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-0.015
 SD0.081
 Sharpe ratio (Glass type estimate) -0.191
 Sharpe ratio (Hedges UMVUE)-0.187
 df39.000
 t-0.349
 p0.636
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.264
 Upperbound of 95% confidence interval for Sharpe Ratio0.884
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.262
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.887
Statistics related to Sortino ratio
 Sortino ratio-0.286
 Upside Potential Ratio1.242
 Upside part of mean0.067
 Downside part of mean-0.082
 Upside SD0.059
 Downside SD0.054
 N nonnegative terms5.000
 N negative terms35.000
Statistics related to linear regression on benchmark
 N of observations40.000
 Mean of predictor0.126
 Mean of criterion-0.015
 SD of predictor0.099
 SD of criterion0.081
 Covariance0.001
 r0.140
 b (slope, estimate of beta)0.114
 a (intercept, estimate of alpha)-0.030
 Mean Square Error0.007
 DF error38.000
 t(b)0.871
 p(b)0.195
 t(a)-0.631
 p(a)0.734
 Lowerbound of 95% confidence interval for beta-0.151
 Upperbound of 95% confidence interval for beta0.380
 Lowerbound of 95% confidence interval for alpha-0.126
 Upperbound of 95% confidence interval for alpha0.066
 Treynor index (mean / b)-0.135
 Jensen alpha (a)-0.030
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.019
 SD0.080
 Sharpe ratio (Glass type estimate) -0.231
 Sharpe ratio (Hedges UMVUE)-0.226
 df39.000
 t-0.421
 p0.662
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.304
 Upperbound of 95% confidence interval for Sharpe Ratio0.845
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.301
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.848
Statistics related to Sortino ratio
 Sortino ratio-0.335
 Upside Potential Ratio1.174
 Upside part of mean0.065
 Downside part of mean-0.084
 Upside SD0.057
 Downside SD0.055
 N nonnegative terms5.000
 N negative terms35.000
Statistics related to linear regression on benchmark
 N of observations40.000
 Mean of predictor0.120
 Mean of criterion-0.019
 SD of predictor0.098
 SD of criterion0.080
 Covariance0.001
 r0.146
 b (slope, estimate of beta)0.121
 a (intercept, estimate of alpha)-0.033
 Mean Square Error0.006
 DF error38.000
 t(b)0.912
 p(b)0.184
 t(a)-0.705
 p(a)0.757
 Lowerbound of 95% confidence interval for beta-0.147
 Upperbound of 95% confidence interval for beta0.388
 Lowerbound of 95% confidence interval for alpha-0.128
 Upperbound of 95% confidence interval for alpha0.062
 Treynor index (mean / b)-0.154
 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%)0.039
 Expected Shortfall on VaR0.048
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.042
ORDER STATISTICS
Quartiles of return rates
 Number of observations40.000
 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 low0.075
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.150
 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)0.052
 Expected Shortfall (regression method)0.074
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)0.027
 Compounded annual return (geometric extrapolation)0.026
 Calmar ratio (compounded annual return / max draw down)0.371
 Compounded annual return / average of 25% largest draw downs0.371
 Compounded annual return / Expected Shortfall lognormal0.537
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.016
 SD0.079
 Sharpe ratio (Glass type estimate) -0.200
 Sharpe ratio (Hedges UMVUE)-0.200
 df1167.000
 t-0.368
 p0.507
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.264
 Upperbound of 95% confidence interval for Sharpe Ratio0.864
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.263
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.864
Statistics related to Sortino ratio
 Sortino ratio-0.279
 Upside Potential Ratio3.546
 Upside part of mean0.201
 Downside part of mean-0.217
 Upside SD0.055
 Downside SD0.057
 N nonnegative terms110.000
 N negative terms1058.000
Statistics related to linear regression on benchmark
 N of observations1168.000
 Mean of predictor0.132
 Mean of criterion-0.016
 SD of predictor0.122
 SD of criterion0.079
 Covariance0.001
 r0.087
 b (slope, estimate of beta)0.057
 a (intercept, estimate of alpha)-0.023
 Mean Square Error0.006
 DF error1166.000
 t(b)2.998
 p(b)0.456
 t(a)-0.544
 p(a)0.508
 Lowerbound of 95% confidence interval for beta0.020
 Upperbound of 95% confidence interval for beta0.094
 Lowerbound of 95% confidence interval for alpha-0.108
 Upperbound of 95% confidence interval for alpha0.061
 Treynor index (mean / b)-0.278
 Jensen alpha (a)-0.023
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.019
 SD0.079
 Sharpe ratio (Glass type estimate) -0.239
 Sharpe ratio (Hedges UMVUE)-0.239
 df1167.000
 t-0.441
 p0.508
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.303
 Upperbound of 95% confidence interval for Sharpe Ratio0.824
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.303
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.825
Statistics related to Sortino ratio
 Sortino ratio-0.330
 Upside Potential Ratio3.476
 Upside part of mean0.200
 Downside part of mean-0.219
 Upside SD0.055
 Downside SD0.058
 N nonnegative terms110.000
 N negative terms1058.000
Statistics related to linear regression on benchmark
 N of observations1168.000
 Mean of predictor0.124
 Mean of criterion-0.019
 SD of predictor0.122
 SD of criterion0.079
 Covariance0.001
 r0.087
 b (slope, estimate of beta)0.057
 a (intercept, estimate of alpha)-0.026
 Mean Square Error0.006
 DF error1166.000
 t(b)2.996
 p(b)0.456
 t(a)-0.607
 p(a)0.509
 Lowerbound of 95% confidence interval for beta0.020
 Upperbound of 95% confidence interval for beta0.094
 Lowerbound of 95% confidence interval for alpha-0.110
 Upperbound of 95% confidence interval for alpha0.058
 Treynor index (mean / b)-0.333
 Jensen alpha (a)-0.026
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 observations1168.000
 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 41.002
 Inter Quartile Range0.000
 Number outliers low70.000
 Percentage of outliers low0.060
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.095
 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)0.006
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)0.026
 Compounded annual return (geometric extrapolation)0.025
 Calmar ratio (compounded annual return / max draw down)0.192
 Compounded annual return / average of 25% largest draw downs0.218
 Compounded annual return / Expected Shortfall lognormal2.867
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 predictor0.068
 Mean of criterion-0.044
 SD of predictor0.133
 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 predictor0.059
 Mean of criterion-0.044
 SD of predictor0.133
 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)-5593907904164720.000
 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)-110743044453571881115505087479808.000
 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