Advanced Statistics: Equity Trader
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 | -0.186 | ||||
| SD | 0.207 | ||||
| Sharpe ratio (Glass type estimate) | -0.900 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.881 | ||||
| df | 35.000 | ||||
| t | -1.559 | ||||
| p | 0.936 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.045 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.257 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.031 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.270 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.888 | ||||
| Upside Potential Ratio | 0.106 | ||||
| Upside part of mean | 0.022 | ||||
| Downside part of mean | -0.208 | ||||
| Upside SD | 0.024 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.546 | ||||
| Mean of criterion | -0.186 | ||||
| SD of predictor | 0.220 | ||||
| SD of criterion | 0.207 | ||||
| Covariance | 0.004 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.078 | ||||
| a (intercept, estimate of alpha) | -0.229 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.482 | ||||
| p(b) | 0.316 | ||||
| t(a) | -1.531 | ||||
| p(a) | 0.933 | ||||
| Lowerbound of 95% confidence interval for beta | -0.249 | ||||
| Upperbound of 95% confidence interval for beta | 0.404 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.532 | ||||
| Upperbound of 95% confidence interval for alpha | 0.075 | ||||
| Treynor index (mean / b) | -2.403 | ||||
| Jensen alpha (a) | -0.229 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.213 | ||||
| SD | 0.243 | ||||
| Sharpe ratio (Glass type estimate) | -0.876 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.857 | ||||
| df | 35.000 | ||||
| t | -1.517 | ||||
| p | 0.931 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.020 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.280 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.006 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.292 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.864 | ||||
| Upside Potential Ratio | 0.089 | ||||
| Upside part of mean | 0.022 | ||||
| Downside part of mean | -0.235 | ||||
| Upside SD | 0.023 | ||||
| Downside SD | 0.247 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | -0.213 | ||||
| SD of predictor | 0.208 | ||||
| SD of criterion | 0.243 | ||||
| Covariance | 0.004 | ||||
| r | 0.075 | ||||
| b (slope, estimate of beta) | 0.088 | ||||
| a (intercept, estimate of alpha) | -0.258 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.441 | ||||
| p(b) | 0.331 | ||||
| t(a) | -1.475 | ||||
| p(a) | 0.925 | ||||
| Lowerbound of 95% confidence interval for beta | -0.319 | ||||
| Upperbound of 95% confidence interval for beta | 0.495 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.614 | ||||
| Upperbound of 95% confidence interval for alpha | 0.098 | ||||
| Treynor index (mean / b) | -2.414 | ||||
| Jensen alpha (a) | -0.258 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.125 | ||||
| Expected Shortfall on VaR | 0.150 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.057 | ||||
| Expected Shortfall on VaR | 0.123 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.684 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.037 | ||||
| Mean of quarter 1 | 0.944 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.874 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 1.020 | ||||
| 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) | 1.673 | ||||
| VaR(95%) (regression method) | 0.048 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.113 | ||||
| Median | 0.222 | ||||
| Quartile 3 | 0.331 | ||||
| Maximum | 0.440 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.440 | ||||
| Inter Quartile Range | 0.218 | ||||
| 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) | -0.133 | ||||
| Compounded annual return (geometric extrapolation) | -0.156 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.353 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.353 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.038 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.195 | ||||
| SD | 0.173 | ||||
| Sharpe ratio (Glass type estimate) | -1.128 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.127 | ||||
| df | 796.000 | ||||
| t | -1.967 | ||||
| p | 0.975 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.252 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.002 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.252 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.001 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.396 | ||||
| Upside Potential Ratio | 1.782 | ||||
| Upside part of mean | 0.249 | ||||
| Downside part of mean | -0.445 | ||||
| Upside SD | 0.103 | ||||
| Downside SD | 0.140 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 797.000 | ||||
| Mean of predictor | 0.591 | ||||
| Mean of criterion | -0.195 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.173 | ||||
| Covariance | 0.003 | ||||
| r | 0.052 | ||||
| b (slope, estimate of beta) | 0.025 | ||||
| a (intercept, estimate of alpha) | -0.210 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 795.000 | ||||
| t(b) | 1.474 | ||||
| p(b) | 0.070 | ||||
| t(a) | -2.106 | ||||
| p(a) | 0.982 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.058 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.406 | ||||
| Upperbound of 95% confidence interval for alpha | -0.014 | ||||
| Treynor index (mean / b) | -7.817 | ||||
| Jensen alpha (a) | -0.210 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.211 | ||||
| SD | 0.176 | ||||
| Sharpe ratio (Glass type estimate) | -1.196 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.195 | ||||
| df | 796.000 | ||||
| t | -2.086 | ||||
| p | 0.981 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.321 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.070 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.320 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.070 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.444 | ||||
| Upside Potential Ratio | 1.674 | ||||
| Upside part of mean | 0.244 | ||||
| Downside part of mean | -0.455 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 797.000 | ||||
| Mean of predictor | 0.526 | ||||
| Mean of criterion | -0.211 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.176 | ||||
| Covariance | 0.003 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.224 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 795.000 | ||||
| t(b) | 1.406 | ||||
| p(b) | 0.080 | ||||
| t(a) | -2.206 | ||||
| p(a) | 0.986 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.423 | ||||
| Upperbound of 95% confidence interval for alpha | -0.025 | ||||
| Treynor index (mean / b) | -8.610 | ||||
| Jensen alpha (a) | -0.224 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 797.000 | ||||
| Minimum | 0.879 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.109 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 65.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 49.000 | ||||
| Percentage of outliers high | 0.061 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.205 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.195 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.021 | ||||
| Maximum | 0.440 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.250 | ||||
| Inter Quartile Range | 0.016 | ||||
| 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 | 0.222 | ||||
| Mean of outliers high | 0.250 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.418 | ||||
| VaR(95%) (moments method) | 0.109 | ||||
| Expected Shortfall (moments method) | 0.245 | ||||
| Extreme Value Index (regression method) | 2.272 | ||||
| VaR(95%) (regression method) | 0.815 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.131 | ||||
| Compounded annual return (geometric extrapolation) | -0.154 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.349 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.614 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.682 | ||||
| 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 | 1.009 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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 | 0.877 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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) | -8750514707594859.000 | ||||
| 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) | -226919610314615670825284760764416.000 | ||||
| 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 | ||||