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Advanced Statistics: Global Allocation

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
 Mean0.154
 SD0.257
 Sharpe ratio (Glass type estimate) 0.601
 Sharpe ratio (Hedges UMVUE)0.593
 df57.000
 t1.322
 p0.096
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.300
 Upperbound of 95% confidence interval for Sharpe Ratio1.497
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.305
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.491
Statistics related to Sortino ratio
 Sortino ratio1.101
 Upside Potential Ratio2.981
 Upside part of mean0.418
 Downside part of mean-0.263
 Upside SD0.217
 Downside SD0.140
 N nonnegative terms31.000
 N negative terms27.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor0.022
 Mean of criterion0.154
 SD of predictor0.238
 SD of criterion0.257
 Covariance0.019
 r0.309
 b (slope, estimate of beta)0.333
 a (intercept, estimate of alpha)0.147
 Mean Square Error0.061
 DF error56.000
 t(b)2.434
 p(b)0.009
 t(a)1.310
 p(a)0.098
 Lowerbound of 95% confidence interval for beta0.059
 Upperbound of 95% confidence interval for beta0.608
 Lowerbound of 95% confidence interval for alpha-0.078
 Upperbound of 95% confidence interval for alpha0.371
 Treynor index (mean / b)0.463
 Jensen alpha (a)0.147
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.122
 SD0.249
 Sharpe ratio (Glass type estimate) 0.491
 Sharpe ratio (Hedges UMVUE)0.485
 df57.000
 t1.080
 p0.142
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.407
 Upperbound of 95% confidence interval for Sharpe Ratio1.385
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.411
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.381
Statistics related to Sortino ratio
 Sortino ratio0.833
 Upside Potential Ratio2.694
 Upside part of mean0.395
 Downside part of mean-0.273
 Upside SD0.201
 Downside SD0.147
 N nonnegative terms31.000
 N negative terms27.000
Statistics related to linear regression on benchmark
 N of observations58.000
 Mean of predictor-0.007
 Mean of criterion0.122
 SD of predictor0.249
 SD of criterion0.249
 Covariance0.018
 r0.285
 b (slope, estimate of beta)0.284
 a (intercept, estimate of alpha)0.124
 Mean Square Error0.058
 DF error56.000
 t(b)2.222
 p(b)0.015
 t(a)1.135
 p(a)0.131
 Lowerbound of 95% confidence interval for beta0.028
 Upperbound of 95% confidence interval for beta0.540
 Lowerbound of 95% confidence interval for alpha-0.095
 Upperbound of 95% confidence interval for alpha0.343
 Treynor index (mean / b)0.430
 Jensen alpha (a)0.124
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.102
 Expected Shortfall on VaR0.128
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.049
 Expected Shortfall on VaR0.091
ORDER STATISTICS
Quartiles of return rates
 Number of observations58.000
 Minimum0.857
 Quartile 10.966
 Median1.015
 Quartile 31.057
 Maximum1.241
 Mean of quarter 10.931
 Mean of quarter 20.992
 Mean of quarter 31.033
 Mean of quarter 41.110
 Inter Quartile Range0.091
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.034
 Mean of outliers high1.232
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.399
 VaR(95%) (moments method)0.073
 Expected Shortfall (moments method)0.085
 Extreme Value Index (regression method)-0.171
 VaR(95%) (regression method)0.071
 Expected Shortfall (regression method)0.087
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.061
 Quartile 10.064
 Median0.066
 Quartile 30.179
 Maximum0.275
 Mean of quarter 10.062
 Mean of quarter 20.066
 Mean of quarter 30.179
 Mean of quarter 40.275
 Inter Quartile Range0.115
 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)0.255
 Compounded annual return (geometric extrapolation)0.181
 Calmar ratio (compounded annual return / max draw down)0.658
 Compounded annual return / average of 25% largest draw downs0.658
 Compounded annual return / Expected Shortfall lognormal1.407
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.150
 SD0.241
 Sharpe ratio (Glass type estimate) 0.623
 Sharpe ratio (Hedges UMVUE)0.623
 df1673.000
 t1.375
 p0.479
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.265
 Upperbound of 95% confidence interval for Sharpe Ratio1.512
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.266
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.512
Statistics related to Sortino ratio
 Sortino ratio0.910
 Upside Potential Ratio8.444
 Upside part of mean1.391
 Downside part of mean-1.241
 Upside SD0.175
 Downside SD0.165
 N nonnegative terms739.000
 N negative terms935.000
Statistics related to linear regression on benchmark
 N of observations1674.000
 Mean of predictor0.032
 Mean of criterion0.150
 SD of predictor0.260
 SD of criterion0.241
 Covariance0.010
 r0.157
 b (slope, estimate of beta)0.145
 a (intercept, estimate of alpha)0.145
 Mean Square Error0.057
 DF error1672.000
 t(b)6.497
 p(b)0.422
 t(a)1.349
 p(a)0.484
 Lowerbound of 95% confidence interval for beta0.101
 Upperbound of 95% confidence interval for beta0.189
 Lowerbound of 95% confidence interval for alpha-0.066
 Upperbound of 95% confidence interval for alpha0.357
 Treynor index (mean / b)1.033
 Jensen alpha (a)0.145
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.121
 SD0.241
 Sharpe ratio (Glass type estimate) 0.502
 Sharpe ratio (Hedges UMVUE)0.502
 df1673.000
 t1.108
 p0.483
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.387
 Upperbound of 95% confidence interval for Sharpe Ratio1.391
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.387
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.391
Statistics related to Sortino ratio
 Sortino ratio0.718
 Upside Potential Ratio8.171
 Upside part of mean1.376
 Downside part of mean-1.255
 Upside SD0.172
 Downside SD0.168
 N nonnegative terms739.000
 N negative terms935.000
Statistics related to linear regression on benchmark
 N of observations1674.000
 Mean of predictor-0.002
 Mean of criterion0.121
 SD of predictor0.260
 SD of criterion0.241
 Covariance0.010
 r0.155
 b (slope, estimate of beta)0.144
 a (intercept, estimate of alpha)0.121
 Mean Square Error0.057
 DF error1672.000
 t(b)6.436
 p(b)0.422
 t(a)1.124
 p(a)0.486
 Lowerbound of 95% confidence interval for beta0.100
 Upperbound of 95% confidence interval for beta0.188
 Lowerbound of 95% confidence interval for alpha-0.090
 Upperbound of 95% confidence interval for alpha0.333
 Treynor index (mean / b)0.840
 Jensen alpha (a)0.121
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 VaR0.026
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.018
ORDER STATISTICS
Quartiles of return rates
 Number of observations1674.000
 Minimum0.886
 Quartile 10.997
 Median1.000
 Quartile 31.005
 Maximum1.080
 Mean of quarter 10.987
 Mean of quarter 20.999
 Mean of quarter 31.002
 Mean of quarter 41.015
 Inter Quartile Range0.008
 Number outliers low115.000
 Percentage of outliers low0.069
 Mean of outliers low0.973
 Number of outliers high119.000
 Percentage of outliers high0.071
 Mean of outliers high1.029
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.285
 VaR(95%) (moments method)0.011
 Expected Shortfall (moments method)0.019
 Extreme Value Index (regression method)0.209
 VaR(95%) (regression method)0.012
 Expected Shortfall (regression method)0.019
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations34.000
 Minimum0.000
 Quartile 10.007
 Median0.031
 Quartile 30.060
 Maximum0.303
 Mean of quarter 10.003
 Mean of quarter 20.016
 Mean of quarter 30.043
 Mean of quarter 40.132
 Inter Quartile Range0.053
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.088
 Mean of outliers high0.223
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.282
 VaR(95%) (moments method)0.144
 Expected Shortfall (moments method)0.236
 Extreme Value Index (regression method)0.389
 VaR(95%) (regression method)0.140
 Expected Shortfall (regression method)0.247
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.253
 Compounded annual return (geometric extrapolation)0.179
 Calmar ratio (compounded annual return / max draw down)0.592
 Compounded annual return / average of 25% largest draw downs1.359
 Compounded annual return / Expected Shortfall lognormal6.877
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.019
 SD0.272
 Sharpe ratio (Glass type estimate) -0.068
 Sharpe ratio (Hedges UMVUE)-0.068
 df171.000
 t-0.048
 p0.502
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.840
 Upperbound of 95% confidence interval for Sharpe Ratio2.703
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.840
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.704
Statistics related to Sortino ratio
 Sortino ratio-0.092
 Upside Potential Ratio4.271
 Upside part of mean0.865
 Downside part of mean-0.884
 Upside SD0.180
 Downside SD0.203
 N nonnegative terms60.000
 N negative terms112.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.380
 Mean of criterion-0.019
 SD of predictor0.115
 SD of criterion0.272
 Covariance0.000
 r0.007
 b (slope, estimate of beta)0.015
 a (intercept, estimate of alpha)-0.024
 Mean Square Error0.074
 DF error170.000
 t(b)0.086
 p(b)0.497
 t(a)-0.062
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.342
 Upperbound of 95% confidence interval for beta0.373
 Lowerbound of 95% confidence interval for alpha-0.798
 Upperbound of 95% confidence interval for alpha0.749
 Treynor index (mean / b)-1.200
 Jensen alpha (a)-0.024
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.056
 SD0.276
 Sharpe ratio (Glass type estimate) -0.203
 Sharpe ratio (Hedges UMVUE)-0.202
 df171.000
 t-0.144
 p0.507
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.975
 Upperbound of 95% confidence interval for Sharpe Ratio2.569
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.974
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.570
Statistics related to Sortino ratio
 Sortino ratio-0.264
 Upside Potential Ratio3.989
 Upside part of mean0.849
 Downside part of mean-0.905
 Upside SD0.175
 Downside SD0.213
 N nonnegative terms60.000
 N negative terms112.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.373
 Mean of criterion-0.056
 SD of predictor0.115
 SD of criterion0.276
 Covariance0.000
 r0.007
 b (slope, estimate of beta)0.017
 a (intercept, estimate of alpha)-0.063
 Mean Square Error0.077
 DF error170.000
 t(b)0.095
 p(b)0.496
 t(a)-0.157
 p(a)0.506
 Lowerbound of 95% confidence interval for beta-0.346
 Upperbound of 95% confidence interval for beta0.381
 Lowerbound of 95% confidence interval for alpha-0.848
 Upperbound of 95% confidence interval for alpha0.723
 Treynor index (mean / b)-3.213
 Jensen alpha (a)-0.063
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.024
 Expected Shortfall on VaR0.030
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.886
 Quartile 10.998
 Median1.000
 Quartile 31.001
 Maximum1.080
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.010
 Inter Quartile Range0.003
 Number outliers low12.000
 Percentage of outliers low0.070
 Mean of outliers low0.976
 Number of outliers high17.000
 Percentage of outliers high0.099
 Mean of outliers high1.021
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.708
 VaR(95%) (moments method)0.008
 Expected Shortfall (moments method)0.029
 Extreme Value Index (regression method)0.493
 VaR(95%) (regression method)0.007
 Expected Shortfall (regression method)0.015
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.105
 Quartile 10.107
 Median0.110
 Quartile 30.112
 Maximum0.114
 Mean of quarter 10.105
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.114
 Inter Quartile Range0.005
 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)-0.012
 Compounded annual return (geometric extrapolation)-0.012
 Calmar ratio (compounded annual return / max draw down)-0.105
 Compounded annual return / average of 25% largest draw downs-0.105
 Compounded annual return / Expected Shortfall lognormal-0.396