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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
 Mean0.020
 SD0.121
 Sharpe ratio (Glass type estimate) 0.162
 Sharpe ratio (Hedges UMVUE)0.154
 df17.000
 t0.198
 p0.469
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.442
 Upperbound of 95% confidence interval for Sharpe Ratio1.761
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.447
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.756
Statistics related to Sortino ratio
 Sortino ratio0.248
 Upside Potential Ratio1.881
 Upside part of mean0.149
 Downside part of mean-0.129
 Upside SD0.088
 Downside SD0.079
 N nonnegative terms5.000
 N negative terms13.000
Statistics related to linear regression on benchmark
 N of observations18.000
 Mean of predictor0.175
 Mean of criterion0.020
 SD of predictor0.098
 SD of criterion0.121
 Covariance0.002
 r0.191
 b (slope, estimate of beta)0.236
 a (intercept, estimate of alpha)-0.022
 Mean Square Error0.015
 DF error16.000
 t(b)0.780
 p(b)0.404
 t(a)-0.191
 p(a)0.524
 Lowerbound of 95% confidence interval for beta-0.406
 Upperbound of 95% confidence interval for beta0.879
 Lowerbound of 95% confidence interval for alpha-0.262
 Upperbound of 95% confidence interval for alpha0.219
 Treynor index (mean / b)0.083
 Jensen alpha (a)-0.022
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.013
 SD0.121
 Sharpe ratio (Glass type estimate) 0.104
 Sharpe ratio (Hedges UMVUE)0.100
 df17.000
 t0.128
 p0.480
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.498
 Upperbound of 95% confidence interval for Sharpe Ratio1.704
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.501
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.700
Statistics related to Sortino ratio
 Sortino ratio0.155
 Upside Potential Ratio1.777
 Upside part of mean0.144
 Downside part of mean-0.132
 Upside SD0.085
 Downside SD0.081
 N nonnegative terms5.000
 N negative terms13.000
Statistics related to linear regression on benchmark
 N of observations18.000
 Mean of predictor0.168
 Mean of criterion0.013
 SD of predictor0.097
 SD of criterion0.121
 Covariance0.002
 r0.204
 b (slope, estimate of beta)0.254
 a (intercept, estimate of alpha)-0.030
 Mean Square Error0.015
 DF error16.000
 t(b)0.831
 p(b)0.398
 t(a)-0.268
 p(a)0.533
 Lowerbound of 95% confidence interval for beta-0.393
 Upperbound of 95% confidence interval for beta0.901
 Lowerbound of 95% confidence interval for alpha-0.268
 Upperbound of 95% confidence interval for alpha0.208
 Treynor index (mean / b)0.050
 Jensen alpha (a)-0.030
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.055
 Expected Shortfall on VaR0.068
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.031
 Expected Shortfall on VaR0.059
ORDER STATISTICS
Quartiles of return rates
 Number of observations18.000
 Minimum0.930
 Quartile 11.000
 Median1.000
 Quartile 31.020
 Maximum1.074
 Mean of quarter 10.971
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.048
 Inter Quartile Range0.020
 Number outliers low2.000
 Percentage of outliers low0.111
 Mean of outliers low0.940
 Number of outliers high2.000
 Percentage of outliers high0.111
 Mean of outliers high1.068
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)0.076
 Expected Shortfall (regression method)0.084
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)0.059
 Compounded annual return (geometric extrapolation)0.058
 Calmar ratio (compounded annual return / max draw down)0.838
 Compounded annual return / average of 25% largest draw downs0.838
 Compounded annual return / Expected Shortfall lognormal0.852
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.019
 SD0.119
 Sharpe ratio (Glass type estimate) 0.159
 Sharpe ratio (Hedges UMVUE)0.159
 df522.000
 t0.197
 p0.422
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.430
 Upperbound of 95% confidence interval for Sharpe Ratio1.749
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.430
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.749
Statistics related to Sortino ratio
 Sortino ratio0.223
 Upside Potential Ratio5.302
 Upside part of mean0.450
 Downside part of mean-0.431
 Upside SD0.083
 Downside SD0.085
 N nonnegative terms110.000
 N negative terms413.000
Statistics related to linear regression on benchmark
 N of observations523.000
 Mean of predictor0.188
 Mean of criterion0.019
 SD of predictor0.133
 SD of criterion0.119
 Covariance0.002
 r0.119
 b (slope, estimate of beta)0.106
 a (intercept, estimate of alpha)-0.001
 Mean Square Error0.014
 DF error521.000
 t(b)2.732
 p(b)0.003
 t(a)-0.010
 p(a)0.504
 Lowerbound of 95% confidence interval for beta0.030
 Upperbound of 95% confidence interval for beta0.182
 Lowerbound of 95% confidence interval for alpha-0.189
 Upperbound of 95% confidence interval for alpha0.187
 Treynor index (mean / b)0.179
 Jensen alpha (a)-0.001
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.012
 SD0.119
 Sharpe ratio (Glass type estimate) 0.100
 Sharpe ratio (Hedges UMVUE)0.100
 df522.000
 t0.123
 p0.451
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.489
 Upperbound of 95% confidence interval for Sharpe Ratio1.690
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.490
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.690
Statistics related to Sortino ratio
 Sortino ratio0.138
 Upside Potential Ratio5.197
 Upside part of mean0.446
 Downside part of mean-0.434
 Upside SD0.082
 Downside SD0.086
 N nonnegative terms110.000
 N negative terms413.000
Statistics related to linear regression on benchmark
 N of observations523.000
 Mean of predictor0.179
 Mean of criterion0.012
 SD of predictor0.133
 SD of criterion0.119
 Covariance0.002
 r0.119
 b (slope, estimate of beta)0.106
 a (intercept, estimate of alpha)-0.007
 Mean Square Error0.014
 DF error521.000
 t(b)2.735
 p(b)0.003
 t(a)-0.074
 p(a)0.529
 Lowerbound of 95% confidence interval for beta0.030
 Upperbound of 95% confidence interval for beta0.182
 Lowerbound of 95% confidence interval for alpha-0.195
 Upperbound of 95% confidence interval for alpha0.181
 Treynor index (mean / b)0.112
 Jensen alpha (a)-0.007
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.013
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.008
ORDER STATISTICS
Quartiles of return rates
 Number of observations523.000
 Minimum0.963
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.037
 Mean of quarter 10.995
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.005
 Inter Quartile Range0.000
 Number outliers low70.000
 Percentage of outliers low0.134
 Mean of outliers low0.991
 Number of outliers high111.000
 Percentage of outliers high0.212
 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)0.002
 Expected Shortfall (moments method)0.005
 Extreme Value Index (regression method)0.070
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.011
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)0.058
 Compounded annual return (geometric extrapolation)0.057
 Calmar ratio (compounded annual return / max draw down)0.436
 Compounded annual return / average of 25% largest draw downs0.495
 Compounded annual return / Expected Shortfall lognormal4.399
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 predictor0.341
 Mean of criterion-0.044
 SD of predictor0.119
 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 predictor0.334
 Mean of criterion-0.044
 SD of predictor0.119
 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)-5532190328353218.000
 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)12735596804952192075225626574848.000
 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