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Advanced Statistics: TryIt

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
 Mean2475.884
 SD1433.383
 Sharpe ratio (Glass type estimate) 1.727
 Sharpe ratio (Hedges UMVUE)1.250
 df3.000
 t0.997
 p0.196
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.029
 Upperbound of 95% confidence interval for Sharpe Ratio5.253
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.289
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.789
Statistics related to Sortino ratio
 Sortino ratio1148.239
 Upside Potential Ratio1150.662
 Upside part of mean2481.108
 Downside part of mean-5.225
 Upside SD1432.400
 Downside SD2.156
 N nonnegative terms2.000
 N negative terms2.000
Statistics related to linear regression on benchmark
 N of observations4.000
 Mean of predictor0.428
 Mean of criterion2475.884
 SD of predictor0.236
 SD of criterion1433.383
 Covariance107.909
 r0.320
 b (slope, estimate of beta)1943.947
 a (intercept, estimate of alpha)1643.742
 Mean Square Error2767225.758
 DF error2.000
 t(b)0.477
 p(b)0.340
 t(a)0.488
 p(a)0.337
 Lowerbound of 95% confidence interval for beta-15595.307
 Upperbound of 95% confidence interval for beta19483.201
 Lowerbound of 95% confidence interval for alpha-12849.620
 Upperbound of 95% confidence interval for alpha16137.103
 Treynor index (mean / b)1.274
 Jensen alpha (a)1643.742
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.483
 SD17.657
 Sharpe ratio (Glass type estimate) -0.027
 Sharpe ratio (Hedges UMVUE)-0.020
 df3.000
 t-0.016
 p0.506
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.420
 Upperbound of 95% confidence interval for Sharpe Ratio3.370
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.415
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.375
Statistics related to Sortino ratio
 Sortino ratio-0.049
 Upside Potential Ratio2.041
 Upside part of mean20.263
 Downside part of mean-20.745
 Upside SD11.632
 Downside SD9.927
 N nonnegative terms2.000
 N negative terms2.000
Statistics related to linear regression on benchmark
 N of observations4.000
 Mean of predictor0.399
 Mean of criterion-0.483
 SD of predictor0.234
 SD of criterion17.657
 Covariance0.946
 r0.229
 b (slope, estimate of beta)17.252
 a (intercept, estimate of alpha)-7.366
 Mean Square Error443.181
 DF error2.000
 t(b)0.332
 p(b)0.386
 t(a)-0.176
 p(a)0.562
 Lowerbound of 95% confidence interval for beta-206.120
 Upperbound of 95% confidence interval for beta240.625
 Lowerbound of 95% confidence interval for alpha-187.799
 Upperbound of 95% confidence interval for alpha173.067
 Treynor index (mean / b)-0.028
 Jensen alpha (a)-7.366
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)1.000
 Expected Shortfall on VaR1.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)1.006
 Expected Shortfall on VaR1.463
ORDER STATISTICS
Quartiles of return rates
 Number of observations4.000
 Minimum0.004
 Quartile 10.197
 Median0.653
 Quartile 3207.783
 Maximum828.000
 Mean of quarter 10.004
 Mean of quarter 20.262
 Mean of quarter 31.043
 Mean of quarter 4828.000
 Inter Quartile Range207.585
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.250
 Mean of outliers high828.000
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)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.999
 Quartile 10.999
 Median0.999
 Quartile 30.999
 Maximum0.999
 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)-0.408
 Compounded annual return (geometric extrapolation)-0.355
 Calmar ratio (compounded annual return / max draw down)-0.355
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.355
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean774.565
 SD341.291
 Sharpe ratio (Glass type estimate) 2.270
 Sharpe ratio (Hedges UMVUE)2.255
 df118.000
 t1.335
 p0.439
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.080
 Upperbound of 95% confidence interval for Sharpe Ratio5.610
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.090
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)5.600
Statistics related to Sortino ratio
 Sortino ratio204.593
 Upside Potential Ratio213.516
 Upside part of mean808.346
 Downside part of mean-33.781
 Upside SD342.389
 Downside SD3.786
 N nonnegative terms50.000
 N negative terms69.000
Statistics related to linear regression on benchmark
 N of observations119.000
 Mean of predictor0.530
 Mean of criterion774.565
 SD of predictor0.204
 SD of criterion341.291
 Covariance17.926
 r0.258
 b (slope, estimate of beta)432.810
 a (intercept, estimate of alpha)545.116
 Mean Square Error109650.043
 DF error117.000
 t(b)2.890
 p(b)0.338
 t(a)0.959
 p(a)0.444
 Lowerbound of 95% confidence interval for beta136.169
 Upperbound of 95% confidence interval for beta729.450
 Lowerbound of 95% confidence interval for alpha-580.916
 Upperbound of 95% confidence interval for alpha1671.148
 Treynor index (mean / b)1.790
 Jensen alpha (a)545.116
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.075
 SD16.111
 Sharpe ratio (Glass type estimate) -0.067
 Sharpe ratio (Hedges UMVUE)-0.066
 df118.000
 t-0.039
 p0.502
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.399
 Upperbound of 95% confidence interval for Sharpe Ratio3.266
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.399
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.266
Statistics related to Sortino ratio
 Sortino ratio-0.103
 Upside Potential Ratio5.424
 Upside part of mean56.757
 Downside part of mean-57.832
 Upside SD12.162
 Downside SD10.463
 N nonnegative terms50.000
 N negative terms69.000
Statistics related to linear regression on benchmark
 N of observations119.000
 Mean of predictor0.509
 Mean of criterion-1.075
 SD of predictor0.203
 SD of criterion16.111
 Covariance1.109
 r0.340
 b (slope, estimate of beta)27.039
 a (intercept, estimate of alpha)-14.846
 Mean Square Error231.545
 DF error117.000
 t(b)3.909
 p(b)0.288
 t(a)-0.569
 p(a)0.533
 Lowerbound of 95% confidence interval for beta13.339
 Upperbound of 95% confidence interval for beta40.739
 Lowerbound of 95% confidence interval for alpha-66.556
 Upperbound of 95% confidence interval for alpha36.864
 Treynor index (mean / b)-0.040
 Jensen alpha (a)-14.846
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.761
 Expected Shortfall on VaR0.826
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.248
 Expected Shortfall on VaR0.479
ORDER STATISTICS
Quartiles of return rates
 Number of observations119.000
 Minimum0.011
 Quartile 10.878
 Median0.983
 Quartile 31.117
 Maximum184.000
 Mean of quarter 10.678
 Mean of quarter 20.933
 Mean of quarter 31.036
 Mean of quarter 410.286
 Inter Quartile Range0.239
 Number outliers low7.000
 Percentage of outliers low0.059
 Mean of outliers low0.294
 Number of outliers high8.000
 Percentage of outliers high0.067
 Mean of outliers high35.142
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.461
 VaR(95%) (moments method)0.347
 Expected Shortfall (moments method)0.716
 Extreme Value Index (regression method)0.132
 VaR(95%) (regression method)0.318
 Expected Shortfall (regression method)0.473
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.206
 Quartile 10.359
 Median0.512
 Quartile 30.755
 Maximum0.999
 Mean of quarter 10.206
 Mean of quarter 20.512
 Mean of quarter 3NA
 Mean of quarter 40.999
 Inter Quartile Range0.397
 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)-0.867
 Compounded annual return (geometric extrapolation)-0.643
 Calmar ratio (compounded annual return / max draw down)-0.644
 Compounded annual return / average of 25% largest draw downs-0.644
 Compounded annual return / Expected Shortfall lognormal-0.779