Advanced Statistics: Equity Equilibrium
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 | 0.035 | ||||
| SD | 0.368 | ||||
| Sharpe ratio (Glass type estimate) | 0.094 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.094 | ||||
| df | 86.000 | ||||
| t | 0.254 | ||||
| p | 0.400 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.634 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.822 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.634 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.822 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.129 | ||||
| Upside Potential Ratio | 1.774 | ||||
| Upside part of mean | 0.479 | ||||
| Downside part of mean | -0.445 | ||||
| Upside SD | 0.247 | ||||
| Downside SD | 0.270 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.183 | ||||
| Mean of criterion | 0.035 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.368 | ||||
| Covariance | 0.079 | ||||
| r | 0.703 | ||||
| b (slope, estimate of beta) | 0.845 | ||||
| a (intercept, estimate of alpha) | -0.120 | ||||
| Mean Square Error | 0.069 | ||||
| DF error | 85.000 | ||||
| t(b) | 9.120 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.209 | ||||
| p(a) | 0.885 | ||||
| Lowerbound of 95% confidence interval for beta | 0.661 | ||||
| Upperbound of 95% confidence interval for beta | 1.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.318 | ||||
| Upperbound of 95% confidence interval for alpha | 0.077 | ||||
| Treynor index (mean / b) | 0.041 | ||||
| Jensen alpha (a) | -0.120 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.037 | ||||
| SD | 0.390 | ||||
| Sharpe ratio (Glass type estimate) | -0.095 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.094 | ||||
| df | 86.000 | ||||
| t | -0.256 | ||||
| p | 0.601 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.823 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.633 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.822 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.634 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.118 | ||||
| Upside Potential Ratio | 1.439 | ||||
| Upside part of mean | 0.450 | ||||
| Downside part of mean | -0.487 | ||||
| Upside SD | 0.228 | ||||
| Downside SD | 0.313 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.137 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.390 | ||||
| Covariance | 0.083 | ||||
| r | 0.706 | ||||
| b (slope, estimate of beta) | 0.911 | ||||
| a (intercept, estimate of alpha) | -0.161 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 85.000 | ||||
| t(b) | 9.186 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.552 | ||||
| p(a) | 0.938 | ||||
| Lowerbound of 95% confidence interval for beta | 0.714 | ||||
| Upperbound of 95% confidence interval for beta | 1.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.368 | ||||
| Upperbound of 95% confidence interval for alpha | 0.045 | ||||
| Treynor index (mean / b) | -0.041 | ||||
| Jensen alpha (a) | -0.161 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.171 | ||||
| Expected Shortfall on VaR | 0.209 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.081 | ||||
| Expected Shortfall on VaR | 0.162 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 87.000 | ||||
| Minimum | 0.616 | ||||
| Quartile 1 | 0.952 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.072 | ||||
| Maximum | 1.274 | ||||
| Mean of quarter 1 | 0.878 | ||||
| Mean of quarter 2 | 0.983 | ||||
| Mean of quarter 3 | 1.037 | ||||
| Mean of quarter 4 | 1.130 | ||||
| Inter Quartile Range | 0.120 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.706 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.011 | ||||
| Mean of outliers high | 1.274 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.365 | ||||
| VaR(95%) (moments method) | 0.128 | ||||
| Expected Shortfall (moments method) | 0.231 | ||||
| Extreme Value Index (regression method) | 0.307 | ||||
| VaR(95%) (regression method) | 0.114 | ||||
| Expected Shortfall (regression method) | 0.187 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.218 | ||||
| Quartile 1 | 0.258 | ||||
| Median | 0.299 | ||||
| Quartile 3 | 0.444 | ||||
| Maximum | 0.588 | ||||
| Mean of quarter 1 | 0.218 | ||||
| Mean of quarter 2 | 0.299 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.588 | ||||
| Inter Quartile Range | 0.185 | ||||
| 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) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.012 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.012 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.034 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.252 | ||||
| SD | 0.725 | ||||
| Sharpe ratio (Glass type estimate) | 0.348 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.348 | ||||
| df | 1917.000 | ||||
| t | 0.941 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.377 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.072 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.377 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.072 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.546 | ||||
| Upside Potential Ratio | 6.799 | ||||
| Upside part of mean | 3.141 | ||||
| Downside part of mean | -2.888 | ||||
| Upside SD | 0.559 | ||||
| Downside SD | 0.462 | ||||
| N nonnegative terms | 963.000 | ||||
| N negative terms | 955.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1918.000 | ||||
| Mean of predictor | 0.349 | ||||
| Mean of criterion | 0.252 | ||||
| SD of predictor | 0.578 | ||||
| SD of criterion | 0.725 | ||||
| Covariance | 0.306 | ||||
| r | 0.731 | ||||
| b (slope, estimate of beta) | 0.918 | ||||
| a (intercept, estimate of alpha) | -0.068 | ||||
| Mean Square Error | 0.245 | ||||
| DF error | 1916.000 | ||||
| t(b) | 46.842 | ||||
| p(b) | 0.135 | ||||
| t(a) | -0.372 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.879 | ||||
| Upperbound of 95% confidence interval for beta | 0.956 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.428 | ||||
| Upperbound of 95% confidence interval for alpha | 0.291 | ||||
| Treynor index (mean / b) | 0.275 | ||||
| Jensen alpha (a) | -0.068 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.713 | ||||
| Sharpe ratio (Glass type estimate) | -0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.003 | ||||
| df | 1917.000 | ||||
| t | -0.009 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.728 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.721 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.728 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.721 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.005 | ||||
| Upside Potential Ratio | 5.880 | ||||
| Upside part of mean | 3.007 | ||||
| Downside part of mean | -3.010 | ||||
| Upside SD | 0.496 | ||||
| Downside SD | 0.511 | ||||
| N nonnegative terms | 963.000 | ||||
| N negative terms | 955.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1918.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 0.713 | ||||
| Covariance | 0.297 | ||||
| r | 0.726 | ||||
| b (slope, estimate of beta) | 0.901 | ||||
| a (intercept, estimate of alpha) | -0.169 | ||||
| Mean Square Error | 0.241 | ||||
| DF error | 1916.000 | ||||
| t(b) | 46.166 | ||||
| p(b) | 0.137 | ||||
| t(a) | -0.931 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.863 | ||||
| Upperbound of 95% confidence interval for beta | 0.939 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.524 | ||||
| Upperbound of 95% confidence interval for alpha | 0.187 | ||||
| Treynor index (mean / b) | -0.003 | ||||
| Jensen alpha (a) | -0.169 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1918.000 | ||||
| Minimum | 0.608 | ||||
| Quartile 1 | 0.988 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.645 | ||||
| Mean of quarter 1 | 0.961 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.043 | ||||
| Inter Quartile Range | 0.025 | ||||
| Number outliers low | 102.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.906 | ||||
| Number of outliers high | 111.000 | ||||
| Percentage of outliers high | 0.058 | ||||
| Mean of outliers high | 1.102 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.503 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.088 | ||||
| Extreme Value Index (regression method) | 0.324 | ||||
| VaR(95%) (regression method) | 0.033 | ||||
| Expected Shortfall (regression method) | 0.059 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.081 | ||||
| Quartile 3 | 0.107 | ||||
| Maximum | 0.603 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.037 | ||||
| Mean of quarter 3 | 0.096 | ||||
| Mean of quarter 4 | 0.386 | ||||
| Inter Quartile Range | 0.092 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.522 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -44.013 | ||||
| VaR(95%) (moments method) | 0.289 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.002 | ||||
| VaR(95%) (regression method) | 0.814 | ||||
| Expected Shortfall (regression method) | 0.837 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.049 | ||||
| Compounded annual return (geometric extrapolation) | 0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.070 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.110 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.490 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.520 | ||||
| Sharpe ratio (Glass type estimate) | -0.059 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.059 | ||||
| df | 130.000 | ||||
| t | -0.042 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.831 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.713 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.831 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.713 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.086 | ||||
| Upside Potential Ratio | 8.599 | ||||
| Upside part of mean | 3.060 | ||||
| Downside part of mean | -3.091 | ||||
| Upside SD | 0.377 | ||||
| Downside SD | 0.356 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.417 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.537 | ||||
| SD of criterion | 0.520 | ||||
| Covariance | 0.162 | ||||
| r | 0.580 | ||||
| b (slope, estimate of beta) | 0.562 | ||||
| a (intercept, estimate of alpha) | -0.828 | ||||
| Mean Square Error | 0.181 | ||||
| DF error | 129.000 | ||||
| t(b) | 8.093 | ||||
| p(b) | 0.153 | ||||
| t(a) | -1.358 | ||||
| p(a) | 0.575 | ||||
| Lowerbound of 95% confidence interval for beta | 0.425 | ||||
| Upperbound of 95% confidence interval for beta | 0.700 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.033 | ||||
| Upperbound of 95% confidence interval for alpha | 0.378 | ||||
| Treynor index (mean / b) | -0.055 | ||||
| Jensen alpha (a) | -0.828 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.165 | ||||
| SD | 0.520 | ||||
| Sharpe ratio (Glass type estimate) | -0.317 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.315 | ||||
| df | 130.000 | ||||
| t | -0.224 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.088 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.456 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.087 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.457 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.449 | ||||
| Upside Potential Ratio | 8.152 | ||||
| Upside part of mean | 2.992 | ||||
| Downside part of mean | -3.157 | ||||
| Upside SD | 0.365 | ||||
| Downside SD | 0.367 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.271 | ||||
| Mean of criterion | -0.165 | ||||
| SD of predictor | 0.536 | ||||
| SD of criterion | 0.520 | ||||
| Covariance | 0.163 | ||||
| r | 0.585 | ||||
| b (slope, estimate of beta) | 0.567 | ||||
| a (intercept, estimate of alpha) | -0.885 | ||||
| Mean Square Error | 0.179 | ||||
| DF error | 129.000 | ||||
| t(b) | 8.185 | ||||
| p(b) | 0.150 | ||||
| t(a) | -1.463 | ||||
| p(a) | 0.581 | ||||
| Lowerbound of 95% confidence interval for beta | 0.430 | ||||
| Upperbound of 95% confidence interval for beta | 0.704 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.082 | ||||
| Upperbound of 95% confidence interval for alpha | 0.312 | ||||
| Treynor index (mean / b) | -0.291 | ||||
| Jensen alpha (a) | -0.885 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.052 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.888 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.018 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.035 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.908 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.094 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.131 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.054 | ||||
| Extreme Value Index (regression method) | 0.093 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.269 | ||||
| Quartile 1 | 0.269 | ||||
| Median | 0.269 | ||||
| Quartile 3 | 0.269 | ||||
| Maximum | 0.269 | ||||
| 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) | -0.117 | ||||
| Compounded annual return (geometric extrapolation) | -0.114 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.422 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.760 | ||||