658