Advanced Statistics: YYZ
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 | 0.046 | ||||
| SD | 0.301 | ||||
| Sharpe ratio (Glass type estimate) | 0.151 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.148 | ||||
| df | 35.000 | ||||
| t | 0.262 | ||||
| p | 0.397 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.982 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.282 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.984 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.325 | ||||
| Upside Potential Ratio | 1.616 | ||||
| Upside part of mean | 0.227 | ||||
| Downside part of mean | -0.181 | ||||
| Upside SD | 0.262 | ||||
| Downside SD | 0.140 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | 0.046 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.301 | ||||
| Covariance | -0.002 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | 0.063 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.172 | ||||
| p(b) | 0.568 | ||||
| t(a) | 0.310 | ||||
| p(a) | 0.379 | ||||
| Lowerbound of 95% confidence interval for beta | -0.421 | ||||
| Upperbound of 95% confidence interval for beta | 0.355 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.350 | ||||
| Upperbound of 95% confidence interval for alpha | 0.475 | ||||
| Treynor index (mean / b) | -1.390 | ||||
| Jensen alpha (a) | 0.063 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.006 | ||||
| SD | 0.276 | ||||
| Sharpe ratio (Glass type estimate) | 0.023 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.023 | ||||
| df | 35.000 | ||||
| t | 0.040 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.108 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.155 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.109 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.154 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.042 | ||||
| Upside Potential Ratio | 1.307 | ||||
| Upside part of mean | 0.198 | ||||
| Downside part of mean | -0.191 | ||||
| Upside SD | 0.226 | ||||
| Downside SD | 0.151 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.481 | ||||
| Mean of criterion | 0.006 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.276 | ||||
| Covariance | -0.001 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.016 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.106 | ||||
| p(b) | 0.542 | ||||
| t(a) | 0.085 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | -0.385 | ||||
| Upperbound of 95% confidence interval for beta | 0.347 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.357 | ||||
| Upperbound of 95% confidence interval for alpha | 0.388 | ||||
| Treynor index (mean / b) | -0.338 | ||||
| Jensen alpha (a) | 0.016 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.122 | ||||
| Expected Shortfall on VaR | 0.151 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.364 | ||||
| Mean of quarter 1 | 0.953 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.077 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.894 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 1.174 | ||||
| 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) | -0.821 | ||||
| VaR(95%) (regression method) | 0.119 | ||||
| Expected Shortfall (regression method) | 0.162 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.331 | ||||
| Quartile 1 | 0.331 | ||||
| Median | 0.331 | ||||
| Quartile 3 | 0.331 | ||||
| Maximum | 0.331 | ||||
| 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) | 0.054 | ||||
| Compounded annual return (geometric extrapolation) | 0.052 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.156 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.343 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.048 | ||||
| SD | 0.294 | ||||
| Sharpe ratio (Glass type estimate) | 0.163 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.162 | ||||
| df | 806.000 | ||||
| t | 0.285 | ||||
| p | 0.388 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.954 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.279 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.954 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.279 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.250 | ||||
| Upside Potential Ratio | 4.405 | ||||
| Upside part of mean | 0.841 | ||||
| Downside part of mean | -0.794 | ||||
| Upside SD | 0.223 | ||||
| Downside SD | 0.191 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 727.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 807.000 | ||||
| Mean of predictor | 0.585 | ||||
| Mean of criterion | 0.048 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.294 | ||||
| Covariance | 0.005 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.045 | ||||
| a (intercept, estimate of alpha) | 0.021 | ||||
| Mean Square Error | 0.086 | ||||
| DF error | 805.000 | ||||
| t(b) | 1.409 | ||||
| p(b) | 0.080 | ||||
| t(a) | 0.126 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.309 | ||||
| Upperbound of 95% confidence interval for alpha | 0.352 | ||||
| Treynor index (mean / b) | 1.055 | ||||
| Jensen alpha (a) | 0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.005 | ||||
| SD | 0.292 | ||||
| Sharpe ratio (Glass type estimate) | 0.017 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.017 | ||||
| df | 806.000 | ||||
| t | 0.031 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.099 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.134 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.099 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.026 | ||||
| Upside Potential Ratio | 4.143 | ||||
| Upside part of mean | 0.818 | ||||
| Downside part of mean | -0.813 | ||||
| Upside SD | 0.214 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 727.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 807.000 | ||||
| Mean of predictor | 0.532 | ||||
| Mean of criterion | 0.005 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.292 | ||||
| Covariance | 0.005 | ||||
| r | 0.049 | ||||
| b (slope, estimate of beta) | 0.044 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 805.000 | ||||
| t(b) | 1.383 | ||||
| p(b) | 0.084 | ||||
| t(a) | -0.108 | ||||
| p(a) | 0.543 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.105 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.346 | ||||
| Upperbound of 95% confidence interval for alpha | 0.310 | ||||
| Treynor index (mean / b) | 0.117 | ||||
| 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%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 807.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.136 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 80.000 | ||||
| Percentage of outliers low | 0.099 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 80.000 | ||||
| Percentage of outliers high | 0.099 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -10.240 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.204 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.036 | ||||
| Median | 0.054 | ||||
| Quartile 3 | 0.104 | ||||
| Maximum | 0.414 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | 0.054 | ||||
| Mean of quarter 3 | 0.104 | ||||
| Mean of quarter 4 | 0.414 | ||||
| Inter Quartile Range | 0.068 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.414 | ||||
| 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) | 0.053 | ||||
| Compounded annual return (geometric extrapolation) | 0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.122 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.122 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.382 | ||||
| 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 | 1.143 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8733674005517795.000 | ||||
| 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) | -941802013088313751033952528760832.000 | ||||
| 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 | ||||