Advanced Statistics: KC's NQ Madness (closed)
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.133 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | -0.834 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.821 | ||||
| df | 48.000 | ||||
| t | -1.685 | ||||
| p | 0.951 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.814 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.154 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.805 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.163 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.819 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.162 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.415 | ||||
| Mean of criterion | -0.133 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | -0.001 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.128 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 47.000 | ||||
| t(b) | -0.150 | ||||
| p(b) | 0.559 | ||||
| t(a) | -1.481 | ||||
| p(a) | 0.927 | ||||
| Lowerbound of 95% confidence interval for beta | -0.174 | ||||
| Upperbound of 95% confidence interval for beta | 0.150 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.302 | ||||
| Upperbound of 95% confidence interval for alpha | 0.046 | ||||
| Treynor index (mean / b) | 11.002 | ||||
| Jensen alpha (a) | -0.128 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.149 | ||||
| SD | 0.192 | ||||
| Sharpe ratio (Glass type estimate) | -0.778 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.766 | ||||
| df | 48.000 | ||||
| t | -1.572 | ||||
| p | 0.939 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.756 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.208 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.748 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.216 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.767 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.149 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.195 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.369 | ||||
| Mean of criterion | -0.149 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.192 | ||||
| Covariance | -0.002 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.020 | ||||
| a (intercept, estimate of alpha) | -0.142 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 47.000 | ||||
| t(b) | -0.199 | ||||
| p(b) | 0.579 | ||||
| t(a) | -1.378 | ||||
| p(a) | 0.913 | ||||
| Lowerbound of 95% confidence interval for beta | -0.224 | ||||
| Upperbound of 95% confidence interval for beta | 0.184 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.349 | ||||
| Upperbound of 95% confidence interval for alpha | 0.065 | ||||
| Treynor index (mean / b) | 7.384 | ||||
| Jensen alpha (a) | -0.142 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.119 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 49.000 | ||||
| Minimum | 0.680 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.972 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.041 | ||||
| Mean of outliers low | 0.819 | ||||
| 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) | 1.704 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | NA | ||||
| 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) | -0.086 | ||||
| Compounded annual return (geometric extrapolation) | -0.100 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.286 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.841 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.132 | ||||
| SD | 0.172 | ||||
| Sharpe ratio (Glass type estimate) | -0.766 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.765 | ||||
| df | 1090.000 | ||||
| t | -1.563 | ||||
| p | 0.524 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.727 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.195 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.726 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.196 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.028 | ||||
| Upside Potential Ratio | 1.207 | ||||
| Upside part of mean | 0.155 | ||||
| Downside part of mean | -0.287 | ||||
| Upside SD | 0.115 | ||||
| Downside SD | 0.128 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 1078.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1091.000 | ||||
| Mean of predictor | 0.472 | ||||
| Mean of criterion | -0.132 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.172 | ||||
| Covariance | -0.005 | ||||
| r | -0.087 | ||||
| b (slope, estimate of beta) | -0.047 | ||||
| a (intercept, estimate of alpha) | -0.110 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 1089.000 | ||||
| t(b) | -2.886 | ||||
| p(b) | 0.555 | ||||
| t(a) | -1.302 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | -0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.276 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 2.837 | ||||
| Jensen alpha (a) | -0.110 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.147 | ||||
| SD | 0.174 | ||||
| Sharpe ratio (Glass type estimate) | -0.844 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.843 | ||||
| df | 1090.000 | ||||
| t | -1.722 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.805 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.118 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.804 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.118 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.083 | ||||
| Upside Potential Ratio | 1.096 | ||||
| Upside part of mean | 0.149 | ||||
| Downside part of mean | -0.296 | ||||
| Upside SD | 0.110 | ||||
| Downside SD | 0.136 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 1078.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1091.000 | ||||
| Mean of predictor | 0.418 | ||||
| Mean of criterion | -0.147 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.174 | ||||
| Covariance | -0.005 | ||||
| r | -0.086 | ||||
| b (slope, estimate of beta) | -0.046 | ||||
| a (intercept, estimate of alpha) | -0.128 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 1089.000 | ||||
| t(b) | -2.849 | ||||
| p(b) | 0.555 | ||||
| t(a) | -1.497 | ||||
| p(a) | 0.529 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | -0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.296 | ||||
| Upperbound of 95% confidence interval for alpha | 0.040 | ||||
| Treynor index (mean / b) | 3.207 | ||||
| Jensen alpha (a) | -0.128 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1091.000 | ||||
| Minimum | 0.842 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.141 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 28.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.012 | ||||
| Mean of outliers high | 1.050 | ||||
| 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) | -0.008 | ||||
| VaR(95%) (regression method) | -0.014 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.025 | ||||
| Quartile 1 | 0.053 | ||||
| Median | 0.080 | ||||
| Quartile 3 | 0.262 | ||||
| Maximum | 0.444 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.080 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.444 | ||||
| Inter Quartile Range | 0.209 | ||||
| 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) | -0.084 | ||||
| Compounded annual return (geometric extrapolation) | -0.098 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.221 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.221 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.351 | ||||
| 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 | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.443 | ||||
| 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 | 0.941 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.444 | ||||
| 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) | -8724732590582339.000 | ||||
| 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) | -82964717310968741311790878556160.000 | ||||
| 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 | ||||