Advanced Statistics: MakeHayWhileTheSunShines
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 | 0.033 | ||||
| SD | 0.202 | ||||
| Sharpe ratio (Glass type estimate) | 0.163 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.161 | ||||
| df | 65.000 | ||||
| t | 0.383 | ||||
| p | 0.351 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.673 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.999 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.675 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.998 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.280 | ||||
| Upside Potential Ratio | 2.036 | ||||
| Upside part of mean | 0.240 | ||||
| Downside part of mean | -0.207 | ||||
| Upside SD | 0.162 | ||||
| Downside SD | 0.118 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 66.000 | ||||
| Mean of predictor | 0.282 | ||||
| Mean of criterion | 0.033 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.202 | ||||
| Covariance | -0.003 | ||||
| r | -0.065 | ||||
| b (slope, estimate of beta) | -0.059 | ||||
| a (intercept, estimate of alpha) | 0.050 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 64.000 | ||||
| t(b) | -0.523 | ||||
| p(b) | 0.699 | ||||
| t(a) | 0.539 | ||||
| p(a) | 0.296 | ||||
| Lowerbound of 95% confidence interval for beta | -0.286 | ||||
| Upperbound of 95% confidence interval for beta | 0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.135 | ||||
| Upperbound of 95% confidence interval for alpha | 0.234 | ||||
| Treynor index (mean / b) | -0.554 | ||||
| Jensen alpha (a) | 0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.197 | ||||
| Sharpe ratio (Glass type estimate) | 0.069 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.068 | ||||
| df | 65.000 | ||||
| t | 0.161 | ||||
| p | 0.436 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.767 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.904 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.768 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.904 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.110 | ||||
| Upside Potential Ratio | 1.847 | ||||
| Upside part of mean | 0.227 | ||||
| Downside part of mean | -0.213 | ||||
| Upside SD | 0.152 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 66.000 | ||||
| Mean of predictor | 0.256 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.212 | ||||
| SD of criterion | 0.197 | ||||
| Covariance | -0.002 | ||||
| r | -0.057 | ||||
| b (slope, estimate of beta) | -0.053 | ||||
| a (intercept, estimate of alpha) | 0.027 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 64.000 | ||||
| t(b) | -0.460 | ||||
| p(b) | 0.677 | ||||
| t(a) | 0.303 | ||||
| p(a) | 0.381 | ||||
| Lowerbound of 95% confidence interval for beta | -0.285 | ||||
| Upperbound of 95% confidence interval for beta | 0.178 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.152 | ||||
| Upperbound of 95% confidence interval for alpha | 0.206 | ||||
| Treynor index (mean / b) | -0.253 | ||||
| Jensen alpha (a) | 0.027 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.088 | ||||
| Expected Shortfall on VaR | 0.109 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 66.000 | ||||
| Minimum | 0.869 | ||||
| Quartile 1 | 0.982 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.186 | ||||
| Mean of quarter 1 | 0.944 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.081 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.182 | ||||
| Mean of outliers high | 1.104 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.332 | ||||
| VaR(95%) (moments method) | 0.048 | ||||
| Expected Shortfall (moments method) | 0.059 | ||||
| Extreme Value Index (regression method) | -0.785 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.157 | ||||
| Maximum | 0.374 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | 0.084 | ||||
| Mean of quarter 4 | 0.374 | ||||
| Inter Quartile Range | 0.125 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.374 | ||||
| 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) | 0.068 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.158 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.158 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.541 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | 0.160 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.160 | ||||
| df | 1455.000 | ||||
| t | 0.378 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.671 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.992 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.671 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.992 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.241 | ||||
| Upside Potential Ratio | 6.734 | ||||
| Upside part of mean | 0.697 | ||||
| Downside part of mean | -0.672 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 427.000 | ||||
| N negative terms | 1029.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1456.000 | ||||
| Mean of predictor | 0.311 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | -0.001 | ||||
| r | -0.031 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.031 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 1454.000 | ||||
| t(b) | -1.164 | ||||
| p(b) | 0.515 | ||||
| t(a) | 0.468 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.161 | ||||
| Treynor index (mean / b) | -1.282 | ||||
| Jensen alpha (a) | 0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.155 | ||||
| Sharpe ratio (Glass type estimate) | 0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.083 | ||||
| df | 1455.000 | ||||
| t | 0.196 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.748 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.915 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.748 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.915 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.123 | ||||
| Upside Potential Ratio | 6.579 | ||||
| Upside part of mean | 0.690 | ||||
| Downside part of mean | -0.677 | ||||
| Upside SD | 0.114 | ||||
| Downside SD | 0.105 | ||||
| N nonnegative terms | 427.000 | ||||
| N negative terms | 1029.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1456.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.155 | ||||
| Covariance | -0.001 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.018 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 1454.000 | ||||
| t(b) | -1.141 | ||||
| p(b) | 0.515 | ||||
| t(a) | 0.276 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.111 | ||||
| Upperbound of 95% confidence interval for alpha | 0.148 | ||||
| Treynor index (mean / b) | -0.682 | ||||
| Jensen alpha (a) | 0.018 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1456.000 | ||||
| Minimum | 0.929 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.113 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 215.000 | ||||
| Percentage of outliers low | 0.148 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 202.000 | ||||
| Percentage of outliers high | 0.139 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.033 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.024 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.031 | ||||
| Maximum | 0.388 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.114 | ||||
| Inter Quartile Range | 0.028 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.152 | ||||
| Mean of outliers high | 0.156 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.625 | ||||
| VaR(95%) (moments method) | 0.113 | ||||
| Expected Shortfall (moments method) | 0.332 | ||||
| Extreme Value Index (regression method) | 1.417 | ||||
| VaR(95%) (regression method) | 0.101 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.067 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.151 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.514 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.003 | ||||
| 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 | 1.049 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.498 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.501 | ||||
| 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) | -8742928729378970.000 | ||||
| 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) | -1823855543698445059511770958266368.000 | ||||
| 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 | ||||