Advanced Statistics: Easy Does It
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.108 | ||||
| SD | 0.148 | ||||
| Sharpe ratio (Glass type estimate) | -0.725 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.712 | ||||
| df | 41.000 | ||||
| t | -1.356 | ||||
| p | 0.909 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.780 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.339 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.771 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.347 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.981 | ||||
| Upside Potential Ratio | 0.498 | ||||
| Upside part of mean | 0.055 | ||||
| Downside part of mean | -0.162 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.484 | ||||
| Mean of criterion | -0.108 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.148 | ||||
| Covariance | -0.002 | ||||
| r | -0.058 | ||||
| b (slope, estimate of beta) | -0.037 | ||||
| a (intercept, estimate of alpha) | -0.090 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 40.000 | ||||
| t(b) | -0.371 | ||||
| p(b) | 0.644 | ||||
| t(a) | -0.959 | ||||
| p(a) | 0.828 | ||||
| Lowerbound of 95% confidence interval for beta | -0.238 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.279 | ||||
| Upperbound of 95% confidence interval for alpha | 0.099 | ||||
| Treynor index (mean / b) | 2.914 | ||||
| Jensen alpha (a) | -0.090 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.118 | ||||
| SD | 0.146 | ||||
| Sharpe ratio (Glass type estimate) | -0.808 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.793 | ||||
| df | 41.000 | ||||
| t | -1.512 | ||||
| p | 0.931 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.865 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.259 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.855 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.269 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.021 | ||||
| Upside Potential Ratio | 0.430 | ||||
| Upside part of mean | 0.050 | ||||
| Downside part of mean | -0.168 | ||||
| Upside SD | 0.093 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | -0.118 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.146 | ||||
| Covariance | -0.002 | ||||
| r | -0.055 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | -0.102 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 40.000 | ||||
| t(b) | -0.346 | ||||
| p(b) | 0.634 | ||||
| t(a) | -1.114 | ||||
| p(a) | 0.864 | ||||
| Lowerbound of 95% confidence interval for beta | -0.245 | ||||
| Upperbound of 95% confidence interval for beta | 0.173 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.288 | ||||
| Upperbound of 95% confidence interval for alpha | 0.083 | ||||
| Treynor index (mean / b) | 3.301 | ||||
| Jensen alpha (a) | -0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.859 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.195 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.143 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.024 | ||||
| Mean of outliers high | 1.195 | ||||
| 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) | -0.296 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.096 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.349 | ||||
| Quartile 1 | 0.349 | ||||
| Median | 0.349 | ||||
| Quartile 3 | 0.349 | ||||
| Maximum | 0.349 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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) | -0.065 | ||||
| Compounded annual return (geometric extrapolation) | -0.072 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.205 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.775 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.072 | ||||
| SD | 0.601 | ||||
| Sharpe ratio (Glass type estimate) | 0.120 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.120 | ||||
| df | 923.000 | ||||
| t | 0.226 | ||||
| p | 0.411 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.923 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.164 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.923 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.164 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.170 | ||||
| Upside Potential Ratio | 2.951 | ||||
| Upside part of mean | 1.259 | ||||
| Downside part of mean | -1.187 | ||||
| Upside SD | 0.422 | ||||
| Downside SD | 0.427 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 865.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 924.000 | ||||
| Mean of predictor | 0.517 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.601 | ||||
| Covariance | -0.001 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | 0.079 | ||||
| Mean Square Error | 0.361 | ||||
| DF error | 922.000 | ||||
| t(b) | -0.207 | ||||
| p(b) | 0.582 | ||||
| t(a) | 0.247 | ||||
| p(a) | 0.403 | ||||
| Lowerbound of 95% confidence interval for beta | -0.142 | ||||
| Upperbound of 95% confidence interval for beta | 0.115 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.552 | ||||
| Upperbound of 95% confidence interval for alpha | 0.711 | ||||
| Treynor index (mean / b) | -5.317 | ||||
| Jensen alpha (a) | 0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.118 | ||||
| SD | 0.629 | ||||
| Sharpe ratio (Glass type estimate) | -0.187 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.187 | ||||
| df | 923.000 | ||||
| t | -0.352 | ||||
| p | 0.637 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.231 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.856 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.231 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.857 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.237 | ||||
| Upside Potential Ratio | 2.379 | ||||
| Upside part of mean | 1.180 | ||||
| Downside part of mean | -1.298 | ||||
| Upside SD | 0.386 | ||||
| Downside SD | 0.496 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 865.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 924.000 | ||||
| Mean of predictor | 0.470 | ||||
| Mean of criterion | -0.118 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 0.629 | ||||
| Covariance | -0.001 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | -0.113 | ||||
| Mean Square Error | 0.396 | ||||
| DF error | 922.000 | ||||
| t(b) | -0.146 | ||||
| p(b) | 0.558 | ||||
| t(a) | -0.336 | ||||
| p(a) | 0.632 | ||||
| Lowerbound of 95% confidence interval for beta | -0.144 | ||||
| Upperbound of 95% confidence interval for beta | 0.124 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.774 | ||||
| Upperbound of 95% confidence interval for alpha | 0.547 | ||||
| Treynor index (mean / b) | 11.856 | ||||
| Jensen alpha (a) | -0.113 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.062 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 924.000 | ||||
| Minimum | 0.609 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.373 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 71.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.943 | ||||
| Number of outliers high | 59.000 | ||||
| Percentage of outliers high | 0.064 | ||||
| Mean of outliers high | 1.075 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.395 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.338 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.055 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.644 | ||||
| Quartile 1 | 0.644 | ||||
| Median | 0.644 | ||||
| Quartile 3 | 0.644 | ||||
| Maximum | 0.644 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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) | -0.065 | ||||
| Compounded annual return (geometric extrapolation) | -0.071 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.110 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.919 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.014 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.895 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8743357945339204.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -136757481524536412400209862066176.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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 observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||