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System Analytics - extreme-os


Advanced Statistics: extreme-os

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
 Mean0.476
 SD0.269
 Sharpe ratio (Glass type estimate) 1.766
 Sharpe ratio (Hedges UMVUE)1.746
 df66.000
 t4.172
 p0.000
 Lowerbound of 95% confidence interval for Sharpe Ratio0.878
 Upperbound of 95% confidence interval for Sharpe Ratio2.642
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.864
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.627
Statistics related to Sortino ratio
 Sortino ratio3.265
 Upside Potential Ratio4.441
 Upside part of mean0.647
 Downside part of mean-0.171
 Upside SD0.263
 Downside SD0.146
 N nonnegative terms50.000
 N negative terms17.000
Statistics related to linear regression on benchmark
 N of observations67.000
 Mean of predictor-0.046
 Mean of criterion0.476
 SD of predictor0.183
 SD of criterion0.269
 Covariance0.017
 r0.337
 b (slope, estimate of beta)0.495
 a (intercept, estimate of alpha)0.498
 Mean Square Error0.065
 DF error65.000
 t(b)2.888
 p(b)0.003
 t(a)4.596
 p(a)0.000
 Lowerbound of 95% confidence interval for beta0.153
 Upperbound of 95% confidence interval for beta0.837
 Lowerbound of 95% confidence interval for alpha0.282
 Upperbound of 95% confidence interval for alpha0.715
 Treynor index (mean / b)0.961
 Jensen alpha (a)0.498
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.430
 SD0.267
 Sharpe ratio (Glass type estimate) 1.609
 Sharpe ratio (Hedges UMVUE)1.591
 df66.000
 t3.802
 p0.000
 Lowerbound of 95% confidence interval for Sharpe Ratio0.730
 Upperbound of 95% confidence interval for Sharpe Ratio2.477
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.718
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.463
Statistics related to Sortino ratio
 Sortino ratio2.716
 Upside Potential Ratio3.869
 Upside part of mean0.613
 Downside part of mean-0.183
 Upside SD0.247
 Downside SD0.158
 N nonnegative terms50.000
 N negative terms17.000
Statistics related to linear regression on benchmark
 N of observations67.000
 Mean of predictor-0.063
 Mean of criterion0.430
 SD of predictor0.190
 SD of criterion0.267
 Covariance0.018
 r0.357
 b (slope, estimate of beta)0.503
 a (intercept, estimate of alpha)0.462
 Mean Square Error0.063
 DF error65.000
 t(b)3.080
 p(b)0.002
 t(a)4.317
 p(a)0.000
 Lowerbound of 95% confidence interval for beta0.177
 Upperbound of 95% confidence interval for beta0.829
 Lowerbound of 95% confidence interval for alpha0.248
 Upperbound of 95% confidence interval for alpha0.676
 Treynor index (mean / b)0.856
 Jensen alpha (a)0.462
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.087
 Expected Shortfall on VaR0.116
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.019
 Expected Shortfall on VaR0.048
ORDER STATISTICS
Quartiles of return rates
 Number of observations67.000
 Minimum0.794
 Quartile 11.003
 Median1.049
 Quartile 31.090
 Maximum1.191
 Mean of quarter 10.947
 Mean of quarter 21.025
 Mean of quarter 31.068
 Mean of quarter 41.135
 Inter Quartile Range0.088
 Number outliers low3.000
 Percentage of outliers low0.045
 Mean of outliers low0.830
 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)-9.214
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.467
 VaR(95%) (regression method)0.043
 Expected Shortfall (regression method)0.119
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations7.000
 Minimum0.016
 Quartile 10.019
 Median0.026
 Quartile 30.089
 Maximum0.400
 Mean of quarter 10.017
 Mean of quarter 20.024
 Mean of quarter 30.030
 Mean of quarter 40.274
 Inter Quartile Range0.070
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.143
 Mean of outliers high0.400
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)2.352
 Compounded annual return (geometric extrapolation)0.607
 Calmar ratio (compounded annual return / max draw down)1.518
 Compounded annual return / average of 25% largest draw downs2.215
 Compounded annual return / Expected Shortfall lognormal5.245
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.475
 SD0.340
 Sharpe ratio (Glass type estimate) 1.395
 Sharpe ratio (Hedges UMVUE)1.394
 df1943.000
 t3.315
 p0.452
 Lowerbound of 95% confidence interval for Sharpe Ratio0.569
 Upperbound of 95% confidence interval for Sharpe Ratio2.220
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.568
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.220
Statistics related to Sortino ratio
 Sortino ratio2.134
 Upside Potential Ratio7.871
 Upside part of mean1.751
 Downside part of mean-1.276
 Upside SD0.259
 Downside SD0.222
 N nonnegative terms918.000
 N negative terms1026.000
Statistics related to linear regression on benchmark
 N of observations1944.000
 Mean of predictor-0.031
 Mean of criterion0.475
 SD of predictor0.237
 SD of criterion0.340
 Covariance0.032
 r0.403
 b (slope, estimate of beta)0.580
 a (intercept, estimate of alpha)0.493
 Mean Square Error0.097
 DF error1942.000
 t(b)19.430
 p(b)0.298
 t(a)3.759
 p(a)0.457
 Lowerbound of 95% confidence interval for beta0.522
 Upperbound of 95% confidence interval for beta0.639
 Lowerbound of 95% confidence interval for alpha0.236
 Upperbound of 95% confidence interval for alpha0.750
 Treynor index (mean / b)0.818
 Jensen alpha (a)0.493
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.417
 SD0.339
 Sharpe ratio (Glass type estimate) 1.231
 Sharpe ratio (Hedges UMVUE)1.230
 df1943.000
 t2.926
 p0.458
 Lowerbound of 95% confidence interval for Sharpe Ratio0.405
 Upperbound of 95% confidence interval for Sharpe Ratio2.056
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.405
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.056
Statistics related to Sortino ratio
 Sortino ratio1.792
 Upside Potential Ratio7.388
 Upside part of mean1.719
 Downside part of mean-1.302
 Upside SD0.247
 Downside SD0.233
 N nonnegative terms918.000
 N negative terms1026.000
Statistics related to linear regression on benchmark
 N of observations1944.000
 Mean of predictor-0.059
 Mean of criterion0.417
 SD of predictor0.237
 SD of criterion0.339
 Covariance0.032
 r0.400
 b (slope, estimate of beta)0.572
 a (intercept, estimate of alpha)0.451
 Mean Square Error0.096
 DF error1942.000
 t(b)19.231
 p(b)0.300
 t(a)3.449
 p(a)0.461
 Lowerbound of 95% confidence interval for beta0.514
 Upperbound of 95% confidence interval for beta0.631
 Lowerbound of 95% confidence interval for alpha0.194
 Upperbound of 95% confidence interval for alpha0.707
 Treynor index (mean / b)0.728
 Jensen alpha (a)0.451
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.028
 Expected Shortfall on VaR0.036
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.019
ORDER STATISTICS
Quartiles of return rates
 Number of observations1944.000
 Minimum0.789
 Quartile 10.998
 Median1.000
 Quartile 31.005
 Maximum1.248
 Mean of quarter 10.986
 Mean of quarter 21.000
 Mean of quarter 31.002
 Mean of quarter 41.018
 Inter Quartile Range0.007
 Number outliers low175.000
 Percentage of outliers low0.090
 Mean of outliers low0.969
 Number of outliers high186.000
 Percentage of outliers high0.096
 Mean of outliers high1.033
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.756
 VaR(95%) (moments method)0.010
 Expected Shortfall (moments method)0.046
 Extreme Value Index (regression method)0.318
 VaR(95%) (regression method)0.012
 Expected Shortfall (regression method)0.024
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations116.000
 Minimum0.000
 Quartile 10.003
 Median0.008
 Quartile 30.022
 Maximum0.553
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.014
 Mean of quarter 40.083
 Inter Quartile Range0.019
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high13.000
 Percentage of outliers high0.112
 Mean of outliers high0.147
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.755
 VaR(95%) (moments method)0.083
 Expected Shortfall (moments method)0.357
 Extreme Value Index (regression method)0.921
 VaR(95%) (regression method)0.063
 Expected Shortfall (regression method)0.691
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)2.217
 Compounded annual return (geometric extrapolation)0.586
 Calmar ratio (compounded annual return / max draw down)1.060
 Compounded annual return / average of 25% largest draw downs7.024
 Compounded annual return / Expected Shortfall lognormal16.366
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.359
 SD0.284
 Sharpe ratio (Glass type estimate) 1.264
 Sharpe ratio (Hedges UMVUE)1.259
 df171.000
 t0.894
 p0.457
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.513
 Upperbound of 95% confidence interval for Sharpe Ratio4.037
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.516
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.034
Statistics related to Sortino ratio
 Sortino ratio1.723
 Upside Potential Ratio7.937
 Upside part of mean1.653
 Downside part of mean-1.294
 Upside SD0.193
 Downside SD0.208
 N nonnegative terms80.000
 N negative terms92.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor-0.103
 Mean of criterion0.359
 SD of predictor0.212
 SD of criterion0.284
 Covariance0.024
 r0.391
 b (slope, estimate of beta)0.523
 a (intercept, estimate of alpha)0.413
 Mean Square Error0.069
 DF error170.000
 t(b)5.538
 p(b)0.305
 t(a)1.114
 p(a)0.457
 Lowerbound of 95% confidence interval for beta0.337
 Upperbound of 95% confidence interval for beta0.709
 Lowerbound of 95% confidence interval for alpha-0.319
 Upperbound of 95% confidence interval for alpha1.144
 Treynor index (mean / b)0.686
 Jensen alpha (a)0.413
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.318
 SD0.287
 Sharpe ratio (Glass type estimate) 1.109
 Sharpe ratio (Hedges UMVUE)1.104
 df171.000
 t0.784
 p0.462
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.667
 Upperbound of 95% confidence interval for Sharpe Ratio3.882
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.670
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.879
Statistics related to Sortino ratio
 Sortino ratio1.482
 Upside Potential Ratio7.616
 Upside part of mean1.634
 Downside part of mean-1.316
 Upside SD0.190
 Downside SD0.215
 N nonnegative terms80.000
 N negative terms92.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor-0.126
 Mean of criterion0.318
 SD of predictor0.212
 SD of criterion0.287
 Covariance0.024
 r0.388
 b (slope, estimate of beta)0.524
 a (intercept, estimate of alpha)0.384
 Mean Square Error0.070
 DF error170.000
 t(b)5.487
 p(b)0.306
 t(a)1.024
 p(a)0.461
 Lowerbound of 95% confidence interval for beta0.336
 Upperbound of 95% confidence interval for beta0.713
 Lowerbound of 95% confidence interval for alpha-0.356
 Upperbound of 95% confidence interval for alpha1.124
 Treynor index (mean / b)0.606
 Jensen alpha (a)0.384
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.024
 Expected Shortfall on VaR0.030
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.019
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.916
 Quartile 10.998
 Median1.000
 Quartile 31.006
 Maximum1.049
 Mean of quarter 10.986
 Mean of quarter 21.000
 Mean of quarter 31.002
 Mean of quarter 41.017
 Inter Quartile Range0.007
 Number outliers low17.000
 Percentage of outliers low0.099
 Mean of outliers low0.972
 Number of outliers high17.000
 Percentage of outliers high0.099
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.668
 VaR(95%) (moments method)0.010
 Expected Shortfall (moments method)0.037
 Extreme Value Index (regression method)0.472
 VaR(95%) (regression method)0.014
 Expected Shortfall (regression method)0.034
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations17.000
 Minimum0.000
 Quartile 10.002
 Median0.013
 Quartile 30.037
 Maximum0.139
 Mean of quarter 10.001
 Mean of quarter 20.006
 Mean of quarter 30.034
 Mean of quarter 40.086
 Inter Quartile Range0.035
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.059
 Mean of outliers high0.139
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.505
 VaR(95%) (moments method)0.081
 Expected Shortfall (moments method)0.084
 Extreme Value Index (regression method)-0.097
 VaR(95%) (regression method)0.112
 Expected Shortfall (regression method)0.148
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.397
 Compounded annual return (geometric extrapolation)0.436
 Calmar ratio (compounded annual return / max draw down)3.149
 Compounded annual return / average of 25% largest draw downs5.070
 Compounded annual return / Expected Shortfall lognormal14.315