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-0.017
 SD0.079
 Sharpe ratio (Glass type estimate) -0.213
 Sharpe ratio (Hedges UMVUE)-0.209
 df41.000
 t-0.399
 p0.654
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.261
 Upperbound of 95% confidence interval for Sharpe Ratio0.837
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.258
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.839
Statistics related to Sortino ratio
 Sortino ratio-0.319
 Upside Potential Ratio1.211
 Upside part of mean0.064
 Downside part of mean-0.080
 Upside SD0.057
 Downside SD0.053
 N nonnegative terms5.000
 N negative terms37.000
Statistics related to linear regression on benchmark
 N of observations42.000
 Mean of predictor0.121
 Mean of criterion-0.017
 SD of predictor0.097
 SD of criterion0.079
 Covariance0.001
 r0.141
 b (slope, estimate of beta)0.115
 a (intercept, estimate of alpha)-0.031
 Mean Square Error0.006
 DF error40.000
 t(b)0.901
 p(b)0.186
 t(a)-0.684
 p(a)0.751
 Lowerbound of 95% confidence interval for beta-0.143
 Upperbound of 95% confidence interval for beta0.373
 Lowerbound of 95% confidence interval for alpha-0.121
 Upperbound of 95% confidence interval for alpha0.060
 Treynor index (mean / b)-0.146
 Jensen alpha (a)-0.031
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.020
 SD0.078
 Sharpe ratio (Glass type estimate) -0.252
 Sharpe ratio (Hedges UMVUE)-0.247
 df41.000
 t-0.471
 p0.680
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.300
 Upperbound of 95% confidence interval for Sharpe Ratio0.799
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.296
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.802
Statistics related to Sortino ratio
 Sortino ratio-0.365
 Upside Potential Ratio1.145
 Upside part of mean0.062
 Downside part of mean-0.082
 Upside SD0.056
 Downside SD0.054
 N nonnegative terms5.000
 N negative terms37.000
Statistics related to linear regression on benchmark
 N of observations42.000
 Mean of predictor0.115
 Mean of criterion-0.020
 SD of predictor0.095
 SD of criterion0.078
 Covariance0.001
 r0.147
 b (slope, estimate of beta)0.121
 a (intercept, estimate of alpha)-0.034
 Mean Square Error0.006
 DF error40.000
 t(b)0.942
 p(b)0.176
 t(a)-0.758
 p(a)0.774
 Lowerbound of 95% confidence interval for beta-0.139
 Upperbound of 95% confidence interval for beta0.381
 Lowerbound of 95% confidence interval for alpha-0.124
 Upperbound of 95% confidence interval for alpha0.056
 Treynor index (mean / b)-0.163
 Jensen alpha (a)-0.034
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.038
 Expected Shortfall on VaR0.047
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 observations42.000
 Minimum0.930
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.074
 Mean of quarter 10.987
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.022
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.071
 Mean of outliers low0.951
 Number of outliers high6.000
 Percentage of outliers high0.143
 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)0.050
 Expected Shortfall (regression method)0.072
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)0.025
 Compounded annual return (geometric extrapolation)0.025
 Calmar ratio (compounded annual return / max draw down)0.353
 Compounded annual return / average of 25% largest draw downs0.353
 Compounded annual return / Expected Shortfall lognormal0.522
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.017
 SD0.077
 Sharpe ratio (Glass type estimate) -0.221
 Sharpe ratio (Hedges UMVUE)-0.221
 df1223.000
 t-0.417
 p0.508
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.260
 Upperbound of 95% confidence interval for Sharpe Ratio0.818
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.260
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.818
Statistics related to Sortino ratio
 Sortino ratio-0.309
 Upside Potential Ratio3.464
 Upside part of mean0.192
 Downside part of mean-0.209
 Upside SD0.054
 Downside SD0.055
 N nonnegative terms110.000
 N negative terms1114.000
Statistics related to linear regression on benchmark
 N of observations1224.000
 Mean of predictor0.125
 Mean of criterion-0.017
 SD of predictor0.122
 SD of criterion0.077
 Covariance0.001
 r0.086
 b (slope, estimate of beta)0.055
 a (intercept, estimate of alpha)-0.024
 Mean Square Error0.006
 DF error1222.000
 t(b)3.006
 p(b)0.457
 t(a)-0.584
 p(a)0.508
 Lowerbound of 95% confidence interval for beta0.019
 Upperbound of 95% confidence interval for beta0.090
 Lowerbound of 95% confidence interval for alpha-0.104
 Upperbound of 95% confidence interval for alpha0.056
 Treynor index (mean / b)-0.314
 Jensen alpha (a)-0.024
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.020
 SD0.078
 Sharpe ratio (Glass type estimate) -0.260
 Sharpe ratio (Hedges UMVUE)-0.260
 df1223.000
 t-0.490
 p0.509
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.299
 Upperbound of 95% confidence interval for Sharpe Ratio0.779
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.299
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.780
Statistics related to Sortino ratio
 Sortino ratio-0.358
 Upside Potential Ratio3.395
 Upside part of mean0.191
 Downside part of mean-0.211
 Upside SD0.053
 Downside SD0.056
 N nonnegative terms110.000
 N negative terms1114.000
Statistics related to linear regression on benchmark
 N of observations1224.000
 Mean of predictor0.117
 Mean of criterion-0.020
 SD of predictor0.121
 SD of criterion0.078
 Covariance0.001
 r0.086
 b (slope, estimate of beta)0.055
 a (intercept, estimate of alpha)-0.027
 Mean Square Error0.006
 DF error1222.000
 t(b)3.003
 p(b)0.457
 t(a)-0.647
 p(a)0.509
 Lowerbound of 95% confidence interval for beta0.019
 Upperbound of 95% confidence interval for beta0.090
 Lowerbound of 95% confidence interval for alpha-0.107
 Upperbound of 95% confidence interval for alpha0.054
 Treynor index (mean / b)-0.368
 Jensen alpha (a)-0.027
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 VaR0.004
ORDER STATISTICS
Quartiles of return rates
 Number of observations1224.000
 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 low0.057
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.091
 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)0.025
 Compounded annual return (geometric extrapolation)0.024
 Calmar ratio (compounded annual return / max draw down)0.183
 Compounded annual return / average of 25% largest draw downs0.208
 Compounded annual return / Expected Shortfall lognormal2.798
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 predictor0.052
 Mean of criterion-0.044
 SD of predictor0.121
 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 predictor0.044
 Mean of criterion-0.044
 SD of predictor0.121
 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)-5594455988942123.000
 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)-53351624040627519258490033930240.000
 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