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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-0.012
 SD0.085
 Sharpe ratio (Glass type estimate) -0.144
 Sharpe ratio (Hedges UMVUE)-0.141
 df35.000
 t-0.249
 p0.598
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.275
 Upperbound of 95% confidence interval for Sharpe Ratio0.989
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.273
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.991
Statistics related to Sortino ratio
 Sortino ratio-0.216
 Upside Potential Ratio1.313
 Upside part of mean0.074
 Downside part of mean-0.087
 Upside SD0.062
 Downside SD0.057
 N nonnegative terms5.000
 N negative terms31.000
Statistics related to linear regression on benchmark
 N of observations36.000
 Mean of predictor0.113
 Mean of criterion-0.012
 SD of predictor0.094
 SD of criterion0.085
 Covariance0.001
 r0.160
 b (slope, estimate of beta)0.145
 a (intercept, estimate of alpha)-0.029
 Mean Square Error0.007
 DF error34.000
 t(b)0.946
 p(b)0.175
 t(a)-0.550
 p(a)0.707
 Lowerbound of 95% confidence interval for beta-0.167
 Upperbound of 95% confidence interval for beta0.458
 Lowerbound of 95% confidence interval for alpha-0.135
 Upperbound of 95% confidence interval for alpha0.077
 Treynor index (mean / b)-0.084
 Jensen alpha (a)-0.029
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.016
 SD0.085
 Sharpe ratio (Glass type estimate) -0.185
 Sharpe ratio (Hedges UMVUE)-0.181
 df35.000
 t-0.321
 p0.625
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.316
 Upperbound of 95% confidence interval for Sharpe Ratio0.948
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.314
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.951
Statistics related to Sortino ratio
 Sortino ratio-0.270
 Upside Potential Ratio1.241
 Upside part of mean0.072
 Downside part of mean-0.088
 Upside SD0.060
 Downside SD0.058
 N nonnegative terms5.000
 N negative terms31.000
Statistics related to linear regression on benchmark
 N of observations36.000
 Mean of predictor0.108
 Mean of criterion-0.016
 SD of predictor0.093
 SD of criterion0.085
 Covariance0.001
 r0.166
 b (slope, estimate of beta)0.150
 a (intercept, estimate of alpha)-0.032
 Mean Square Error0.007
 DF error34.000
 t(b)0.979
 p(b)0.167
 t(a)-0.618
 p(a)0.730
 Lowerbound of 95% confidence interval for beta-0.162
 Upperbound of 95% confidence interval for beta0.463
 Lowerbound of 95% confidence interval for alpha-0.137
 Upperbound of 95% confidence interval for alpha0.073
 Treynor index (mean / b)-0.104
 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%)0.041
 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 observations36.000
 Minimum0.930
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.074
 Mean of quarter 10.984
 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 low0.083
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.167
 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)0.057
 Expected Shortfall (regression method)0.076
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)0.030
 Compounded annual return (geometric extrapolation)0.029
 Calmar ratio (compounded annual return / max draw down)0.413
 Compounded annual return / average of 25% largest draw downs0.413
 Compounded annual return / Expected Shortfall lognormal0.570
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.012
 SD0.084
 Sharpe ratio (Glass type estimate) -0.148
 Sharpe ratio (Hedges UMVUE)-0.148
 df1040.000
 t-0.257
 p0.504
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.274
 Upperbound of 95% confidence interval for Sharpe Ratio0.979
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.274
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.979
Statistics related to Sortino ratio
 Sortino ratio-0.206
 Upside Potential Ratio3.757
 Upside part of mean0.226
 Downside part of mean-0.238
 Upside SD0.059
 Downside SD0.060
 N nonnegative terms110.000
 N negative terms931.000
Statistics related to linear regression on benchmark
 N of observations1041.000
 Mean of predictor0.123
 Mean of criterion-0.012
 SD of predictor0.122
 SD of criterion0.084
 Covariance0.001
 r0.093
 b (slope, estimate of beta)0.064
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.007
 DF error1039.000
 t(b)3.006
 p(b)0.441
 t(a)-0.422
 p(a)0.508
 Lowerbound of 95% confidence interval for beta0.022
 Upperbound of 95% confidence interval for beta0.106
 Lowerbound of 95% confidence interval for alpha-0.115
 Upperbound of 95% confidence interval for alpha0.074
 Treynor index (mean / b)-0.194
 Jensen alpha (a)-0.020
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.016
 SD0.084
 Sharpe ratio (Glass type estimate) -0.190
 Sharpe ratio (Hedges UMVUE)-0.189
 df1040.000
 t-0.330
 p0.505
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.316
 Upperbound of 95% confidence interval for Sharpe Ratio0.937
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.316
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.937
Statistics related to Sortino ratio
 Sortino ratio-0.262
 Upside Potential Ratio3.682
 Upside part of mean0.224
 Downside part of mean-0.240
 Upside SD0.058
 Downside SD0.061
 N nonnegative terms110.000
 N negative terms931.000
Statistics related to linear regression on benchmark
 N of observations1041.000
 Mean of predictor0.116
 Mean of criterion-0.016
 SD of predictor0.122
 SD of criterion0.084
 Covariance0.001
 r0.093
 b (slope, estimate of beta)0.064
 a (intercept, estimate of alpha)-0.023
 Mean Square Error0.007
 DF error1039.000
 t(b)3.004
 p(b)0.441
 t(a)-0.485
 p(a)0.510
 Lowerbound of 95% confidence interval for beta0.022
 Upperbound of 95% confidence interval for beta0.106
 Lowerbound of 95% confidence interval for alpha-0.118
 Upperbound of 95% confidence interval for alpha0.071
 Treynor index (mean / b)-0.248
 Jensen alpha (a)-0.023
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 observations1041.000
 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 low0.067
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.107
 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)0.029
 Compounded annual return (geometric extrapolation)0.028
 Calmar ratio (compounded annual return / max draw down)0.216
 Compounded annual return / average of 25% largest draw downs0.245
 Compounded annual return / Expected Shortfall lognormal3.046
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 predictor0.007
 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 predictor0.001
 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)-5595543651914180.000
 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)-45664293043261538899758671724544.000
 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