Advanced Statistics: Top Performers' Steady Gains
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 | 0.035 | ||||
| SD | 0.540 | ||||
| Sharpe ratio (Glass type estimate) | 0.065 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.065 | ||||
| df | 70.000 | ||||
| t | 0.159 | ||||
| p | 0.437 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.741 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.871 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.741 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.870 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.144 | ||||
| Upside Potential Ratio | 2.072 | ||||
| Upside part of mean | 0.505 | ||||
| Downside part of mean | -0.470 | ||||
| Upside SD | 0.477 | ||||
| Downside SD | 0.244 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.221 | ||||
| Mean of criterion | 0.035 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.540 | ||||
| Covariance | 0.013 | ||||
| r | 0.084 | ||||
| b (slope, estimate of beta) | 0.162 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.293 | ||||
| DF error | 69.000 | ||||
| t(b) | 0.699 | ||||
| p(b) | 0.244 | ||||
| t(a) | -0.003 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.301 | ||||
| Upperbound of 95% confidence interval for beta | 0.626 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.457 | ||||
| Upperbound of 95% confidence interval for alpha | 0.455 | ||||
| Treynor index (mean / b) | 0.217 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.441 | ||||
| Sharpe ratio (Glass type estimate) | -0.164 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.162 | ||||
| df | 70.000 | ||||
| t | -0.399 | ||||
| p | 0.654 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.970 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.643 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.968 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.644 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.271 | ||||
| Upside Potential Ratio | 1.613 | ||||
| Upside part of mean | 0.430 | ||||
| Downside part of mean | -0.502 | ||||
| Upside SD | 0.348 | ||||
| Downside SD | 0.266 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.183 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.441 | ||||
| Covariance | 0.010 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.134 | ||||
| a (intercept, estimate of alpha) | -0.097 | ||||
| Mean Square Error | 0.196 | ||||
| DF error | 69.000 | ||||
| t(b) | 0.681 | ||||
| p(b) | 0.249 | ||||
| t(a) | -0.522 | ||||
| p(a) | 0.698 | ||||
| Lowerbound of 95% confidence interval for beta | -0.259 | ||||
| Upperbound of 95% confidence interval for beta | 0.527 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.466 | ||||
| Upperbound of 95% confidence interval for alpha | 0.273 | ||||
| Treynor index (mean / b) | -0.538 | ||||
| Jensen alpha (a) | -0.097 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.194 | ||||
| Expected Shortfall on VaR | 0.235 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.174 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.746 | ||||
| Quartile 1 | 0.937 | ||||
| Median | 0.999 | ||||
| Quartile 3 | 1.044 | ||||
| Maximum | 2.060 | ||||
| Mean of quarter 1 | 0.880 | ||||
| Mean of quarter 2 | 0.974 | ||||
| Mean of quarter 3 | 1.017 | ||||
| Mean of quarter 4 | 1.157 | ||||
| Inter Quartile Range | 0.107 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.746 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.028 | ||||
| Mean of outliers high | 1.656 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.153 | ||||
| VaR(95%) (moments method) | 0.128 | ||||
| Expected Shortfall (moments method) | 0.182 | ||||
| Extreme Value Index (regression method) | 0.572 | ||||
| VaR(95%) (regression method) | 0.094 | ||||
| Expected Shortfall (regression method) | 0.160 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.043 | ||||
| Quartile 1 | 0.052 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.349 | ||||
| Maximum | 0.636 | ||||
| Mean of quarter 1 | 0.043 | ||||
| Mean of quarter 2 | 0.061 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.636 | ||||
| Inter Quartile Range | 0.296 | ||||
| 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) | -0.026 | ||||
| Compounded annual return (geometric extrapolation) | -0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.044 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.044 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.118 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.408 | ||||
| SD | 1.036 | ||||
| Sharpe ratio (Glass type estimate) | 0.394 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.394 | ||||
| df | 1554.000 | ||||
| t | 0.960 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.411 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.199 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.411 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.198 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.712 | ||||
| Upside Potential Ratio | 6.521 | ||||
| Upside part of mean | 3.736 | ||||
| Downside part of mean | -3.328 | ||||
| Upside SD | 0.863 | ||||
| Downside SD | 0.573 | ||||
| N nonnegative terms | 700.000 | ||||
| N negative terms | 855.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1555.000 | ||||
| Mean of predictor | 0.371 | ||||
| Mean of criterion | 0.408 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 1.036 | ||||
| Covariance | 0.195 | ||||
| r | 0.331 | ||||
| b (slope, estimate of beta) | 0.605 | ||||
| a (intercept, estimate of alpha) | 0.184 | ||||
| Mean Square Error | 0.956 | ||||
| DF error | 1553.000 | ||||
| t(b) | 13.843 | ||||
| p(b) | 0.293 | ||||
| t(a) | 0.457 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | 0.519 | ||||
| Upperbound of 95% confidence interval for beta | 0.690 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.604 | ||||
| Upperbound of 95% confidence interval for alpha | 0.971 | ||||
| Treynor index (mean / b) | 0.675 | ||||
| Jensen alpha (a) | 0.184 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.967 | ||||
| Sharpe ratio (Glass type estimate) | -0.075 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.075 | ||||
| df | 1554.000 | ||||
| t | -0.182 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.879 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.730 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.879 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.730 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.109 | ||||
| Upside Potential Ratio | 5.209 | ||||
| Upside part of mean | 3.454 | ||||
| Downside part of mean | -3.526 | ||||
| Upside SD | 0.703 | ||||
| Downside SD | 0.663 | ||||
| N nonnegative terms | 700.000 | ||||
| N negative terms | 855.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1555.000 | ||||
| Mean of predictor | 0.211 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.567 | ||||
| SD of criterion | 0.967 | ||||
| Covariance | 0.183 | ||||
| r | 0.335 | ||||
| b (slope, estimate of beta) | 0.570 | ||||
| a (intercept, estimate of alpha) | -0.192 | ||||
| Mean Square Error | 0.830 | ||||
| DF error | 1553.000 | ||||
| t(b) | 13.990 | ||||
| p(b) | 0.291 | ||||
| t(a) | -0.514 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.490 | ||||
| Upperbound of 95% confidence interval for beta | 0.650 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.926 | ||||
| Upperbound of 95% confidence interval for alpha | 0.542 | ||||
| Treynor index (mean / b) | -0.126 | ||||
| Jensen alpha (a) | -0.192 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.094 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1555.000 | ||||
| Minimum | 0.535 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.963 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.053 | ||||
| Inter Quartile Range | 0.024 | ||||
| Number outliers low | 99.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 109.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.127 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.552 | ||||
| VaR(95%) (moments method) | 0.044 | ||||
| Expected Shortfall (moments method) | 0.110 | ||||
| Extreme Value Index (regression method) | 0.405 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.072 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.040 | ||||
| Median | 0.080 | ||||
| Quartile 3 | 0.133 | ||||
| Maximum | 0.682 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.066 | ||||
| Mean of quarter 3 | 0.102 | ||||
| Mean of quarter 4 | 0.426 | ||||
| Inter Quartile Range | 0.092 | ||||
| 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 | 0.154 | ||||
| Mean of outliers high | 0.505 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.997 | ||||
| VaR(95%) (moments method) | 0.338 | ||||
| Expected Shortfall (moments method) | 0.345 | ||||
| Extreme Value Index (regression method) | 0.063 | ||||
| VaR(95%) (regression method) | 0.588 | ||||
| Expected Shortfall (regression method) | 0.883 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.026 | ||||
| Compounded annual return (geometric extrapolation) | -0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.041 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.065 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.238 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.778 | ||||
| SD | 1.368 | ||||
| Sharpe ratio (Glass type estimate) | 1.300 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.292 | ||||
| df | 130.000 | ||||
| t | 0.919 | ||||
| p | 0.460 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.479 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.074 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.484 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.069 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 18.630 | ||||
| Upside Potential Ratio | 23.565 | ||||
| Upside part of mean | 2.249 | ||||
| Downside part of mean | -0.471 | ||||
| Upside SD | 1.364 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 99.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.968 | ||||
| Mean of criterion | 1.778 | ||||
| SD of predictor | 0.666 | ||||
| SD of criterion | 1.368 | ||||
| Covariance | 0.100 | ||||
| r | 0.110 | ||||
| b (slope, estimate of beta) | 0.226 | ||||
| a (intercept, estimate of alpha) | 1.334 | ||||
| Mean Square Error | 1.863 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.256 | ||||
| p(b) | 0.430 | ||||
| t(a) | 0.680 | ||||
| p(a) | 0.462 | ||||
| Lowerbound of 95% confidence interval for beta | -0.130 | ||||
| Upperbound of 95% confidence interval for beta | 0.581 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.549 | ||||
| Upperbound of 95% confidence interval for alpha | 5.216 | ||||
| Treynor index (mean / b) | 7.873 | ||||
| Jensen alpha (a) | 1.334 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.193 | ||||
| SD | 0.963 | ||||
| Sharpe ratio (Glass type estimate) | 1.239 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.232 | ||||
| df | 130.000 | ||||
| t | 0.876 | ||||
| p | 0.462 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.539 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.013 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.544 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.008 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 12.338 | ||||
| Upside Potential Ratio | 17.255 | ||||
| Upside part of mean | 1.669 | ||||
| Downside part of mean | -0.476 | ||||
| Upside SD | 0.957 | ||||
| Downside SD | 0.097 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 99.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.741 | ||||
| Mean of criterion | 1.193 | ||||
| SD of predictor | 0.669 | ||||
| SD of criterion | 0.963 | ||||
| Covariance | 0.071 | ||||
| r | 0.110 | ||||
| b (slope, estimate of beta) | 0.158 | ||||
| a (intercept, estimate of alpha) | 0.919 | ||||
| Mean Square Error | 0.923 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.252 | ||||
| p(b) | 0.430 | ||||
| t(a) | 0.668 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | -0.091 | ||||
| Upperbound of 95% confidence interval for beta | 0.407 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.804 | ||||
| Upperbound of 95% confidence interval for alpha | 3.641 | ||||
| Treynor index (mean / b) | 7.565 | ||||
| Jensen alpha (a) | 0.919 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.089 | ||||
| Expected Shortfall on VaR | 0.111 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.962 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.963 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 15.000 | ||||
| Percentage of outliers low | 0.115 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.099 | ||||
| Mean of outliers high | 1.087 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -7.813 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.280 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 22.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.106 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.018 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.000 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 0.106 | ||||
| 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) | 1.713 | ||||
| Compounded annual return (geometric extrapolation) | 2.446 | ||||
| Calmar ratio (compounded annual return / max draw down) | 23.100 | ||||
| Compounded annual return / average of 25% largest draw downs | 137.068 | ||||
| Compounded annual return / Expected Shortfall lognormal | 21.997 | ||||