Advanced Statistics: MARKET TRENDS
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 | -0.015 | ||||
| SD | 0.168 | ||||
| Sharpe ratio (Glass type estimate) | -0.089 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.087 | ||||
| df | 57.000 | ||||
| t | -0.195 | ||||
| p | 0.577 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.980 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.803 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.979 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.804 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.126 | ||||
| Upside Potential Ratio | 1.186 | ||||
| Upside part of mean | 0.141 | ||||
| Downside part of mean | -0.156 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.119 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.168 | ||||
| Covariance | 0.003 | ||||
| r | 0.076 | ||||
| b (slope, estimate of beta) | 0.051 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 56.000 | ||||
| t(b) | 0.572 | ||||
| p(b) | 0.285 | ||||
| t(a) | -0.404 | ||||
| p(a) | 0.656 | ||||
| Lowerbound of 95% confidence interval for beta | -0.127 | ||||
| Upperbound of 95% confidence interval for beta | 0.229 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.202 | ||||
| Upperbound of 95% confidence interval for alpha | 0.134 | ||||
| Treynor index (mean / b) | -0.294 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.170 | ||||
| Sharpe ratio (Glass type estimate) | -0.170 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.168 | ||||
| df | 57.000 | ||||
| t | -0.375 | ||||
| p | 0.645 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.062 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.722 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.060 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.724 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.227 | ||||
| Upside Potential Ratio | 1.052 | ||||
| Upside part of mean | 0.134 | ||||
| Downside part of mean | -0.163 | ||||
| Upside SD | 0.110 | ||||
| Downside SD | 0.127 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.336 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.170 | ||||
| Covariance | 0.004 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.063 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 56.000 | ||||
| t(b) | 0.667 | ||||
| p(b) | 0.254 | ||||
| t(a) | -0.596 | ||||
| p(a) | 0.723 | ||||
| Lowerbound of 95% confidence interval for beta | -0.125 | ||||
| Upperbound of 95% confidence interval for beta | 0.251 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.218 | ||||
| Upperbound of 95% confidence interval for alpha | 0.118 | ||||
| Treynor index (mean / b) | -0.462 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.080 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 58.000 | ||||
| Minimum | 0.817 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.169 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.048 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.121 | ||||
| Mean of outliers low | 0.918 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.172 | ||||
| Mean of outliers high | 1.072 | ||||
| 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) | -0.300 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | 0.097 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.156 | ||||
| Quartile 1 | 0.192 | ||||
| Median | 0.228 | ||||
| Quartile 3 | 0.264 | ||||
| Maximum | 0.300 | ||||
| Mean of quarter 1 | 0.156 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.300 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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) | 0.016 | ||||
| Compounded annual return (geometric extrapolation) | 0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.051 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.051 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.154 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 0.282 | ||||
| Sharpe ratio (Glass type estimate) | 0.036 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.036 | ||||
| df | 1272.000 | ||||
| t | 0.080 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.853 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.853 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.925 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.055 | ||||
| Upside Potential Ratio | 3.403 | ||||
| Upside part of mean | 0.636 | ||||
| Downside part of mean | -0.625 | ||||
| Upside SD | 0.210 | ||||
| Downside SD | 0.187 | ||||
| N nonnegative terms | 145.000 | ||||
| N negative terms | 1128.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1273.000 | ||||
| Mean of predictor | 0.406 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.282 | ||||
| Covariance | 0.012 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 0.101 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 1271.000 | ||||
| t(b) | 4.418 | ||||
| p(b) | 0.422 | ||||
| t(a) | -0.243 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.146 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.280 | ||||
| Upperbound of 95% confidence interval for alpha | 0.219 | ||||
| Treynor index (mean / b) | 0.101 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.280 | ||||
| Sharpe ratio (Glass type estimate) | -0.104 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.104 | ||||
| df | 1272.000 | ||||
| t | -0.228 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.993 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.786 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.993 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.786 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.146 | ||||
| Upside Potential Ratio | 3.085 | ||||
| Upside part of mean | 0.615 | ||||
| Downside part of mean | -0.644 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.199 | ||||
| N nonnegative terms | 145.000 | ||||
| N negative terms | 1128.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1273.000 | ||||
| Mean of predictor | 0.345 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.353 | ||||
| SD of criterion | 0.280 | ||||
| Covariance | 0.012 | ||||
| r | 0.121 | ||||
| b (slope, estimate of beta) | 0.096 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 1271.000 | ||||
| t(b) | 4.328 | ||||
| p(b) | 0.423 | ||||
| t(a) | -0.491 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.139 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.310 | ||||
| Upperbound of 95% confidence interval for alpha | 0.186 | ||||
| Treynor index (mean / b) | -0.304 | ||||
| Jensen alpha (a) | -0.062 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1273.000 | ||||
| Minimum | 0.781 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.280 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 143.000 | ||||
| Percentage of outliers low | 0.112 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 147.000 | ||||
| Percentage of outliers high | 0.115 | ||||
| Mean of outliers high | 1.021 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.172 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.291 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.047 | ||||
| Median | 0.069 | ||||
| Quartile 3 | 0.145 | ||||
| Maximum | 0.305 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.058 | ||||
| Mean of quarter 3 | 0.094 | ||||
| Mean of quarter 4 | 0.232 | ||||
| Inter Quartile Range | 0.098 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.305 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.200 | ||||
| VaR(95%) (moments method) | 0.266 | ||||
| Expected Shortfall (moments method) | 0.271 | ||||
| Extreme Value Index (regression method) | -0.160 | ||||
| VaR(95%) (regression method) | 0.310 | ||||
| Expected Shortfall (regression method) | 0.379 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.016 | ||||
| Compounded annual return (geometric extrapolation) | 0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.050 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.065 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.430 | ||||
| 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 | 1.082 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.391 | ||||
| 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 | 1.003 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.395 | ||||
| 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) | -8692781469209642.000 | ||||
| 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) | -53339313784406104269343770542080.000 | ||||
| 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 | ||||