Advanced Statistics: Test system 1
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 | -0.043 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.767 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.761 | ||||
| df | 102.000 | ||||
| t | -2.247 | ||||
| p | 0.609 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.442 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.088 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.439 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.084 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.201 | ||||
| Upside Potential Ratio | 0.554 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.062 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 99.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 103.000 | ||||
| Mean of predictor | 0.199 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | -0.002 | ||||
| r | -0.129 | ||||
| b (slope, estimate of beta) | -0.023 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 101.000 | ||||
| t(b) | -1.308 | ||||
| p(b) | 0.903 | ||||
| t(a) | -1.984 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.057 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | 1.885 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.054 | ||||
| Sharpe ratio (Glass type estimate) | -0.816 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.810 | ||||
| df | 102.000 | ||||
| t | -2.391 | ||||
| p | 0.615 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.493 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.136 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.488 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.132 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.212 | ||||
| Upside Potential Ratio | 0.515 | ||||
| Upside part of mean | 0.019 | ||||
| Downside part of mean | -0.063 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 99.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 103.000 | ||||
| Mean of predictor | 0.148 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.054 | ||||
| Covariance | -0.002 | ||||
| r | -0.136 | ||||
| b (slope, estimate of beta) | -0.023 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 101.000 | ||||
| t(b) | -1.376 | ||||
| p(b) | 0.914 | ||||
| t(a) | -2.193 | ||||
| p(a) | 0.985 | ||||
| Lowerbound of 95% confidence interval for beta | -0.057 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | -0.004 | ||||
| Treynor index (mean / b) | 1.894 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 103.000 | ||||
| Minimum | 0.933 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.131 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.126 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.146 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.626 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.445 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.035 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.121 | ||||
| Quartile 1 | 0.121 | ||||
| Median | 0.121 | ||||
| Quartile 3 | 0.121 | ||||
| Maximum | 0.121 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.001 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.039 | ||||
| SD | 0.102 | ||||
| Sharpe ratio (Glass type estimate) | -0.384 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.384 | ||||
| df | 2249.000 | ||||
| t | -1.126 | ||||
| p | 0.870 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.053 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.285 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.053 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.285 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.644 | ||||
| Upside Potential Ratio | 1.666 | ||||
| Upside part of mean | 0.101 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.082 | ||||
| Downside SD | 0.061 | ||||
| N nonnegative terms | 125.000 | ||||
| N negative terms | 2125.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2250.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 0.102 | ||||
| Covariance | -0.016 | ||||
| r | -0.273 | ||||
| b (slope, estimate of beta) | -0.048 | ||||
| a (intercept, estimate of alpha) | -0.024 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 2248.000 | ||||
| t(b) | -13.467 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.714 | ||||
| p(a) | 0.762 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | -0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.089 | ||||
| Upperbound of 95% confidence interval for alpha | 0.042 | ||||
| Treynor index (mean / b) | 0.808 | ||||
| Jensen alpha (a) | -0.024 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.444 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.444 | ||||
| df | 2249.000 | ||||
| t | -1.301 | ||||
| p | 0.903 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.113 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.225 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.113 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.225 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.706 | ||||
| Upside Potential Ratio | 1.570 | ||||
| Upside part of mean | 0.098 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 125.000 | ||||
| N negative terms | 2125.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2250.000 | ||||
| Mean of predictor | 0.152 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.572 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | -0.016 | ||||
| r | -0.280 | ||||
| b (slope, estimate of beta) | -0.049 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 2248.000 | ||||
| t(b) | -13.841 | ||||
| p(b) | 1.000 | ||||
| t(a) | -1.129 | ||||
| p(a) | 0.870 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | -0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.027 | ||||
| Treynor index (mean / b) | 0.906 | ||||
| Jensen alpha (a) | -0.037 | ||||
| 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 VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2250.000 | ||||
| Minimum | 0.930 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.173 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 211.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 224.000 | ||||
| Percentage of outliers high | 0.100 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.101 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.153 | ||||
| Quartile 1 | 0.153 | ||||
| Median | 0.153 | ||||
| Quartile 3 | 0.153 | ||||
| Maximum | 0.153 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.004 | ||||
| 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 | 1.052 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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 | 0.933 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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) | -8738104744152888.000 | ||||
| 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) | 361153360662985975406649088671744.000 | ||||
| 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 | ||||