Advanced Statistics: Keith's Mini Russell 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 | -0.060 | ||||
| SD | 0.027 | ||||
| Sharpe ratio (Glass type estimate) | -2.199 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.175 | ||||
| df | 71.000 | ||||
| t | -5.385 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.070 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.314 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.052 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.299 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.865 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.305 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.220 | ||||
| SD of criterion | 0.027 | ||||
| Covariance | 0.000 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 70.000 | ||||
| t(b) | 0.319 | ||||
| p(b) | 0.375 | ||||
| t(a) | -5.081 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.085 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | -12.691 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.028 | ||||
| Sharpe ratio (Glass type estimate) | -2.156 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.133 | ||||
| df | 71.000 | ||||
| t | -5.280 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.024 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.274 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.006 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.259 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.839 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.210 | ||||
| SD of criterion | 0.028 | ||||
| Covariance | 0.000 | ||||
| r | 0.034 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 70.000 | ||||
| t(b) | 0.284 | ||||
| p(b) | 0.388 | ||||
| t(a) | -4.997 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | -13.309 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.947 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.028 | ||||
| Mean of outliers low | 0.953 | ||||
| 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) | -2.731 | ||||
| VaR(95%) (regression method) | -0.064 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.092 | ||||
| Quartile 1 | 0.092 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.092 | ||||
| Maximum | 0.092 | ||||
| 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) | -0.015 | ||||
| Compounded annual return (geometric extrapolation) | -0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.173 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.746 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.057 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.733 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.733 | ||||
| df | 1574.000 | ||||
| t | -1.798 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.533 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.067 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.533 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.067 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.945 | ||||
| Upside Potential Ratio | 0.890 | ||||
| Upside part of mean | 0.054 | ||||
| Downside part of mean | -0.111 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 1562.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1575.000 | ||||
| Mean of predictor | 0.323 | ||||
| Mean of criterion | -0.057 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | -0.001 | ||||
| r | -0.054 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1573.000 | ||||
| t(b) | -2.146 | ||||
| p(b) | 0.534 | ||||
| t(a) | -1.647 | ||||
| p(a) | 0.526 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.115 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | 3.893 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.766 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.766 | ||||
| df | 1574.000 | ||||
| t | -1.878 | ||||
| p | 0.524 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.566 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.034 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.566 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.034 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.963 | ||||
| Upside Potential Ratio | 0.842 | ||||
| Upside part of mean | 0.053 | ||||
| Downside part of mean | -0.113 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 1562.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1575.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | -0.001 | ||||
| r | -0.053 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | -0.056 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1573.000 | ||||
| t(b) | -2.114 | ||||
| p(b) | 0.534 | ||||
| t(a) | -1.749 | ||||
| p(a) | 0.528 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.007 | ||||
| Treynor index (mean / b) | 4.136 | ||||
| Jensen alpha (a) | -0.056 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1575.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 17.000 | ||||
| Percentage of outliers low | 0.011 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 20.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -14.816 | ||||
| VaR(95%) (moments method) | -1154470116.027 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.615 | ||||
| VaR(95%) (regression method) | -0.156 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.092 | ||||
| Quartile 1 | 0.092 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.092 | ||||
| Maximum | 0.092 | ||||
| Mean of quarter 1 | 0.092 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.092 | ||||
| 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) | -0.015 | ||||
| Compounded annual return (geometric extrapolation) | -0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.173 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.173 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.564 | ||||
| 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 | 1.084 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.332 | ||||
| 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 | 1.027 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.332 | ||||
| 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) | -8642337894641679.000 | ||||
| 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) | -213708542204917763528741170970624.000 | ||||
| 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 | ||||