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Advanced Statistics: Bompus Stocks B

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
 Mean0.207
 SD0.323
 Sharpe ratio (Glass type estimate) 0.639
 Sharpe ratio (Hedges UMVUE)0.629
 df49.000
 t1.304
 p0.099
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.333
 Upperbound of 95% confidence interval for Sharpe Ratio1.604
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.339
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.597
Statistics related to Sortino ratio
 Sortino ratio0.969
 Upside Potential Ratio2.474
 Upside part of mean0.527
 Downside part of mean-0.321
 Upside SD0.246
 Downside SD0.213
 N nonnegative terms29.000
 N negative terms21.000
Statistics related to linear regression on benchmark
 N of observations50.000
 Mean of predictor-0.030
 Mean of criterion0.207
 SD of predictor0.265
 SD of criterion0.323
 Covariance0.064
 r0.747
 b (slope, estimate of beta)0.911
 a (intercept, estimate of alpha)0.233
 Mean Square Error0.047
 DF error48.000
 t(b)7.790
 p(b)0.000
 t(a)2.194
 p(a)0.017
 Lowerbound of 95% confidence interval for beta0.676
 Upperbound of 95% confidence interval for beta1.146
 Lowerbound of 95% confidence interval for alpha0.019
 Upperbound of 95% confidence interval for alpha0.447
 Treynor index (mean / b)0.227
 Jensen alpha (a)0.233
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.152
 SD0.331
 Sharpe ratio (Glass type estimate) 0.460
 Sharpe ratio (Hedges UMVUE)0.453
 df49.000
 t0.938
 p0.176
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.507
 Upperbound of 95% confidence interval for Sharpe Ratio1.422
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.512
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.417
Statistics related to Sortino ratio
 Sortino ratio0.638
 Upside Potential Ratio2.089
 Upside part of mean0.498
 Downside part of mean-0.346
 Upside SD0.229
 Downside SD0.238
 N nonnegative terms29.000
 N negative terms21.000
Statistics related to linear regression on benchmark
 N of observations50.000
 Mean of predictor-0.066
 Mean of criterion0.152
 SD of predictor0.279
 SD of criterion0.331
 Covariance0.072
 r0.776
 b (slope, estimate of beta)0.921
 a (intercept, estimate of alpha)0.213
 Mean Square Error0.044
 DF error48.000
 t(b)8.529
 p(b)0.000
 t(a)2.058
 p(a)0.022
 Lowerbound of 95% confidence interval for beta0.704
 Upperbound of 95% confidence interval for beta1.138
 Lowerbound of 95% confidence interval for alpha0.005
 Upperbound of 95% confidence interval for alpha0.421
 Treynor index (mean / b)0.165
 Jensen alpha (a)0.213
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.134
 Expected Shortfall on VaR0.168
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.054
 Expected Shortfall on VaR0.115
ORDER STATISTICS
Quartiles of return rates
 Number of observations50.000
 Minimum0.707
 Quartile 10.984
 Median1.030
 Quartile 31.074
 Maximum1.251
 Mean of quarter 10.908
 Mean of quarter 21.000
 Mean of quarter 31.051
 Mean of quarter 41.125
 Inter Quartile Range0.090
 Number outliers low1.000
 Percentage of outliers low0.020
 Mean of outliers low0.707
 Number of outliers high1.000
 Percentage of outliers high0.020
 Mean of outliers high1.251
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.119
 VaR(95%) (moments method)0.057
 Expected Shortfall (moments method)0.078
 Extreme Value Index (regression method)-0.323
 VaR(95%) (regression method)0.094
 Expected Shortfall (regression method)0.122
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations7.000
 Minimum0.001
 Quartile 10.024
 Median0.051
 Quartile 30.117
 Maximum0.417
 Mean of quarter 10.006
 Mean of quarter 20.044
 Mean of quarter 30.113
 Mean of quarter 40.269
 Inter Quartile Range0.093
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.143
 Mean of outliers high0.417
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)0.303
 Compounded annual return (geometric extrapolation)0.217
 Calmar ratio (compounded annual return / max draw down)0.519
 Compounded annual return / average of 25% largest draw downs0.805
 Compounded annual return / Expected Shortfall lognormal1.291
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.172
 SD0.311
 Sharpe ratio (Glass type estimate) 0.554
 Sharpe ratio (Hedges UMVUE)0.554
 df1455.000
 t1.140
 p0.481
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.399
 Upperbound of 95% confidence interval for Sharpe Ratio1.507
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.399
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.507
Statistics related to Sortino ratio
 Sortino ratio0.811
 Upside Potential Ratio8.987
 Upside part of mean1.908
 Downside part of mean-1.736
 Upside SD0.227
 Downside SD0.212
 N nonnegative terms620.000
 N negative terms836.000
Statistics related to linear regression on benchmark
 N of observations1456.000
 Mean of predictor0.015
 Mean of criterion0.172
 SD of predictor0.288
 SD of criterion0.311
 Covariance0.032
 r0.357
 b (slope, estimate of beta)0.385
 a (intercept, estimate of alpha)0.167
 Mean Square Error0.084
 DF error1454.000
 t(b)14.585
 p(b)0.321
 t(a)1.181
 p(a)0.485
 Lowerbound of 95% confidence interval for beta0.333
 Upperbound of 95% confidence interval for beta0.437
 Lowerbound of 95% confidence interval for alpha-0.110
 Upperbound of 95% confidence interval for alpha0.443
 Treynor index (mean / b)0.447
 Jensen alpha (a)0.167
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.124
 SD0.310
 Sharpe ratio (Glass type estimate) 0.400
 Sharpe ratio (Hedges UMVUE)0.400
 df1455.000
 t0.823
 p0.486
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.553
 Upperbound of 95% confidence interval for Sharpe Ratio1.353
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.553
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.352
Statistics related to Sortino ratio
 Sortino ratio0.573
 Upside Potential Ratio8.690
 Upside part of mean1.883
 Downside part of mean-1.759
 Upside SD0.222
 Downside SD0.217
 N nonnegative terms620.000
 N negative terms836.000
Statistics related to linear regression on benchmark
 N of observations1456.000
 Mean of predictor-0.027
 Mean of criterion0.124
 SD of predictor0.288
 SD of criterion0.310
 Covariance0.032
 r0.356
 b (slope, estimate of beta)0.383
 a (intercept, estimate of alpha)0.134
 Mean Square Error0.084
 DF error1454.000
 t(b)14.519
 p(b)0.322
 t(a)0.953
 p(a)0.488
 Lowerbound of 95% confidence interval for beta0.331
 Upperbound of 95% confidence interval for beta0.434
 Lowerbound of 95% confidence interval for alpha-0.142
 Upperbound of 95% confidence interval for alpha0.411
 Treynor index (mean / b)0.324
 Jensen alpha (a)0.134
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.027
 Expected Shortfall on VaR0.034
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.013
 Expected Shortfall on VaR0.025
ORDER STATISTICS
Quartiles of return rates
 Number of observations1456.000
 Minimum0.893
 Quartile 10.994
 Median1.000
 Quartile 31.007
 Maximum1.134
 Mean of quarter 10.982
 Mean of quarter 20.999
 Mean of quarter 31.002
 Mean of quarter 41.020
 Inter Quartile Range0.013
 Number outliers low80.000
 Percentage of outliers low0.055
 Mean of outliers low0.962
 Number of outliers high75.000
 Percentage of outliers high0.052
 Mean of outliers high1.041
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.301
 VaR(95%) (moments method)0.017
 Expected Shortfall (moments method)0.030
 Extreme Value Index (regression method)0.050
 VaR(95%) (regression method)0.017
 Expected Shortfall (regression method)0.025
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations27.000
 Minimum0.002
 Quartile 10.013
 Median0.028
 Quartile 30.105
 Maximum0.476
 Mean of quarter 10.009
 Mean of quarter 20.023
 Mean of quarter 30.059
 Mean of quarter 40.204
 Inter Quartile Range0.092
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.074
 Mean of outliers high0.368
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.330
 VaR(95%) (moments method)0.230
 Expected Shortfall (moments method)0.381
 Extreme Value Index (regression method)0.950
 VaR(95%) (regression method)0.231
 Expected Shortfall (regression method)3.091
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.245
 Compounded annual return (geometric extrapolation)0.183
 Calmar ratio (compounded annual return / max draw down)0.385
 Compounded annual return / average of 25% largest draw downs0.899
 Compounded annual return / Expected Shortfall lognormal5.455
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.414
 SD0.414
 Sharpe ratio (Glass type estimate) 1.000
 Sharpe ratio (Hedges UMVUE)0.995
 df171.000
 t0.707
 p0.466
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.776
 Upperbound of 95% confidence interval for Sharpe Ratio3.772
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.779
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.769
Statistics related to Sortino ratio
 Sortino ratio1.525
 Upside Potential Ratio11.071
 Upside part of mean3.005
 Downside part of mean-2.591
 Upside SD0.312
 Downside SD0.271
 N nonnegative terms79.000
 N negative terms93.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.695
 Mean of criterion0.414
 SD of predictor0.263
 SD of criterion0.414
 Covariance0.041
 r0.372
 b (slope, estimate of beta)0.585
 a (intercept, estimate of alpha)0.008
 Mean Square Error0.149
 DF error170.000
 t(b)5.225
 p(b)0.314
 t(a)0.014
 p(a)0.499
 Lowerbound of 95% confidence interval for beta0.364
 Upperbound of 95% confidence interval for beta0.805
 Lowerbound of 95% confidence interval for alpha-1.079
 Upperbound of 95% confidence interval for alpha1.095
 Treynor index (mean / b)0.708
 Jensen alpha (a)0.008
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.329
 SD0.413
 Sharpe ratio (Glass type estimate) 0.796
 Sharpe ratio (Hedges UMVUE)0.793
 df171.000
 t0.563
 p0.473
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.978
 Upperbound of 95% confidence interval for Sharpe Ratio3.568
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.980
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.566
Statistics related to Sortino ratio
 Sortino ratio1.189
 Upside Potential Ratio10.694
 Upside part of mean2.958
 Downside part of mean-2.629
 Upside SD0.306
 Downside SD0.277
 N nonnegative terms79.000
 N negative terms93.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.660
 Mean of criterion0.329
 SD of predictor0.262
 SD of criterion0.413
 Covariance0.040
 r0.369
 b (slope, estimate of beta)0.580
 a (intercept, estimate of alpha)-0.054
 Mean Square Error0.148
 DF error170.000
 t(b)5.173
 p(b)0.316
 t(a)-0.098
 p(a)0.504
 Lowerbound of 95% confidence interval for beta0.359
 Upperbound of 95% confidence interval for beta0.802
 Lowerbound of 95% confidence interval for alpha-1.139
 Upperbound of 95% confidence interval for alpha1.031
 Treynor index (mean / b)0.567
 Jensen alpha (a)-0.054
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.035
 Expected Shortfall on VaR0.044
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.034
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.942
 Quartile 10.990
 Median1.000
 Quartile 31.013
 Maximum1.059
 Mean of quarter 10.974
 Mean of quarter 20.996
 Mean of quarter 31.006
 Mean of quarter 41.030
 Inter Quartile Range0.023
 Number outliers low6.000
 Percentage of outliers low0.035
 Mean of outliers low0.950
 Number of outliers high8.000
 Percentage of outliers high0.047
 Mean of outliers high1.054
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.282
 VaR(95%) (moments method)0.024
 Expected Shortfall (moments method)0.029
 Extreme Value Index (regression method)-0.340
 VaR(95%) (regression method)0.027
 Expected Shortfall (regression method)0.033
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations9.000
 Minimum0.008
 Quartile 10.009
 Median0.017
 Quartile 30.112
 Maximum0.260
 Mean of quarter 10.009
 Mean of quarter 20.014
 Mean of quarter 30.067
 Mean of quarter 40.200
 Inter Quartile Range0.103
 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)-0.491
 VaR(95%) (moments method)0.206
 Expected Shortfall (moments method)0.235
 Extreme Value Index (regression method)1.046
 VaR(95%) (regression method)0.311
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.410
 Compounded annual return (geometric extrapolation)0.452
 Calmar ratio (compounded annual return / max draw down)1.738
 Compounded annual return / average of 25% largest draw downs2.256
 Compounded annual return / Expected Shortfall lognormal10.282