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Advanced Statistics: Iron Box .618

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
 Mean-0.371
 SD1.625
 Sharpe ratio (Glass type estimate) -0.228
 Sharpe ratio (Hedges UMVUE)-0.210
 df10.000
 t-0.218
 p0.584
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.272
 Upperbound of 95% confidence interval for Sharpe Ratio1.827
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.260
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.839
Statistics related to Sortino ratio
 Sortino ratio-0.372
 Upside Potential Ratio1.552
 Upside part of mean1.547
 Downside part of mean-1.918
 Upside SD1.191
 Downside SD0.996
 N nonnegative terms2.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations11.000
 Mean of predictor0.032
 Mean of criterion-0.371
 SD of predictor0.252
 SD of criterion1.625
 Covariance-0.304
 r-0.742
 b (slope, estimate of beta)-4.780
 a (intercept, estimate of alpha)-0.218
 Mean Square Error1.317
 DF error9.000
 t(b)-3.322
 p(b)0.996
 t(a)-0.182
 p(a)0.570
 Lowerbound of 95% confidence interval for beta-8.035
 Upperbound of 95% confidence interval for beta-1.526
 Lowerbound of 95% confidence interval for alpha-2.931
 Upperbound of 95% confidence interval for alpha2.496
 Treynor index (mean / b)0.078
 Jensen alpha (a)-0.218
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.885
 SD2.020
 Sharpe ratio (Glass type estimate) -0.933
 Sharpe ratio (Hedges UMVUE)-0.861
 df10.000
 t-0.894
 p0.804
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.998
 Upperbound of 95% confidence interval for Sharpe Ratio1.175
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.943
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.220
Statistics related to Sortino ratio
 Sortino ratio-1.034
 Upside Potential Ratio0.609
 Upside part of mean1.110
 Downside part of mean-2.995
 Upside SD0.823
 Downside SD1.824
 N nonnegative terms2.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations11.000
 Mean of predictor0.003
 Mean of criterion-1.885
 SD of predictor0.254
 SD of criterion2.020
 Covariance-0.354
 r-0.691
 b (slope, estimate of beta)-5.507
 a (intercept, estimate of alpha)-1.870
 Mean Square Error2.366
 DF error9.000
 t(b)-2.870
 p(b)0.991
 t(a)-1.164
 p(a)0.863
 Lowerbound of 95% confidence interval for beta-9.847
 Upperbound of 95% confidence interval for beta-1.167
 Lowerbound of 95% confidence interval for alpha-5.504
 Upperbound of 95% confidence interval for alpha1.765
 Treynor index (mean / b)0.342
 Jensen alpha (a)-1.870
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.672
 Expected Shortfall on VaR0.738
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.488
 Expected Shortfall on VaR0.834
ORDER STATISTICS
Quartiles of return rates
 Number of observations11.000
 Minimum0.195
 Quartile 10.758
 Median1.000
 Quartile 31.001
 Maximum2.096
 Mean of quarter 10.515
 Mean of quarter 20.909
 Mean of quarter 31.000
 Mean of quarter 41.476
 Inter Quartile Range0.244
 Number outliers low1.000
 Percentage of outliers low0.091
 Mean of outliers low0.195
 Number of outliers high1.000
 Percentage of outliers high0.091
 Mean of outliers high2.096
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.445
 VaR(95%) (moments method)0.582
 Expected Shortfall (moments method)1.058
 Extreme Value Index (regression method)6.821
 VaR(95%) (regression method)2.617
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.816
 Quartile 10.816
 Median0.816
 Quartile 30.816
 Maximum0.816
 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)-0.889
 Compounded annual return (geometric extrapolation)-0.841
 Calmar ratio (compounded annual return / max draw down)-1.032
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.140
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-1.282
 SD0.939
 Sharpe ratio (Glass type estimate) -1.365
 Sharpe ratio (Hedges UMVUE)-1.362
 df338.000
 t-1.355
 p0.912
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.342
 Upperbound of 95% confidence interval for Sharpe Ratio0.613
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.339
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.615
Statistics related to Sortino ratio
 Sortino ratio-1.713
 Upside Potential Ratio4.220
 Upside part of mean3.159
 Downside part of mean-4.441
 Upside SD0.569
 Downside SD0.749
 N nonnegative terms80.000
 N negative terms259.000
Statistics related to linear regression on benchmark
 N of observations339.000
 Mean of predictor0.206
 Mean of criterion-1.282
 SD of predictor0.264
 SD of criterion0.939
 Covariance-0.042
 r-0.169
 b (slope, estimate of beta)-0.600
 a (intercept, estimate of alpha)-1.159
 Mean Square Error0.859
 DF error337.000
 t(b)-3.141
 p(b)0.999
 t(a)-1.240
 p(a)0.892
 Lowerbound of 95% confidence interval for beta-0.976
 Upperbound of 95% confidence interval for beta-0.224
 Lowerbound of 95% confidence interval for alpha-2.997
 Upperbound of 95% confidence interval for alpha0.680
 Treynor index (mean / b)2.137
 Jensen alpha (a)-1.159
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.757
 SD0.992
 Sharpe ratio (Glass type estimate) -1.771
 Sharpe ratio (Hedges UMVUE)-1.767
 df338.000
 t-1.758
 p0.960
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.748
 Upperbound of 95% confidence interval for Sharpe Ratio0.209
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.746
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.212
Statistics related to Sortino ratio
 Sortino ratio-2.085
 Upside Potential Ratio3.575
 Upside part of mean3.011
 Downside part of mean-4.768
 Upside SD0.530
 Downside SD0.842
 N nonnegative terms80.000
 N negative terms259.000
Statistics related to linear regression on benchmark
 N of observations339.000
 Mean of predictor0.171
 Mean of criterion-1.757
 SD of predictor0.264
 SD of criterion0.992
 Covariance-0.044
 r-0.168
 b (slope, estimate of beta)-0.631
 a (intercept, estimate of alpha)-1.649
 Mean Square Error0.959
 DF error337.000
 t(b)-3.130
 p(b)0.999
 t(a)-1.670
 p(a)0.952
 Lowerbound of 95% confidence interval for beta-1.028
 Upperbound of 95% confidence interval for beta-0.235
 Lowerbound of 95% confidence interval for alpha-3.590
 Upperbound of 95% confidence interval for alpha0.293
 Treynor index (mean / b)2.782
 Jensen alpha (a)-1.649
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.089
 Expected Shortfall on VaR0.109
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.038
 Expected Shortfall on VaR0.081
ORDER STATISTICS
Quartiles of return rates
 Number of observations339.000
 Minimum0.701
 Quartile 10.998
 Median1.000
 Quartile 31.000
 Maximum1.252
 Mean of quarter 10.949
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.037
 Inter Quartile Range0.002
 Number outliers low79.000
 Percentage of outliers low0.233
 Mean of outliers low0.945
 Number of outliers high69.000
 Percentage of outliers high0.204
 Mean of outliers high1.045
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.395
 VaR(95%) (moments method)0.012
 Expected Shortfall (moments method)0.026
 Extreme Value Index (regression method)0.134
 VaR(95%) (regression method)0.040
 Expected Shortfall (regression method)0.071
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.003
 Quartile 10.206
 Median0.410
 Quartile 30.614
 Maximum0.817
 Mean of quarter 10.003
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.817
 Inter Quartile Range0.407
 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)-0.827
 Compounded annual return (geometric extrapolation)-0.820
 Calmar ratio (compounded annual return / max draw down)-1.003
 Compounded annual return / average of 25% largest draw downs-1.003
 Compounded annual return / Expected Shortfall lognormal-7.530
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-2.629
 SD0.855
 Sharpe ratio (Glass type estimate) -3.075
 Sharpe ratio (Hedges UMVUE)-3.062
 df171.000
 t-2.174
 p0.604
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.861
 Upperbound of 95% confidence interval for Sharpe Ratio-0.280
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.852
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.271
Statistics related to Sortino ratio
 Sortino ratio-3.141
 Upside Potential Ratio0.554
 Upside part of mean0.464
 Downside part of mean-3.093
 Upside SD0.215
 Downside SD0.837
 N nonnegative terms7.000
 N negative terms165.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.609
 Mean of criterion-2.629
 SD of predictor0.277
 SD of criterion0.855
 Covariance-0.034
 r-0.142
 b (slope, estimate of beta)-0.439
 a (intercept, estimate of alpha)-2.362
 Mean Square Error0.720
 DF error170.000
 t(b)-1.874
 p(b)0.571
 t(a)-1.954
 p(a)0.574
 Lowerbound of 95% confidence interval for beta-0.902
 Upperbound of 95% confidence interval for beta0.023
 Lowerbound of 95% confidence interval for alpha-4.748
 Upperbound of 95% confidence interval for alpha0.024
 Treynor index (mean / b)5.984
 Jensen alpha (a)-2.362
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-3.076
 SD0.980
 Sharpe ratio (Glass type estimate) -3.139
 Sharpe ratio (Hedges UMVUE)-3.125
 df171.000
 t-2.220
 p0.606
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.927
 Upperbound of 95% confidence interval for Sharpe Ratio-0.343
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.917
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.334
Statistics related to Sortino ratio
 Sortino ratio-3.171
 Upside Potential Ratio0.456
 Upside part of mean0.443
 Downside part of mean-3.519
 Upside SD0.202
 Downside SD0.970
 N nonnegative terms7.000
 N negative terms165.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.570
 Mean of criterion-3.076
 SD of predictor0.276
 SD of criterion0.980
 Covariance-0.037
 r-0.137
 b (slope, estimate of beta)-0.488
 a (intercept, estimate of alpha)-2.798
 Mean Square Error0.948
 DF error170.000
 t(b)-1.808
 p(b)0.569
 t(a)-2.020
 p(a)0.577
 Lowerbound of 95% confidence interval for beta-1.022
 Upperbound of 95% confidence interval for beta0.045
 Lowerbound of 95% confidence interval for alpha-5.532
 Upperbound of 95% confidence interval for alpha-0.063
 Treynor index (mean / b)6.298
 Jensen alpha (a)-2.798
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.091
 Expected Shortfall on VaR0.111
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.030
 Expected Shortfall on VaR0.068
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.701
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.145
 Mean of quarter 10.965
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.005
 Inter Quartile Range0.000
 Number outliers low10.000
 Percentage of outliers low0.058
 Mean of outliers low0.847
 Number of outliers high7.000
 Percentage of outliers high0.041
 Mean of outliers high1.033
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)-0.900
 VaR(95%) (regression method)0.045
 Expected Shortfall (regression method)0.132
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.003
 Quartile 10.026
 Median0.049
 Quartile 30.429
 Maximum0.809
 Mean of quarter 10.003
 Mean of quarter 20.049
 Mean of quarter 3NA
 Mean of quarter 40.809
 Inter Quartile Range0.403
 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)-1.561
 Compounded annual return (geometric extrapolation)-0.952
 Calmar ratio (compounded annual return / max draw down)-1.176
 Compounded annual return / average of 25% largest draw downs-1.176
 Compounded annual return / Expected Shortfall lognormal-8.570