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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-0.009
 SD0.089
 Sharpe ratio (Glass type estimate) -0.105
 Sharpe ratio (Hedges UMVUE)-0.103
 df32.000
 t-0.174
 p0.569
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.286
 Upperbound of 95% confidence interval for Sharpe Ratio1.078
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.285
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.080
Statistics related to Sortino ratio
 Sortino ratio-0.158
 Upside Potential Ratio1.374
 Upside part of mean0.081
 Downside part of mean-0.090
 Upside SD0.065
 Downside SD0.059
 N nonnegative terms5.000
 N negative terms28.000
Statistics related to linear regression on benchmark
 N of observations33.000
 Mean of predictor0.147
 Mean of criterion-0.009
 SD of predictor0.086
 SD of criterion0.089
 Covariance0.001
 r0.169
 b (slope, estimate of beta)0.174
 a (intercept, estimate of alpha)-0.035
 Mean Square Error0.008
 DF error31.000
 t(b)0.953
 p(b)0.174
 t(a)-0.582
 p(a)0.717
 Lowerbound of 95% confidence interval for beta-0.198
 Upperbound of 95% confidence interval for beta0.546
 Lowerbound of 95% confidence interval for alpha-0.157
 Upperbound of 95% confidence interval for alpha0.088
 Treynor index (mean / b)-0.054
 Jensen alpha (a)-0.035
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.013
 SD0.089
 Sharpe ratio (Glass type estimate) -0.148
 Sharpe ratio (Hedges UMVUE)-0.145
 df32.000
 t-0.246
 p0.596
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.329
 Upperbound of 95% confidence interval for Sharpe Ratio1.036
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.327
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.038
Statistics related to Sortino ratio
 Sortino ratio-0.216
 Upside Potential Ratio1.299
 Upside part of mean0.079
 Downside part of mean-0.092
 Upside SD0.063
 Downside SD0.061
 N nonnegative terms5.000
 N negative terms28.000
Statistics related to linear regression on benchmark
 N of observations33.000
 Mean of predictor0.142
 Mean of criterion-0.013
 SD of predictor0.085
 SD of criterion0.089
 Covariance0.001
 r0.177
 b (slope, estimate of beta)0.184
 a (intercept, estimate of alpha)-0.039
 Mean Square Error0.008
 DF error31.000
 t(b)1.002
 p(b)0.162
 t(a)-0.660
 p(a)0.743
 Lowerbound of 95% confidence interval for beta-0.190
 Upperbound of 95% confidence interval for beta0.558
 Lowerbound of 95% confidence interval for alpha-0.160
 Upperbound of 95% confidence interval for alpha0.082
 Treynor index (mean / b)-0.071
 Jensen alpha (a)-0.039
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%)0.024
 Expected Shortfall on VaR0.046
ORDER STATISTICS
Quartiles of return rates
 Number of observations33.000
 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 41.030
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.091
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.182
 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)0.061
 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)0.032
 Compounded annual return (geometric extrapolation)0.031
 Calmar ratio (compounded annual return / max draw down)0.451
 Compounded annual return / average of 25% largest draw downs0.451
 Compounded annual return / Expected Shortfall lognormal0.599
ANALYSIS BASED ON DAILY 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) -0.110
 Sharpe ratio (Hedges UMVUE)-0.110
 df957.000
 t-0.184
 p0.573
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.285
 Upperbound of 95% confidence interval for Sharpe Ratio1.064
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.285
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.064
Statistics related to Sortino ratio
 Sortino ratio-0.154
 Upside Potential Ratio3.916
 Upside part of mean0.246
 Downside part of mean-0.255
 Upside SD0.061
 Downside SD0.063
 N nonnegative terms110.000
 N negative terms848.000
Statistics related to linear regression on benchmark
 N of observations958.000
 Mean of predictor0.147
 Mean of criterion-0.010
 SD of predictor0.121
 SD of criterion0.088
 Covariance0.001
 r0.097
 b (slope, estimate of beta)0.070
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.008
 DF error956.000
 t(b)3.021
 p(b)0.001
 t(a)-0.382
 p(a)0.649
 Lowerbound of 95% confidence interval for beta0.025
 Upperbound of 95% confidence interval for beta0.116
 Lowerbound of 95% confidence interval for alpha-0.123
 Upperbound of 95% confidence interval for alpha0.083
 Treynor index (mean / b)-0.137
 Jensen alpha (a)-0.020
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.014
 SD0.088
 Sharpe ratio (Glass type estimate) -0.154
 Sharpe ratio (Hedges UMVUE)-0.154
 df957.000
 t-0.257
 p0.601
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.329
 Upperbound of 95% confidence interval for Sharpe Ratio1.020
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.328
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.021
Statistics related to Sortino ratio
 Sortino ratio-0.213
 Upside Potential Ratio3.839
 Upside part of mean0.244
 Downside part of mean-0.257
 Upside SD0.060
 Downside SD0.063
 N nonnegative terms110.000
 N negative terms848.000
Statistics related to linear regression on benchmark
 N of observations958.000
 Mean of predictor0.139
 Mean of criterion-0.014
 SD of predictor0.121
 SD of criterion0.088
 Covariance0.001
 r0.097
 b (slope, estimate of beta)0.071
 a (intercept, estimate of alpha)-0.023
 Mean Square Error0.008
 DF error956.000
 t(b)3.020
 p(b)0.001
 t(a)-0.445
 p(a)0.672
 Lowerbound of 95% confidence interval for beta0.025
 Upperbound of 95% confidence interval for beta0.116
 Lowerbound of 95% confidence interval for alpha-0.126
 Upperbound of 95% confidence interval for alpha0.079
 Treynor index (mean / b)-0.191
 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%)0.008
 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 observations958.000
 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 low0.073
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.116
 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)0.032
 Compounded annual return (geometric extrapolation)0.031
 Calmar ratio (compounded annual return / max draw down)0.235
 Compounded annual return / average of 25% largest draw downs0.267
 Compounded annual return / Expected Shortfall lognormal3.183
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 predictor0.180
 Mean of criterion-0.044
 SD of predictor0.090
 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 predictor0.176
 Mean of criterion-0.044
 SD of predictor0.090
 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)-5564903584844009.000
 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)7799489386165264032818408718336.000
 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