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Advanced Statistics: MultiTrader

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
 Mean0.081
 SD0.117
 Sharpe ratio (Glass type estimate) 0.696
 Sharpe ratio (Hedges UMVUE)0.674
 df24.000
 t1.005
 p0.162
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.683
 Upperbound of 95% confidence interval for Sharpe Ratio2.061
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.697
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.046
Statistics related to Sortino ratio
 Sortino ratio1.434
 Upside Potential Ratio3.314
 Upside part of mean0.188
 Downside part of mean-0.106
 Upside SD0.102
 Downside SD0.057
 N nonnegative terms15.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations25.000
 Mean of predictor0.193
 Mean of criterion0.081
 SD of predictor0.176
 SD of criterion0.117
 Covariance0.010
 r0.471
 b (slope, estimate of beta)0.313
 a (intercept, estimate of alpha)0.021
 Mean Square Error0.011
 DF error23.000
 t(b)2.563
 p(b)0.009
 t(a)0.271
 p(a)0.394
 Lowerbound of 95% confidence interval for beta0.060
 Upperbound of 95% confidence interval for beta0.565
 Lowerbound of 95% confidence interval for alpha-0.137
 Upperbound of 95% confidence interval for alpha0.179
 Treynor index (mean / b)0.260
 Jensen alpha (a)0.021
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.074
 SD0.113
 Sharpe ratio (Glass type estimate) 0.659
 Sharpe ratio (Hedges UMVUE)0.638
 df24.000
 t0.951
 p0.175
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.718
 Upperbound of 95% confidence interval for Sharpe Ratio2.023
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.732
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.008
Statistics related to Sortino ratio
 Sortino ratio1.296
 Upside Potential Ratio3.171
 Upside part of mean0.182
 Downside part of mean-0.108
 Upside SD0.097
 Downside SD0.057
 N nonnegative terms15.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations25.000
 Mean of predictor0.177
 Mean of criterion0.074
 SD of predictor0.175
 SD of criterion0.113
 Covariance0.009
 r0.471
 b (slope, estimate of beta)0.303
 a (intercept, estimate of alpha)0.021
 Mean Square Error0.010
 DF error23.000
 t(b)2.559
 p(b)0.009
 t(a)0.284
 p(a)0.389
 Lowerbound of 95% confidence interval for beta0.058
 Upperbound of 95% confidence interval for beta0.548
 Lowerbound of 95% confidence interval for alpha-0.131
 Upperbound of 95% confidence interval for alpha0.173
 Treynor index (mean / b)0.246
 Jensen alpha (a)0.021
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.046
 Expected Shortfall on VaR0.059
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 observations25.000
 Minimum0.957
 Quartile 10.989
 Median1.016
 Quartile 31.023
 Maximum1.129
 Mean of quarter 10.975
 Mean of quarter 21.004
 Mean of quarter 31.022
 Mean of quarter 41.047
 Inter Quartile Range0.034
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.040
 Mean of outliers high1.129
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.678
 VaR(95%) (moments method)0.026
 Expected Shortfall (moments method)0.029
 Extreme Value Index (regression method)-0.361
 VaR(95%) (regression method)0.026
 Expected Shortfall (regression method)0.031
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations4.000
 Minimum0.014
 Quartile 10.015
 Median0.024
 Quartile 30.043
 Maximum0.075
 Mean of quarter 10.014
 Mean of quarter 20.015
 Mean of quarter 30.033
 Mean of quarter 40.075
 Inter Quartile Range0.028
 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)0.134
 Compounded annual return (geometric extrapolation)0.126
 Calmar ratio (compounded annual return / max draw down)1.684
 Compounded annual return / average of 25% largest draw downs1.684
 Compounded annual return / Expected Shortfall lognormal2.126
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.075
 SD0.180
 Sharpe ratio (Glass type estimate) 0.418
 Sharpe ratio (Hedges UMVUE)0.418
 df734.000
 t0.612
 p0.270
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.923
 Upperbound of 95% confidence interval for Sharpe Ratio1.759
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.923
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.759
Statistics related to Sortino ratio
 Sortino ratio0.696
 Upside Potential Ratio6.928
 Upside part of mean0.750
 Downside part of mean-0.675
 Upside SD0.144
 Downside SD0.108
 N nonnegative terms349.000
 N negative terms386.000
Statistics related to linear regression on benchmark
 N of observations735.000
 Mean of predictor0.270
 Mean of criterion0.075
 SD of predictor0.231
 SD of criterion0.180
 Covariance0.004
 r0.107
 b (slope, estimate of beta)0.084
 a (intercept, estimate of alpha)0.053
 Mean Square Error0.032
 DF error733.000
 t(b)2.923
 p(b)0.002
 t(a)0.430
 p(a)0.334
 Lowerbound of 95% confidence interval for beta0.028
 Upperbound of 95% confidence interval for beta0.140
 Lowerbound of 95% confidence interval for alpha-0.189
 Upperbound of 95% confidence interval for alpha0.294
 Treynor index (mean / b)0.901
 Jensen alpha (a)0.053
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.060
 SD0.177
 Sharpe ratio (Glass type estimate) 0.336
 Sharpe ratio (Hedges UMVUE)0.336
 df734.000
 t0.491
 p0.312
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.005
 Upperbound of 95% confidence interval for Sharpe Ratio1.677
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.005
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.677
Statistics related to Sortino ratio
 Sortino ratio0.535
 Upside Potential Ratio6.653
 Upside part of mean0.741
 Downside part of mean-0.681
 Upside SD0.138
 Downside SD0.111
 N nonnegative terms349.000
 N negative terms386.000
Statistics related to linear regression on benchmark
 N of observations735.000
 Mean of predictor0.243
 Mean of criterion0.060
 SD of predictor0.231
 SD of criterion0.177
 Covariance0.004
 r0.108
 b (slope, estimate of beta)0.083
 a (intercept, estimate of alpha)0.039
 Mean Square Error0.031
 DF error733.000
 t(b)2.934
 p(b)0.002
 t(a)0.326
 p(a)0.372
 Lowerbound of 95% confidence interval for beta0.027
 Upperbound of 95% confidence interval for beta0.138
 Lowerbound of 95% confidence interval for alpha-0.198
 Upperbound of 95% confidence interval for alpha0.277
 Treynor index (mean / b)0.720
 Jensen alpha (a)0.039
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.015
 Expected Shortfall on VaR0.019
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.010
ORDER STATISTICS
Quartiles of return rates
 Number of observations735.000
 Minimum0.915
 Quartile 10.998
 Median1.000
 Quartile 31.003
 Maximum1.138
 Mean of quarter 10.993
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.008
 Inter Quartile Range0.005
 Number outliers low32.000
 Percentage of outliers low0.044
 Mean of outliers low0.982
 Number of outliers high19.000
 Percentage of outliers high0.026
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.509
 VaR(95%) (moments method)0.007
 Expected Shortfall (moments method)0.015
 Extreme Value Index (regression method)0.400
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.011
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations35.000
 Minimum0.000
 Quartile 10.003
 Median0.007
 Quartile 30.019
 Maximum0.119
 Mean of quarter 10.001
 Mean of quarter 20.004
 Mean of quarter 30.011
 Mean of quarter 40.057
 Inter Quartile Range0.017
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high4.000
 Percentage of outliers high0.114
 Mean of outliers high0.088
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.049
 VaR(95%) (moments method)0.053
 Expected Shortfall (moments method)0.072
 Extreme Value Index (regression method)0.225
 VaR(95%) (regression method)0.069
 Expected Shortfall (regression method)0.113
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.116
 Compounded annual return (geometric extrapolation)0.109
 Calmar ratio (compounded annual return / max draw down)0.919
 Compounded annual return / average of 25% largest draw downs1.918
 Compounded annual return / Expected Shortfall lognormal5.639
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.092
 SD0.107
 Sharpe ratio (Glass type estimate) -0.856
 Sharpe ratio (Hedges UMVUE)-0.853
 df171.000
 t-0.606
 p0.529
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.629
 Upperbound of 95% confidence interval for Sharpe Ratio1.918
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.626
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.921
Statistics related to Sortino ratio
 Sortino ratio-1.144
 Upside Potential Ratio8.492
 Upside part of mean0.680
 Downside part of mean-0.772
 Upside SD0.071
 Downside SD0.080
 N nonnegative terms79.000
 N negative terms93.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.615
 Mean of criterion-0.092
 SD of predictor0.277
 SD of criterion0.107
 Covariance0.005
 r0.166
 b (slope, estimate of beta)0.064
 a (intercept, estimate of alpha)-0.131
 Mean Square Error0.011
 DF error170.000
 t(b)2.195
 p(b)0.417
 t(a)-0.869
 p(a)0.533
 Lowerbound of 95% confidence interval for beta0.006
 Upperbound of 95% confidence interval for beta0.122
 Lowerbound of 95% confidence interval for alpha-0.429
 Upperbound of 95% confidence interval for alpha0.166
 Treynor index (mean / b)-1.430
 Jensen alpha (a)-0.131
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.097
 SD0.107
 Sharpe ratio (Glass type estimate) -0.909
 Sharpe ratio (Hedges UMVUE)-0.905
 df171.000
 t-0.643
 p0.531
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.681
 Upperbound of 95% confidence interval for Sharpe Ratio1.866
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.678
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.869
Statistics related to Sortino ratio
 Sortino ratio-1.208
 Upside Potential Ratio8.410
 Upside part of mean0.678
 Downside part of mean-0.775
 Upside SD0.070
 Downside SD0.081
 N nonnegative terms79.000
 N negative terms93.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.576
 Mean of criterion-0.097
 SD of predictor0.277
 SD of criterion0.107
 Covariance0.005
 r0.165
 b (slope, estimate of beta)0.064
 a (intercept, estimate of alpha)-0.134
 Mean Square Error0.011
 DF error170.000
 t(b)2.183
 p(b)0.417
 t(a)-0.890
 p(a)0.534
 Lowerbound of 95% confidence interval for beta0.006
 Upperbound of 95% confidence interval for beta0.122
 Lowerbound of 95% confidence interval for alpha-0.432
 Upperbound of 95% confidence interval for alpha0.163
 Treynor index (mean / b)-1.523
 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%)0.010
 Expected Shortfall on VaR0.012
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.010
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.977
 Quartile 10.997
 Median1.000
 Quartile 31.003
 Maximum1.021
 Mean of quarter 10.993
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.007
 Inter Quartile Range0.006
 Number outliers low3.000
 Percentage of outliers low0.017
 Mean of outliers low0.982
 Number of outliers high2.000
 Percentage of outliers high0.012
 Mean of outliers high1.018
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.226
 VaR(95%) (moments method)0.007
 Expected Shortfall (moments method)0.009
 Extreme Value Index (regression method)-0.068
 VaR(95%) (regression method)0.009
 Expected Shortfall (regression method)0.012
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.003
 Quartile 10.005
 Median0.030
 Quartile 30.035
 Maximum0.061
 Mean of quarter 10.004
 Mean of quarter 20.030
 Mean of quarter 30.035
 Mean of quarter 40.061
 Inter Quartile Range0.030
 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)-0.053
 Compounded annual return (geometric extrapolation)-0.052
 Calmar ratio (compounded annual return / max draw down)-0.857
 Compounded annual return / average of 25% largest draw downs-0.857
 Compounded annual return / Expected Shortfall lognormal-4.284