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Advanced Statistics: Dux II

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
 Mean0.086
 SD0.122
 Sharpe ratio (Glass type estimate) 0.702
 Sharpe ratio (Hedges UMVUE)0.675
 df20.000
 t0.928
 p0.398
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.804
 Upperbound of 95% confidence interval for Sharpe Ratio2.190
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.821
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.171
Statistics related to Sortino ratio
 Sortino ratio1.429
 Upside Potential Ratio3.374
 Upside part of mean0.202
 Downside part of mean-0.117
 Upside SD0.106
 Downside SD0.060
 N nonnegative terms12.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.135
 Mean of criterion0.086
 SD of predictor0.121
 SD of criterion0.122
 Covariance-0.001
 r-0.055
 b (slope, estimate of beta)-0.055
 a (intercept, estimate of alpha)0.093
 Mean Square Error0.016
 DF error19.000
 t(b)-0.239
 p(b)0.535
 t(a)0.935
 p(a)0.367
 Lowerbound of 95% confidence interval for beta-0.540
 Upperbound of 95% confidence interval for beta0.429
 Lowerbound of 95% confidence interval for alpha-0.115
 Upperbound of 95% confidence interval for alpha0.302
 Treynor index (mean / b)-1.547
 Jensen alpha (a)0.093
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.078
 SD0.119
 Sharpe ratio (Glass type estimate) 0.655
 Sharpe ratio (Hedges UMVUE)0.630
 df20.000
 t0.867
 p0.405
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.848
 Upperbound of 95% confidence interval for Sharpe Ratio2.143
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.864
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.125
Statistics related to Sortino ratio
 Sortino ratio1.287
 Upside Potential Ratio3.229
 Upside part of mean0.196
 Downside part of mean-0.118
 Upside SD0.102
 Downside SD0.061
 N nonnegative terms12.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.127
 Mean of criterion0.078
 SD of predictor0.119
 SD of criterion0.119
 Covariance-0.001
 r-0.055
 b (slope, estimate of beta)-0.055
 a (intercept, estimate of alpha)0.085
 Mean Square Error0.015
 DF error19.000
 t(b)-0.239
 p(b)0.535
 t(a)0.879
 p(a)0.375
 Lowerbound of 95% confidence interval for beta-0.535
 Upperbound of 95% confidence interval for beta0.426
 Lowerbound of 95% confidence interval for alpha-0.118
 Upperbound of 95% confidence interval for alpha0.288
 Treynor index (mean / b)-1.429
 Jensen alpha (a)0.085
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.049
 Expected Shortfall on VaR0.062
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.021
 Expected Shortfall on VaR0.038
ORDER STATISTICS
Quartiles of return rates
 Number of observations21.000
 Minimum0.967
 Quartile 10.991
 Median1.010
 Quartile 31.019
 Maximum1.099
 Mean of quarter 10.973
 Mean of quarter 21.002
 Mean of quarter 31.016
 Mean of quarter 41.060
 Inter Quartile Range0.028
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.143
 Mean of outliers high1.076
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-174.188
 VaR(95%) (moments method)0.020
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)-2.598
 VaR(95%) (regression method)0.026
 Expected Shortfall (regression method)0.026
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.009
 Quartile 10.018
 Median0.028
 Quartile 30.066
 Maximum0.105
 Mean of quarter 10.009
 Mean of quarter 20.028
 Mean of quarter 3NA
 Mean of quarter 40.105
 Inter Quartile Range0.048
 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)0.136
 Compounded annual return (geometric extrapolation)0.130
 Calmar ratio (compounded annual return / max draw down)1.243
 Compounded annual return / average of 25% largest draw downs1.243
 Compounded annual return / Expected Shortfall lognormal2.082
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.089
 SD0.108
 Sharpe ratio (Glass type estimate) 0.830
 Sharpe ratio (Hedges UMVUE)0.829
 df619.000
 t1.114
 p0.133
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.631
 Upperbound of 95% confidence interval for Sharpe Ratio2.290
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.632
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.290
Statistics related to Sortino ratio
 Sortino ratio1.313
 Upside Potential Ratio9.586
 Upside part of mean0.652
 Downside part of mean-0.562
 Upside SD0.083
 Downside SD0.068
 N nonnegative terms248.000
 N negative terms372.000
Statistics related to linear regression on benchmark
 N of observations620.000
 Mean of predictor0.165
 Mean of criterion0.089
 SD of predictor0.165
 SD of criterion0.108
 Covariance0.000
 r0.000
 b (slope, estimate of beta)0.000
 a (intercept, estimate of alpha)0.089
 Mean Square Error0.012
 DF error618.000
 t(b)0.011
 p(b)0.496
 t(a)1.111
 p(a)0.133
 Lowerbound of 95% confidence interval for beta-0.051
 Upperbound of 95% confidence interval for beta0.052
 Lowerbound of 95% confidence interval for alpha-0.068
 Upperbound of 95% confidence interval for alpha0.247
 Treynor index (mean / b)315.609
 Jensen alpha (a)0.089
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.083
 SD0.107
 Sharpe ratio (Glass type estimate) 0.778
 Sharpe ratio (Hedges UMVUE)0.777
 df619.000
 t1.044
 p0.148
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.683
 Upperbound of 95% confidence interval for Sharpe Ratio2.238
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.684
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.238
Statistics related to Sortino ratio
 Sortino ratio1.220
 Upside Potential Ratio9.473
 Upside part of mean0.648
 Downside part of mean-0.565
 Upside SD0.083
 Downside SD0.068
 N nonnegative terms248.000
 N negative terms372.000
Statistics related to linear regression on benchmark
 N of observations620.000
 Mean of predictor0.151
 Mean of criterion0.083
 SD of predictor0.165
 SD of criterion0.107
 Covariance0.000
 r0.000
 b (slope, estimate of beta)0.000
 a (intercept, estimate of alpha)0.083
 Mean Square Error0.012
 DF error618.000
 t(b)0.011
 p(b)0.496
 t(a)1.042
 p(a)0.149
 Lowerbound of 95% confidence interval for beta-0.051
 Upperbound of 95% confidence interval for beta0.052
 Lowerbound of 95% confidence interval for alpha-0.074
 Upperbound of 95% confidence interval for alpha0.241
 Treynor index (mean / b)290.111
 Jensen alpha (a)0.083
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.012
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 observations620.000
 Minimum0.973
 Quartile 10.998
 Median1.000
 Quartile 31.002
 Maximum1.031
 Mean of quarter 10.994
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.007
 Inter Quartile Range0.004
 Number outliers low36.000
 Percentage of outliers low0.058
 Mean of outliers low0.988
 Number of outliers high48.000
 Percentage of outliers high0.077
 Mean of outliers high1.014
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.242
 VaR(95%) (moments method)0.005
 Expected Shortfall (moments method)0.009
 Extreme Value Index (regression method)0.045
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.008
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations26.000
 Minimum0.001
 Quartile 10.002
 Median0.008
 Quartile 30.015
 Maximum0.120
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.011
 Mean of quarter 40.056
 Inter Quartile Range0.013
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high5.000
 Percentage of outliers high0.192
 Mean of outliers high0.071
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.614
 VaR(95%) (moments method)0.046
 Expected Shortfall (moments method)0.053
 Extreme Value Index (regression method)-0.128
 VaR(95%) (regression method)0.083
 Expected Shortfall (regression method)0.116
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.143
 Compounded annual return (geometric extrapolation)0.136
 Calmar ratio (compounded annual return / max draw down)1.137
 Compounded annual return / average of 25% largest draw downs2.424
 Compounded annual return / Expected Shortfall lognormal11.701
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.129
 SD0.064
 Sharpe ratio (Glass type estimate) -1.996
 Sharpe ratio (Hedges UMVUE)-1.988
 df171.000
 t-1.412
 p0.568
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.773
 Upperbound of 95% confidence interval for Sharpe Ratio0.786
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.767
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.792
Statistics related to Sortino ratio
 Sortino ratio-2.528
 Upside Potential Ratio6.039
 Upside part of mean0.307
 Downside part of mean-0.436
 Upside SD0.040
 Downside SD0.051
 N nonnegative terms64.000
 N negative terms108.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.377
 Mean of criterion-0.129
 SD of predictor0.115
 SD of criterion0.064
 Covariance0.001
 r0.080
 b (slope, estimate of beta)0.045
 a (intercept, estimate of alpha)-0.145
 Mean Square Error0.004
 DF error170.000
 t(b)1.042
 p(b)0.460
 t(a)-1.572
 p(a)0.560
 Lowerbound of 95% confidence interval for beta-0.040
 Upperbound of 95% confidence interval for beta0.129
 Lowerbound of 95% confidence interval for alpha-0.328
 Upperbound of 95% confidence interval for alpha0.037
 Treynor index (mean / b)-2.888
 Jensen alpha (a)-0.145
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.131
 SD0.065
 Sharpe ratio (Glass type estimate) -2.026
 Sharpe ratio (Hedges UMVUE)-2.017
 df171.000
 t-1.433
 p0.569
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.804
 Upperbound of 95% confidence interval for Sharpe Ratio0.757
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.797
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.763
Statistics related to Sortino ratio
 Sortino ratio-2.558
 Upside Potential Ratio5.996
 Upside part of mean0.307
 Downside part of mean-0.437
 Upside SD0.040
 Downside SD0.051
 N nonnegative terms64.000
 N negative terms108.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.370
 Mean of criterion-0.131
 SD of predictor0.115
 SD of criterion0.065
 Covariance0.001
 r0.080
 b (slope, estimate of beta)0.045
 a (intercept, estimate of alpha)-0.147
 Mean Square Error0.004
 DF error170.000
 t(b)1.047
 p(b)0.460
 t(a)-1.592
 p(a)0.561
 Lowerbound of 95% confidence interval for beta-0.040
 Upperbound of 95% confidence interval for beta0.129
 Lowerbound of 95% confidence interval for alpha-0.330
 Upperbound of 95% confidence interval for alpha0.035
 Treynor index (mean / b)-2.913
 Jensen alpha (a)-0.147
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.008
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.007
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.985
 Quartile 10.999
 Median1.000
 Quartile 31.001
 Maximum1.012
 Mean of quarter 10.996
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.004
 Inter Quartile Range0.002
 Number outliers low12.000
 Percentage of outliers low0.070
 Mean of outliers low0.992
 Number of outliers high10.000
 Percentage of outliers high0.058
 Mean of outliers high1.008
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.163
 VaR(95%) (moments method)0.004
 Expected Shortfall (moments method)0.006
 Extreme Value Index (regression method)-0.106
 VaR(95%) (regression method)0.004
 Expected Shortfall (regression method)0.005
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.000
 Quartile 10.002
 Median0.003
 Quartile 30.034
 Maximum0.088
 Mean of quarter 10.001
 Mean of quarter 20.003
 Mean of quarter 30.034
 Mean of quarter 40.088
 Inter Quartile Range0.032
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.200
 Mean of outliers high0.088
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)-0.085
 Compounded annual return (geometric extrapolation)-0.083
 Calmar ratio (compounded annual return / max draw down)-0.941
 Compounded annual return / average of 25% largest draw downs-0.941
 Compounded annual return / Expected Shortfall lognormal-11.038