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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-0.010
 SD0.088
 Sharpe ratio (Glass type estimate) -0.118
 Sharpe ratio (Hedges UMVUE)-0.116
 df33.000
 t-0.199
 p0.578
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.282
 Upperbound of 95% confidence interval for Sharpe Ratio1.047
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.280
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.049
Statistics related to Sortino ratio
 Sortino ratio-0.178
 Upside Potential Ratio1.353
 Upside part of mean0.079
 Downside part of mean-0.089
 Upside SD0.064
 Downside SD0.058
 N nonnegative terms5.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations34.000
 Mean of predictor0.137
 Mean of criterion-0.010
 SD of predictor0.087
 SD of criterion0.088
 Covariance0.001
 r0.169
 b (slope, estimate of beta)0.171
 a (intercept, estimate of alpha)-0.034
 Mean Square Error0.008
 DF error32.000
 t(b)0.971
 p(b)0.169
 t(a)-0.587
 p(a)0.719
 Lowerbound of 95% confidence interval for beta-0.188
 Upperbound of 95% confidence interval for beta0.529
 Lowerbound of 95% confidence interval for alpha-0.151
 Upperbound of 95% confidence interval for alpha0.083
 Treynor index (mean / b)-0.061
 Jensen alpha (a)-0.034
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.014
 SD0.087
 Sharpe ratio (Glass type estimate) -0.161
 Sharpe ratio (Hedges UMVUE)-0.157
 df33.000
 t-0.271
 p0.606
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.325
 Upperbound of 95% confidence interval for Sharpe Ratio1.005
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.322
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.008
Statistics related to Sortino ratio
 Sortino ratio-0.235
 Upside Potential Ratio1.279
 Upside part of mean0.076
 Downside part of mean-0.090
 Upside SD0.062
 Downside SD0.060
 N nonnegative terms5.000
 N negative terms29.000
Statistics related to linear regression on benchmark
 N of observations34.000
 Mean of predictor0.132
 Mean of criterion-0.014
 SD of predictor0.086
 SD of criterion0.087
 Covariance0.001
 r0.177
 b (slope, estimate of beta)0.180
 a (intercept, estimate of alpha)-0.038
 Mean Square Error0.008
 DF error32.000
 t(b)1.017
 p(b)0.158
 t(a)-0.664
 p(a)0.744
 Lowerbound of 95% confidence interval for beta-0.180
 Upperbound of 95% confidence interval for beta0.540
 Lowerbound of 95% confidence interval for alpha-0.153
 Upperbound of 95% confidence interval for alpha0.078
 Treynor index (mean / b)-0.078
 Jensen alpha (a)-0.038
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.042
 Expected Shortfall on VaR0.052
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.045
ORDER STATISTICS
Quartiles of return rates
 Number of observations34.000
 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 low0.088
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.176
 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)0.059
 Expected Shortfall (regression method)0.077
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)0.031
 Compounded annual return (geometric extrapolation)0.030
 Calmar ratio (compounded annual return / max draw down)0.438
 Compounded annual return / average of 25% largest draw downs0.438
 Compounded annual return / Expected Shortfall lognormal0.589
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.011
 SD0.086
 Sharpe ratio (Glass type estimate) -0.127
 Sharpe ratio (Hedges UMVUE)-0.126
 df992.000
 t-0.215
 p0.585
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.280
 Upperbound of 95% confidence interval for Sharpe Ratio1.027
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.280
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.027
Statistics related to Sortino ratio
 Sortino ratio-0.177
 Upside Potential Ratio3.846
 Upside part of mean0.237
 Downside part of mean-0.248
 Upside SD0.060
 Downside SD0.062
 N nonnegative terms110.000
 N negative terms883.000
Statistics related to linear regression on benchmark
 N of observations993.000
 Mean of predictor0.144
 Mean of criterion-0.011
 SD of predictor0.120
 SD of criterion0.086
 Covariance0.001
 r0.096
 b (slope, estimate of beta)0.069
 a (intercept, estimate of alpha)-0.021
 Mean Square Error0.007
 DF error991.000
 t(b)3.041
 p(b)0.001
 t(a)-0.412
 p(a)0.660
 Lowerbound of 95% confidence interval for beta0.024
 Upperbound of 95% confidence interval for beta0.113
 Lowerbound of 95% confidence interval for alpha-0.120
 Upperbound of 95% confidence interval for alpha0.078
 Treynor index (mean / b)-0.158
 Jensen alpha (a)-0.021
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.015
 SD0.086
 Sharpe ratio (Glass type estimate) -0.169
 Sharpe ratio (Hedges UMVUE)-0.169
 df992.000
 t-0.288
 p0.613
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.323
 Upperbound of 95% confidence interval for Sharpe Ratio0.984
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.323
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.984
Statistics related to Sortino ratio
 Sortino ratio-0.234
 Upside Potential Ratio3.770
 Upside part of mean0.235
 Downside part of mean-0.250
 Upside SD0.059
 Downside SD0.062
 N nonnegative terms110.000
 N negative terms883.000
Statistics related to linear regression on benchmark
 N of observations993.000
 Mean of predictor0.137
 Mean of criterion-0.015
 SD of predictor0.120
 SD of criterion0.086
 Covariance0.001
 r0.096
 b (slope, estimate of beta)0.069
 a (intercept, estimate of alpha)-0.024
 Mean Square Error0.007
 DF error991.000
 t(b)3.039
 p(b)0.001
 t(a)-0.475
 p(a)0.683
 Lowerbound of 95% confidence interval for beta0.024
 Upperbound of 95% confidence interval for beta0.114
 Lowerbound of 95% confidence interval for alpha-0.123
 Upperbound of 95% confidence interval for alpha0.075
 Treynor index (mean / b)-0.211
 Jensen alpha (a)-0.024
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%)0.002
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations993.000
 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 low0.070
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.112
 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)0.031
 Compounded annual return (geometric extrapolation)0.030
 Calmar ratio (compounded annual return / max draw down)0.227
 Compounded annual return / average of 25% largest draw downs0.257
 Compounded annual return / Expected Shortfall lognormal3.123
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 predictor0.123
 Mean of criterion-0.044
 SD of predictor0.091
 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 predictor0.119
 Mean of criterion-0.044
 SD of predictor0.091
 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)-5581478764903726.000
 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)-9019063994717765964113983307776.000
 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