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Advanced Statistics: ETF OPTION TIMER

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-0.005
 SD0.095
 Sharpe ratio (Glass type estimate) -0.048
 Sharpe ratio (Hedges UMVUE)-0.047
 df28.000
 t-0.074
 p0.529
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.308
 Upperbound of 95% confidence interval for Sharpe Ratio1.213
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.307
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.214
Statistics related to Sortino ratio
 Sortino ratio-0.072
 Upside Potential Ratio1.470
 Upside part of mean0.092
 Downside part of mean-0.097
 Upside SD0.069
 Downside SD0.063
 N nonnegative terms5.000
 N negative terms24.000
Statistics related to linear regression on benchmark
 N of observations29.000
 Mean of predictor0.148
 Mean of criterion-0.005
 SD of predictor0.090
 SD of criterion0.095
 Covariance0.001
 r0.172
 b (slope, estimate of beta)0.181
 a (intercept, estimate of alpha)-0.031
 Mean Square Error0.009
 DF error27.000
 t(b)0.908
 p(b)0.186
 t(a)-0.462
 p(a)0.676
 Lowerbound of 95% confidence interval for beta-0.228
 Upperbound of 95% confidence interval for beta0.591
 Lowerbound of 95% confidence interval for alpha-0.171
 Upperbound of 95% confidence interval for alpha0.108
 Treynor index (mean / b)-0.025
 Jensen alpha (a)-0.031
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.009
 SD0.095
 Sharpe ratio (Glass type estimate) -0.094
 Sharpe ratio (Hedges UMVUE)-0.091
 df28.000
 t-0.145
 p0.557
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.354
 Upperbound of 95% confidence interval for Sharpe Ratio1.168
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.352
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.170
Statistics related to Sortino ratio
 Sortino ratio-0.137
 Upside Potential Ratio1.389
 Upside part of mean0.090
 Downside part of mean-0.098
 Upside SD0.067
 Downside SD0.065
 N nonnegative terms5.000
 N negative terms24.000
Statistics related to linear regression on benchmark
 N of observations29.000
 Mean of predictor0.143
 Mean of criterion-0.009
 SD of predictor0.089
 SD of criterion0.095
 Covariance0.002
 r0.181
 b (slope, estimate of beta)0.192
 a (intercept, estimate of alpha)-0.036
 Mean Square Error0.009
 DF error27.000
 t(b)0.956
 p(b)0.174
 t(a)-0.538
 p(a)0.703
 Lowerbound of 95% confidence interval for beta-0.220
 Upperbound of 95% confidence interval for beta0.603
 Lowerbound of 95% confidence interval for alpha-0.174
 Upperbound of 95% confidence interval for alpha0.102
 Treynor index (mean / b)-0.046
 Jensen alpha (a)-0.036
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.055
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.025
 Expected Shortfall on VaR0.048
ORDER STATISTICS
Quartiles of return rates
 Number of observations29.000
 Minimum0.930
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.074
 Mean of quarter 10.982
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.035
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.103
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.207
 Mean of outliers high1.040
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)-1.319
 VaR(95%) (regression method)0.065
 Expected Shortfall (regression method)0.079
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.027
 Quartile 10.037
 Median0.048
 Quartile 30.059
 Maximum0.070
 Mean of quarter 10.027
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.070
 Inter Quartile Range0.021
 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)0.037
 Compounded annual return (geometric extrapolation)0.036
 Calmar ratio (compounded annual return / max draw down)0.515
 Compounded annual return / average of 25% largest draw downs0.515
 Compounded annual return / Expected Shortfall lognormal0.646
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.006
 SD0.093
 Sharpe ratio (Glass type estimate) -0.060
 Sharpe ratio (Hedges UMVUE)-0.060
 df854.000
 t-0.094
 p0.537
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.303
 Upperbound of 95% confidence interval for Sharpe Ratio1.184
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.303
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.184
Statistics related to Sortino ratio
 Sortino ratio-0.083
 Upside Potential Ratio4.146
 Upside part of mean0.275
 Downside part of mean-0.281
 Upside SD0.065
 Downside SD0.066
 N nonnegative terms110.000
 N negative terms745.000
Statistics related to linear regression on benchmark
 N of observations855.000
 Mean of predictor0.145
 Mean of criterion-0.006
 SD of predictor0.126
 SD of criterion0.093
 Covariance0.001
 r0.099
 b (slope, estimate of beta)0.073
 a (intercept, estimate of alpha)-0.016
 Mean Square Error0.009
 DF error853.000
 t(b)2.909
 p(b)0.002
 t(a)-0.275
 p(a)0.608
 Lowerbound of 95% confidence interval for beta0.024
 Upperbound of 95% confidence interval for beta0.123
 Lowerbound of 95% confidence interval for alpha-0.131
 Upperbound of 95% confidence interval for alpha0.099
 Treynor index (mean / b)-0.076
 Jensen alpha (a)-0.016
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.010
 SD0.093
 Sharpe ratio (Glass type estimate) -0.106
 Sharpe ratio (Hedges UMVUE)-0.106
 df854.000
 t-0.167
 p0.566
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.349
 Upperbound of 95% confidence interval for Sharpe Ratio1.137
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.349
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.137
Statistics related to Sortino ratio
 Sortino ratio-0.146
 Upside Potential Ratio4.064
 Upside part of mean0.273
 Downside part of mean-0.283
 Upside SD0.064
 Downside SD0.067
 N nonnegative terms110.000
 N negative terms745.000
Statistics related to linear regression on benchmark
 N of observations855.000
 Mean of predictor0.137
 Mean of criterion-0.010
 SD of predictor0.125
 SD of criterion0.093
 Covariance0.001
 r0.099
 b (slope, estimate of beta)0.073
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.009
 DF error853.000
 t(b)2.908
 p(b)0.002
 t(a)-0.338
 p(a)0.632
 Lowerbound of 95% confidence interval for beta0.024
 Upperbound of 95% confidence interval for beta0.123
 Lowerbound of 95% confidence interval for alpha-0.135
 Upperbound of 95% confidence interval for alpha0.095
 Treynor index (mean / b)-0.134
 Jensen alpha (a)-0.020
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.008
 Expected Shortfall on VaR0.010
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.006
ORDER STATISTICS
Quartiles of return rates
 Number of observations855.000
 Minimum0.963
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.037
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.003
 Inter Quartile Range0.000
 Number outliers low70.000
 Percentage of outliers low0.082
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.130
 Mean of outliers high1.006
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.169
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.004
 Extreme Value Index (regression method)0.070
 VaR(95%) (regression method)0.003
 Expected Shortfall (regression method)0.008
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations9.000
 Minimum0.000
 Quartile 10.002
 Median0.004
 Quartile 30.083
 Maximum0.132
 Mean of quarter 10.001
 Mean of quarter 20.004
 Mean of quarter 30.046
 Mean of quarter 40.116
 Inter Quartile Range0.081
 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)-2.125
 VaR(95%) (moments method)0.121
 Expected Shortfall (moments method)0.122
 Extreme Value Index (regression method)-0.179
 VaR(95%) (regression method)0.141
 Expected Shortfall (regression method)0.165
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.036
 Compounded annual return (geometric extrapolation)0.035
 Calmar ratio (compounded annual return / max draw down)0.264
 Compounded annual return / average of 25% largest draw downs0.299
 Compounded annual return / Expected Shortfall lognormal3.381
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) NA
 Sharpe ratio (Hedges UMVUE)NA
 dfNA
 tNA
 pNA
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.075
 Mean of criterion-0.044
 SD of predictor0.110
 SD of criterion0.000
 Covariance0.000
 rNA
 b (slope, estimate of beta)NA
 a (intercept, estimate of alpha)NA
 Mean Square ErrorNA
 DF errorNA
 t(b)NA
 p(b)NA
 t(a)NA
 p(a)NA
 Lowerbound of 95% confidence interval for betaNA
 Upperbound of 95% confidence interval for betaNA
 Lowerbound of 95% confidence interval for alphaNA
 Upperbound of 95% confidence interval for alphaNA
 Treynor index (mean / b)NA
 Jensen alpha (a)NA
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) -7936535306446244.000
 Sharpe ratio (Hedges UMVUE)-7901674975671223.000
 df171.000
 t-5611977934314593.000
 p1.000
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8739115425704417.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-7064234525638030.000
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.069
 Mean of criterion-0.044
 SD of predictor0.111
 SD of criterion0.000
 Covariance0.000
 r0.000
 b (slope, estimate of beta)0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error170.000
 t(b)0.000
 p(b)0.500
 t(a)-5592398559240949.000
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.000
 Upperbound of 95% confidence interval for beta0.000
 Lowerbound of 95% confidence interval for alpha-0.044
 Upperbound of 95% confidence interval for alpha-0.044
 Treynor index (mean / b)-11873362712668898085609297412096.000
 Jensen alpha (a)-0.044
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 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 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 observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 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 lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 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)0.000
 Compounded annual return (geometric extrapolation)0.000
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.000