Advanced Statistics: MAGIC TRADE
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 | 0.143 | ||||
| SD | 0.238 | ||||
| Sharpe ratio (Glass type estimate) | 0.600 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.590 | ||||
| df | 43.000 | ||||
| t | 1.149 | ||||
| p | 0.128 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.435 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.628 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.441 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.621 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.962 | ||||
| Upside Potential Ratio | 4.277 | ||||
| Upside part of mean | 0.206 | ||||
| Downside part of mean | -0.063 | ||||
| Upside SD | 0.234 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 44.000 | ||||
| Mean of predictor | 0.479 | ||||
| Mean of criterion | 0.143 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.238 | ||||
| Covariance | -0.006 | ||||
| r | -0.088 | ||||
| b (slope, estimate of beta) | -0.080 | ||||
| a (intercept, estimate of alpha) | 0.181 | ||||
| Mean Square Error | 0.058 | ||||
| DF error | 42.000 | ||||
| t(b) | -0.574 | ||||
| p(b) | 0.716 | ||||
| t(a) | 1.276 | ||||
| p(a) | 0.104 | ||||
| Lowerbound of 95% confidence interval for beta | -0.360 | ||||
| Upperbound of 95% confidence interval for beta | 0.201 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.467 | ||||
| Treynor index (mean / b) | -1.790 | ||||
| Jensen alpha (a) | 0.181 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.118 | ||||
| SD | 0.210 | ||||
| Sharpe ratio (Glass type estimate) | 0.562 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.552 | ||||
| df | 43.000 | ||||
| t | 1.076 | ||||
| p | 0.144 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.472 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.589 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.478 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.582 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.356 | ||||
| Upside Potential Ratio | 3.639 | ||||
| Upside part of mean | 0.183 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 44.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | 0.118 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.210 | ||||
| Covariance | -0.004 | ||||
| r | -0.081 | ||||
| b (slope, estimate of beta) | -0.068 | ||||
| a (intercept, estimate of alpha) | 0.148 | ||||
| Mean Square Error | 0.045 | ||||
| DF error | 42.000 | ||||
| t(b) | -0.529 | ||||
| p(b) | 0.700 | ||||
| t(a) | 1.191 | ||||
| p(a) | 0.120 | ||||
| Lowerbound of 95% confidence interval for beta | -0.329 | ||||
| Upperbound of 95% confidence interval for beta | 0.192 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.399 | ||||
| Treynor index (mean / b) | -1.729 | ||||
| Jensen alpha (a) | 0.148 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.086 | ||||
| Expected Shortfall on VaR | 0.109 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 44.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.346 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.070 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.914 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 1.154 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.086 | ||||
| Quartile 1 | 0.086 | ||||
| Median | 0.086 | ||||
| Quartile 3 | 0.086 | ||||
| Maximum | 0.086 | ||||
| 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) | 0.222 | ||||
| Compounded annual return (geometric extrapolation) | 0.176 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.054 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.619 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.206 | ||||
| SD | 0.429 | ||||
| Sharpe ratio (Glass type estimate) | 0.482 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.481 | ||||
| df | 970.000 | ||||
| t | 0.928 | ||||
| p | 0.177 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.537 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.500 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.537 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.500 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.785 | ||||
| Upside Potential Ratio | 3.419 | ||||
| Upside part of mean | 0.900 | ||||
| Downside part of mean | -0.693 | ||||
| Upside SD | 0.338 | ||||
| Downside SD | 0.263 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 925.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 971.000 | ||||
| Mean of predictor | 0.498 | ||||
| Mean of criterion | 0.206 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.429 | ||||
| Covariance | 0.004 | ||||
| r | 0.030 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | 0.187 | ||||
| Mean Square Error | 0.184 | ||||
| DF error | 969.000 | ||||
| t(b) | 0.931 | ||||
| p(b) | 0.176 | ||||
| t(a) | 0.838 | ||||
| p(a) | 0.201 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.119 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.626 | ||||
| Treynor index (mean / b) | 5.375 | ||||
| Jensen alpha (a) | 0.187 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.117 | ||||
| SD | 0.423 | ||||
| Sharpe ratio (Glass type estimate) | 0.276 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.275 | ||||
| df | 970.000 | ||||
| t | 0.530 | ||||
| p | 0.298 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.743 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.294 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.743 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.294 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.411 | ||||
| Upside Potential Ratio | 2.992 | ||||
| Upside part of mean | 0.848 | ||||
| Downside part of mean | -0.731 | ||||
| Upside SD | 0.314 | ||||
| Downside SD | 0.283 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 925.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 971.000 | ||||
| Mean of predictor | 0.442 | ||||
| Mean of criterion | 0.117 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.423 | ||||
| Covariance | 0.004 | ||||
| r | 0.031 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | 0.099 | ||||
| Mean Square Error | 0.179 | ||||
| DF error | 969.000 | ||||
| t(b) | 0.957 | ||||
| p(b) | 0.169 | ||||
| t(a) | 0.451 | ||||
| p(a) | 0.326 | ||||
| Lowerbound of 95% confidence interval for beta | -0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.119 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.333 | ||||
| Upperbound of 95% confidence interval for alpha | 0.532 | ||||
| Treynor index (mean / b) | 3.000 | ||||
| Jensen alpha (a) | 0.099 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 971.000 | ||||
| Minimum | 0.782 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.279 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 41.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.941 | ||||
| Number of outliers high | 48.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.070 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.517 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.131 | ||||
| VaR(95%) (regression method) | -0.007 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.023 | ||||
| Quartile 1 | 0.036 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.118 | ||||
| Maximum | 0.371 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | 0.047 | ||||
| Mean of quarter 3 | 0.091 | ||||
| Mean of quarter 4 | 0.246 | ||||
| Inter Quartile Range | 0.082 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.371 | ||||
| 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) | 0.219 | ||||
| Compounded annual return (geometric extrapolation) | 0.174 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.469 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.709 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.349 | ||||
| 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 | 1.233 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.398 | ||||
| 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 | 1.151 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.398 | ||||
| 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) | -8661634576880682.000 | ||||
| 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) | -97908728537013927023840818364416.000 | ||||
| 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 | ||||