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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-0.011
 SD0.086
 Sharpe ratio (Glass type estimate) -0.131
 Sharpe ratio (Hedges UMVUE)-0.128
 df34.000
 t-0.224
 p0.588
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.278
 Upperbound of 95% confidence interval for Sharpe Ratio1.018
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.276
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.020
Statistics related to Sortino ratio
 Sortino ratio-0.197
 Upside Potential Ratio1.333
 Upside part of mean0.076
 Downside part of mean-0.088
 Upside SD0.063
 Downside SD0.057
 N nonnegative terms5.000
 N negative terms30.000
Statistics related to linear regression on benchmark
 N of observations35.000
 Mean of predictor0.137
 Mean of criterion-0.011
 SD of predictor0.085
 SD of criterion0.086
 Covariance0.001
 r0.169
 b (slope, estimate of beta)0.171
 a (intercept, estimate of alpha)-0.035
 Mean Square Error0.007
 DF error33.000
 t(b)0.985
 p(b)0.166
 t(a)-0.621
 p(a)0.731
 Lowerbound of 95% confidence interval for beta-0.182
 Upperbound of 95% confidence interval for beta0.523
 Lowerbound of 95% confidence interval for alpha-0.148
 Upperbound of 95% confidence interval for alpha0.079
 Treynor index (mean / b)-0.066
 Jensen alpha (a)-0.035
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.015
 SD0.086
 Sharpe ratio (Glass type estimate) -0.173
 Sharpe ratio (Hedges UMVUE)-0.169
 df34.000
 t-0.296
 p0.615
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.320
 Upperbound of 95% confidence interval for Sharpe Ratio0.976
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.318
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.979
Statistics related to Sortino ratio
 Sortino ratio-0.252
 Upside Potential Ratio1.260
 Upside part of mean0.074
 Downside part of mean-0.089
 Upside SD0.061
 Downside SD0.059
 N nonnegative terms5.000
 N negative terms30.000
Statistics related to linear regression on benchmark
 N of observations35.000
 Mean of predictor0.132
 Mean of criterion-0.015
 SD of predictor0.085
 SD of criterion0.086
 Covariance0.001
 r0.177
 b (slope, estimate of beta)0.180
 a (intercept, estimate of alpha)-0.039
 Mean Square Error0.007
 DF error33.000
 t(b)1.032
 p(b)0.155
 t(a)-0.699
 p(a)0.755
 Lowerbound of 95% confidence interval for beta-0.175
 Upperbound of 95% confidence interval for beta0.534
 Lowerbound of 95% confidence interval for alpha-0.151
 Upperbound of 95% confidence interval for alpha0.074
 Treynor index (mean / b)-0.083
 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%)0.041
 Expected Shortfall on VaR0.051
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 observations35.000
 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 low0.086
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.171
 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)0.058
 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)0.030
 Calmar ratio (compounded annual return / max draw down)0.425
 Compounded annual return / average of 25% largest draw downs0.425
 Compounded annual return / Expected Shortfall lognormal0.579
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.012
 SD0.085
 Sharpe ratio (Glass type estimate) -0.139
 Sharpe ratio (Hedges UMVUE)-0.138
 df1019.000
 t-0.239
 p0.505
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.277
 Upperbound of 95% confidence interval for Sharpe Ratio1.000
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.277
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.000
Statistics related to Sortino ratio
 Sortino ratio-0.193
 Upside Potential Ratio3.795
 Upside part of mean0.231
 Downside part of mean-0.242
 Upside SD0.059
 Downside SD0.061
 N nonnegative terms110.000
 N negative terms910.000
Statistics related to linear regression on benchmark
 N of observations1020.000
 Mean of predictor0.130
 Mean of criterion-0.012
 SD of predictor0.120
 SD of criterion0.085
 Covariance0.001
 r0.095
 b (slope, estimate of beta)0.067
 a (intercept, estimate of alpha)-0.021
 Mean Square Error0.007
 DF error1018.000
 t(b)3.053
 p(b)0.452
 t(a)-0.417
 p(a)0.507
 Lowerbound of 95% confidence interval for beta0.024
 Upperbound of 95% confidence interval for beta0.111
 Lowerbound of 95% confidence interval for alpha-0.117
 Upperbound of 95% confidence interval for alpha0.076
 Treynor index (mean / b)-0.174
 Jensen alpha (a)-0.021
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.015
 SD0.085
 Sharpe ratio (Glass type estimate) -0.181
 Sharpe ratio (Hedges UMVUE)-0.181
 df1019.000
 t-0.311
 p0.506
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.319
 Upperbound of 95% confidence interval for Sharpe Ratio0.957
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.319
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.958
Statistics related to Sortino ratio
 Sortino ratio-0.250
 Upside Potential Ratio3.720
 Upside part of mean0.229
 Downside part of mean-0.244
 Upside SD0.058
 Downside SD0.062
 N nonnegative terms110.000
 N negative terms910.000
Statistics related to linear regression on benchmark
 N of observations1020.000
 Mean of predictor0.122
 Mean of criterion-0.015
 SD of predictor0.120
 SD of criterion0.085
 Covariance0.001
 r0.095
 b (slope, estimate of beta)0.068
 a (intercept, estimate of alpha)-0.024
 Mean Square Error0.007
 DF error1018.000
 t(b)3.051
 p(b)0.452
 t(a)-0.480
 p(a)0.508
 Lowerbound of 95% confidence interval for beta0.024
 Upperbound of 95% confidence interval for beta0.111
 Lowerbound of 95% confidence interval for alpha-0.120
 Upperbound of 95% confidence interval for alpha0.073
 Treynor index (mean / b)-0.227
 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 VaR0.009
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 observations1020.000
 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 low0.069
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.109
 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)0.030
 Compounded annual return (geometric extrapolation)0.029
 Calmar ratio (compounded annual return / max draw down)0.221
 Compounded annual return / average of 25% largest draw downs0.250
 Compounded annual return / Expected Shortfall lognormal3.079
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 predictor0.038
 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 predictor0.034
 Mean of criterion-0.044
 SD of predictor0.091
 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)-5594433438679532.000
 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)18501910055537237641048180654080.000
 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