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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-0.014
 SD0.083
 Sharpe ratio (Glass type estimate) -0.168
 Sharpe ratio (Hedges UMVUE)-0.165
 df37.000
 t-0.299
 p0.617
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.269
 Upperbound of 95% confidence interval for Sharpe Ratio0.935
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.267
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.937
Statistics related to Sortino ratio
 Sortino ratio-0.252
 Upside Potential Ratio1.276
 Upside part of mean0.070
 Downside part of mean-0.084
 Upside SD0.060
 Downside SD0.055
 N nonnegative terms5.000
 N negative terms33.000
Statistics related to linear regression on benchmark
 N of observations38.000
 Mean of predictor0.136
 Mean of criterion-0.014
 SD of predictor0.100
 SD of criterion0.083
 Covariance0.001
 r0.138
 b (slope, estimate of beta)0.114
 a (intercept, estimate of alpha)-0.029
 Mean Square Error0.007
 DF error36.000
 t(b)0.837
 p(b)0.204
 t(a)-0.585
 p(a)0.719
 Lowerbound of 95% confidence interval for beta-0.162
 Upperbound of 95% confidence interval for beta0.390
 Lowerbound of 95% confidence interval for alpha-0.131
 Upperbound of 95% confidence interval for alpha0.072
 Treynor index (mean / b)-0.122
 Jensen alpha (a)-0.029
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.017
 SD0.082
 Sharpe ratio (Glass type estimate) -0.208
 Sharpe ratio (Hedges UMVUE)-0.204
 df37.000
 t-0.371
 p0.644
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.310
 Upperbound of 95% confidence interval for Sharpe Ratio0.895
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.307
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.898
Statistics related to Sortino ratio
 Sortino ratio-0.303
 Upside Potential Ratio1.206
 Upside part of mean0.068
 Downside part of mean-0.086
 Upside SD0.059
 Downside SD0.057
 N nonnegative terms5.000
 N negative terms33.000
Statistics related to linear regression on benchmark
 N of observations38.000
 Mean of predictor0.130
 Mean of criterion-0.017
 SD of predictor0.099
 SD of criterion0.082
 Covariance0.001
 r0.145
 b (slope, estimate of beta)0.121
 a (intercept, estimate of alpha)-0.033
 Mean Square Error0.007
 DF error36.000
 t(b)0.880
 p(b)0.192
 t(a)-0.660
 p(a)0.743
 Lowerbound of 95% confidence interval for beta-0.157
 Upperbound of 95% confidence interval for beta0.398
 Lowerbound of 95% confidence interval for alpha-0.134
 Upperbound of 95% confidence interval for alpha0.068
 Treynor index (mean / b)-0.143
 Jensen alpha (a)-0.033
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 VaR0.049
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.043
ORDER STATISTICS
Quartiles of return rates
 Number of observations38.000
 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 41.024
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.079
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.158
 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)0.055
 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)0.028
 Compounded annual return (geometric extrapolation)0.027
 Calmar ratio (compounded annual return / max draw down)0.391
 Compounded annual return / average of 25% largest draw downs0.391
 Compounded annual return / Expected Shortfall lognormal0.553
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.014
 SD0.082
 Sharpe ratio (Glass type estimate) -0.171
 Sharpe ratio (Hedges UMVUE)-0.171
 df1096.000
 t-0.306
 p0.505
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.269
 Upperbound of 95% confidence interval for Sharpe Ratio0.926
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.269
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.926
Statistics related to Sortino ratio
 Sortino ratio-0.239
 Upside Potential Ratio3.659
 Upside part of mean0.214
 Downside part of mean-0.228
 Upside SD0.057
 Downside SD0.059
 N nonnegative terms110.000
 N negative terms987.000
Statistics related to linear regression on benchmark
 N of observations1097.000
 Mean of predictor0.129
 Mean of criterion-0.014
 SD of predictor0.121
 SD of criterion0.082
 Covariance0.001
 r0.091
 b (slope, estimate of beta)0.061
 a (intercept, estimate of alpha)-0.022
 Mean Square Error0.007
 DF error1095.000
 t(b)3.021
 p(b)0.442
 t(a)-0.480
 p(a)0.509
 Lowerbound of 95% confidence interval for beta0.022
 Upperbound of 95% confidence interval for beta0.101
 Lowerbound of 95% confidence interval for alpha-0.112
 Upperbound of 95% confidence interval for alpha0.068
 Treynor index (mean / b)-0.228
 Jensen alpha (a)-0.022
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.017
 SD0.082
 Sharpe ratio (Glass type estimate) -0.212
 Sharpe ratio (Hedges UMVUE)-0.212
 df1096.000
 t-0.379
 p0.506
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.310
 Upperbound of 95% confidence interval for Sharpe Ratio0.886
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.310
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.886
Statistics related to Sortino ratio
 Sortino ratio-0.293
 Upside Potential Ratio3.587
 Upside part of mean0.213
 Downside part of mean-0.230
 Upside SD0.056
 Downside SD0.059
 N nonnegative terms110.000
 N negative terms987.000
Statistics related to linear regression on benchmark
 N of observations1097.000
 Mean of predictor0.121
 Mean of criterion-0.017
 SD of predictor0.121
 SD of criterion0.082
 Covariance0.001
 r0.091
 b (slope, estimate of beta)0.062
 a (intercept, estimate of alpha)-0.025
 Mean Square Error0.007
 DF error1095.000
 t(b)3.018
 p(b)0.442
 t(a)-0.543
 p(a)0.510
 Lowerbound of 95% confidence interval for beta0.022
 Upperbound of 95% confidence interval for beta0.102
 Lowerbound of 95% confidence interval for alpha-0.115
 Upperbound of 95% confidence interval for alpha0.065
 Treynor index (mean / b)-0.282
 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 observations1097.000
 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 low0.064
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.101
 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)0.001
 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)0.027
 Calmar ratio (compounded annual return / max draw down)0.205
 Compounded annual return / average of 25% largest draw downs0.232
 Compounded annual return / Expected Shortfall lognormal2.963
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 predictor0.016
 Mean of criterion-0.044
 SD of predictor0.115
 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 predictor0.009
 Mean of criterion-0.044
 SD of predictor0.115
 SD of criterion0.000
 Covariance-0.000
 r-0.000
 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)-5595490259468162.000
 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)382608600236975855708360696397824.000
 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