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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-0.013
 SD0.084
 Sharpe ratio (Glass type estimate) -0.156
 Sharpe ratio (Hedges UMVUE)-0.153
 df36.000
 t-0.274
 p0.607
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.272
 Upperbound of 95% confidence interval for Sharpe Ratio0.962
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.270
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.964
Statistics related to Sortino ratio
 Sortino ratio-0.234
 Upside Potential Ratio1.294
 Upside part of mean0.072
 Downside part of mean-0.085
 Upside SD0.061
 Downside SD0.056
 N nonnegative terms5.000
 N negative terms32.000
Statistics related to linear regression on benchmark
 N of observations37.000
 Mean of predictor0.138
 Mean of criterion-0.013
 SD of predictor0.102
 SD of criterion0.084
 Covariance0.001
 r0.138
 b (slope, estimate of beta)0.114
 a (intercept, estimate of alpha)-0.029
 Mean Square Error0.007
 DF error35.000
 t(b)0.823
 p(b)0.208
 t(a)-0.556
 p(a)0.709
 Lowerbound of 95% confidence interval for beta-0.167
 Upperbound of 95% confidence interval for beta0.394
 Lowerbound of 95% confidence interval for alpha-0.134
 Upperbound of 95% confidence interval for alpha0.076
 Treynor index (mean / b)-0.115
 Jensen alpha (a)-0.029
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.016
 SD0.084
 Sharpe ratio (Glass type estimate) -0.197
 Sharpe ratio (Hedges UMVUE)-0.193
 df36.000
 t-0.346
 p0.634
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.313
 Upperbound of 95% confidence interval for Sharpe Ratio0.921
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.310
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.924
Statistics related to Sortino ratio
 Sortino ratio-0.287
 Upside Potential Ratio1.223
 Upside part of mean0.070
 Downside part of mean-0.087
 Upside SD0.059
 Downside SD0.057
 N nonnegative terms5.000
 N negative terms32.000
Statistics related to linear regression on benchmark
 N of observations37.000
 Mean of predictor0.131
 Mean of criterion-0.016
 SD of predictor0.101
 SD of criterion0.084
 Covariance0.001
 r0.145
 b (slope, estimate of beta)0.120
 a (intercept, estimate of alpha)-0.032
 Mean Square Error0.007
 DF error35.000
 t(b)0.865
 p(b)0.196
 t(a)-0.631
 p(a)0.734
 Lowerbound of 95% confidence interval for beta-0.162
 Upperbound of 95% confidence interval for beta0.402
 Lowerbound of 95% confidence interval for alpha-0.136
 Upperbound of 95% confidence interval for alpha0.072
 Treynor index (mean / b)-0.137
 Jensen alpha (a)-0.032
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.040
 Expected Shortfall on VaR0.050
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.044
ORDER STATISTICS
Quartiles of return rates
 Number of observations37.000
 Minimum0.930
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.074
 Mean of quarter 10.985
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.027
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.081
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.162
 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)0.056
 Expected Shortfall (regression method)0.075
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)0.029
 Compounded annual return (geometric extrapolation)0.028
 Calmar ratio (compounded annual return / max draw down)0.402
 Compounded annual return / average of 25% largest draw downs0.402
 Compounded annual return / Expected Shortfall lognormal0.561
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.013
 SD0.083
 Sharpe ratio (Glass type estimate) -0.161
 Sharpe ratio (Hedges UMVUE)-0.161
 df1071.000
 t-0.284
 p0.506
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.271
 Upperbound of 95% confidence interval for Sharpe Ratio0.949
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.271
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.949
Statistics related to Sortino ratio
 Sortino ratio-0.225
 Upside Potential Ratio3.702
 Upside part of mean0.219
 Downside part of mean-0.233
 Upside SD0.058
 Downside SD0.059
 N nonnegative terms110.000
 N negative terms962.000
Statistics related to linear regression on benchmark
 N of observations1072.000
 Mean of predictor0.141
 Mean of criterion-0.013
 SD of predictor0.121
 SD of criterion0.083
 Covariance0.001
 r0.092
 b (slope, estimate of beta)0.063
 a (intercept, estimate of alpha)-0.022
 Mean Square Error0.007
 DF error1070.000
 t(b)3.026
 p(b)0.454
 t(a)-0.474
 p(a)0.507
 Lowerbound of 95% confidence interval for beta0.022
 Upperbound of 95% confidence interval for beta0.104
 Lowerbound of 95% confidence interval for alpha-0.114
 Upperbound of 95% confidence interval for alpha0.070
 Treynor index (mean / b)-0.211
 Jensen alpha (a)-0.022
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.017
 SD0.083
 Sharpe ratio (Glass type estimate) -0.202
 Sharpe ratio (Hedges UMVUE)-0.202
 df1071.000
 t-0.357
 p0.507
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.312
 Upperbound of 95% confidence interval for Sharpe Ratio0.908
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.312
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.908
Statistics related to Sortino ratio
 Sortino ratio-0.279
 Upside Potential Ratio3.628
 Upside part of mean0.218
 Downside part of mean-0.235
 Upside SD0.057
 Downside SD0.060
 N nonnegative terms110.000
 N negative terms962.000
Statistics related to linear regression on benchmark
 N of observations1072.000
 Mean of predictor0.133
 Mean of criterion-0.017
 SD of predictor0.121
 SD of criterion0.083
 Covariance0.001
 r0.092
 b (slope, estimate of beta)0.063
 a (intercept, estimate of alpha)-0.025
 Mean Square Error0.007
 DF error1070.000
 t(b)3.023
 p(b)0.454
 t(a)-0.538
 p(a)0.508
 Lowerbound of 95% confidence interval for beta0.022
 Upperbound of 95% confidence interval for beta0.104
 Lowerbound of 95% confidence interval for alpha-0.117
 Upperbound of 95% confidence interval for alpha0.067
 Treynor index (mean / b)-0.265
 Jensen alpha (a)-0.025
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.009
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.002
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations1072.000
 Minimum0.963
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.037
 Mean of quarter 10.998
 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 low0.065
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.104
 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)0.003
 Extreme Value Index (regression method)0.070
 VaR(95%) (regression method)0.002
 Expected Shortfall (regression method)0.007
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)0.028
 Compounded annual return (geometric extrapolation)0.028
 Calmar ratio (compounded annual return / max draw down)0.210
 Compounded annual return / average of 25% largest draw downs0.238
 Compounded annual return / Expected Shortfall lognormal3.000
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 predictor0.102
 Mean of criterion-0.044
 SD of predictor0.105
 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 predictor0.096
 Mean of criterion-0.044
 SD of predictor0.105
 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)-5588716715232872.000
 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)-9280288721107812351565671432192.000
 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