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Advanced Statistics: CYCLE

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-0.090
 SD0.028
 Sharpe ratio (Glass type estimate) -3.157
 Sharpe ratio (Hedges UMVUE)-2.284
 df3.000
 t-1.823
 p0.917
 Lowerbound of 95% confidence interval for Sharpe Ratio-7.164
 Upperbound of 95% confidence interval for Sharpe Ratio1.156
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.140
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.571
Statistics related to Sortino ratio
 Sortino ratio-2.511
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.090
 Upside SD0.000
 Downside SD0.036
 N nonnegative terms0.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations4.000
 Mean of predictor0.663
 Mean of criterion-0.090
 SD of predictor0.292
 SD of criterion0.028
 Covariance0.003
 r0.401
 b (slope, estimate of beta)0.039
 a (intercept, estimate of alpha)-0.116
 Mean Square Error0.001
 DF error2.000
 t(b)0.619
 p(b)0.299
 t(a)-1.669
 p(a)0.882
 Lowerbound of 95% confidence interval for beta-0.232
 Upperbound of 95% confidence interval for beta0.311
 Lowerbound of 95% confidence interval for alpha-0.415
 Upperbound of 95% confidence interval for alpha0.183
 Treynor index (mean / b)-2.301
 Jensen alpha (a)-0.116
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.090
 SD0.029
 Sharpe ratio (Glass type estimate) -3.145
 Sharpe ratio (Hedges UMVUE)-2.276
 df3.000
 t-1.816
 p0.916
 Lowerbound of 95% confidence interval for Sharpe Ratio-7.147
 Upperbound of 95% confidence interval for Sharpe Ratio1.162
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.128
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.577
Statistics related to Sortino ratio
 Sortino ratio-2.507
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.090
 Upside SD0.000
 Downside SD0.036
 N nonnegative terms0.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations4.000
 Mean of predictor0.616
 Mean of criterion-0.090
 SD of predictor0.269
 SD of criterion0.029
 Covariance0.003
 r0.417
 b (slope, estimate of beta)0.045
 a (intercept, estimate of alpha)-0.118
 Mean Square Error0.001
 DF error2.000
 t(b)0.649
 p(b)0.291
 t(a)-1.690
 p(a)0.883
 Lowerbound of 95% confidence interval for beta-0.251
 Upperbound of 95% confidence interval for beta0.340
 Lowerbound of 95% confidence interval for alpha-0.417
 Upperbound of 95% confidence interval for alpha0.182
 Treynor index (mean / b)-2.024
 Jensen alpha (a)-0.118
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.021
 Expected Shortfall on VaR0.024
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.028
ORDER STATISTICS
Quartiles of return rates
 Number of observations4.000
 Minimum0.984
 Quartile 10.995
 Median0.999
 Quartile 31.000
 Maximum1.003
 Mean of quarter 10.984
 Mean of quarter 20.999
 Mean of quarter 30.999
 Mean of quarter 41.003
 Inter Quartile Range0.005
 Number outliers low1.000
 Percentage of outliers low0.250
 Mean of outliers low0.984
 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 observations1.000
 Minimum0.017
 Quartile 10.017
 Median0.017
 Quartile 30.017
 Maximum0.017
 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 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)-0.046
 Compounded annual return (geometric extrapolation)-0.045
 Calmar ratio (compounded annual return / max draw down)-2.691
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.859
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.082
 SD0.126
 Sharpe ratio (Glass type estimate) -0.655
 Sharpe ratio (Hedges UMVUE)-0.651
 df114.000
 t-0.379
 p0.518
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.045
 Upperbound of 95% confidence interval for Sharpe Ratio2.737
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.042
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.740
Statistics related to Sortino ratio
 Sortino ratio-0.957
 Upside Potential Ratio8.853
 Upside part of mean0.762
 Downside part of mean-0.844
 Upside SD0.091
 Downside SD0.086
 N nonnegative terms47.000
 N negative terms68.000
Statistics related to linear regression on benchmark
 N of observations115.000
 Mean of predictor0.638
 Mean of criterion-0.082
 SD of predictor0.219
 SD of criterion0.126
 Covariance0.010
 r0.377
 b (slope, estimate of beta)0.216
 a (intercept, estimate of alpha)-0.220
 Mean Square Error0.014
 DF error113.000
 t(b)4.326
 p(b)0.266
 t(a)-1.077
 p(a)0.564
 Lowerbound of 95% confidence interval for beta0.117
 Upperbound of 95% confidence interval for beta0.315
 Lowerbound of 95% confidence interval for alpha-0.626
 Upperbound of 95% confidence interval for alpha0.185
 Treynor index (mean / b)-0.381
 Jensen alpha (a)-0.220
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.090
 SD0.125
 Sharpe ratio (Glass type estimate) -0.719
 Sharpe ratio (Hedges UMVUE)-0.714
 df114.000
 t-0.415
 p0.519
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.108
 Upperbound of 95% confidence interval for Sharpe Ratio2.674
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.105
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.677
Statistics related to Sortino ratio
 Sortino ratio-1.041
 Upside Potential Ratio8.753
 Upside part of mean0.758
 Downside part of mean-0.848
 Upside SD0.090
 Downside SD0.087
 N nonnegative terms47.000
 N negative terms68.000
Statistics related to linear regression on benchmark
 N of observations115.000
 Mean of predictor0.614
 Mean of criterion-0.090
 SD of predictor0.218
 SD of criterion0.125
 Covariance0.010
 r0.376
 b (slope, estimate of beta)0.216
 a (intercept, estimate of alpha)-0.223
 Mean Square Error0.014
 DF error113.000
 t(b)4.311
 p(b)0.267
 t(a)-1.090
 p(a)0.565
 Lowerbound of 95% confidence interval for beta0.117
 Upperbound of 95% confidence interval for beta0.315
 Lowerbound of 95% confidence interval for alpha-0.627
 Upperbound of 95% confidence interval for alpha0.182
 Treynor index (mean / b)-0.417
 Jensen alpha (a)-0.223
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.014
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.012
ORDER STATISTICS
Quartiles of return rates
 Number of observations115.000
 Minimum0.981
 Quartile 10.997
 Median1.000
 Quartile 31.003
 Maximum1.022
 Mean of quarter 10.992
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.008
 Inter Quartile Range0.006
 Number outliers low5.000
 Percentage of outliers low0.043
 Mean of outliers low0.985
 Number of outliers high7.000
 Percentage of outliers high0.061
 Mean of outliers high1.017
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.472
 VaR(95%) (moments method)0.008
 Expected Shortfall (moments method)0.009
 Extreme Value Index (regression method)-0.292
 VaR(95%) (regression method)0.008
 Expected Shortfall (regression method)0.010
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.020
 Quartile 10.031
 Median0.042
 Quartile 30.055
 Maximum0.067
 Mean of quarter 10.020
 Mean of quarter 20.042
 Mean of quarter 3NA
 Mean of quarter 40.067
 Inter Quartile Range0.024
 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)-0.046
 Compounded annual return (geometric extrapolation)-0.045
 Calmar ratio (compounded annual return / max draw down)-0.669
 Compounded annual return / average of 25% largest draw downs-0.669
 Compounded annual return / Expected Shortfall lognormal-3.194