Advanced Statistics: Test System 3
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 | 13648.640 | ||||
| SD | 27854.503 | ||||
| Sharpe ratio (Glass type estimate) | 0.490 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.482 | ||||
| df | 49.000 | ||||
| t | 1.000 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.477 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.453 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.482 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.447 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 17269.286 | ||||
| Upside Potential Ratio | 17270.345 | ||||
| Upside part of mean | 13649.477 | ||||
| Downside part of mean | -0.837 | ||||
| Upside SD | 27854.617 | ||||
| Downside SD | 0.790 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | 13648.640 | ||||
| SD of predictor | 0.424 | ||||
| SD of criterion | 27854.503 | ||||
| Covariance | 10273.008 | ||||
| r | 0.869 | ||||
| b (slope, estimate of beta) | 57034.457 | ||||
| a (intercept, estimate of alpha) | -18070.298 | ||||
| Mean Square Error | 193915380.858 | ||||
| DF error | 48.000 | ||||
| t(b) | 12.168 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.474 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | 47609.896 | ||||
| Upperbound of 95% confidence interval for beta | 66459.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -32754.149 | ||||
| Upperbound of 95% confidence interval for alpha | -3386.447 | ||||
| Treynor index (mean / b) | 0.239 | ||||
| Jensen alpha (a) | -18070.298 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.254 | ||||
| SD | 9.474 | ||||
| Sharpe ratio (Glass type estimate) | -0.238 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.234 | ||||
| df | 49.000 | ||||
| t | -0.486 | ||||
| p | 0.685 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.198 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.725 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.196 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.727 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.296 | ||||
| Upside Potential Ratio | 0.455 | ||||
| Upside part of mean | 3.458 | ||||
| Downside part of mean | -5.713 | ||||
| Upside SD | 5.528 | ||||
| Downside SD | 7.604 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.480 | ||||
| Mean of criterion | -2.254 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 9.474 | ||||
| Covariance | 1.193 | ||||
| r | 0.376 | ||||
| b (slope, estimate of beta) | 10.638 | ||||
| a (intercept, estimate of alpha) | -7.358 | ||||
| Mean Square Error | 78.664 | ||||
| DF error | 48.000 | ||||
| t(b) | 2.812 | ||||
| p(b) | 0.004 | ||||
| t(a) | -1.563 | ||||
| p(a) | 0.938 | ||||
| Lowerbound of 95% confidence interval for beta | 3.032 | ||||
| Upperbound of 95% confidence interval for beta | 18.243 | ||||
| Lowerbound of 95% confidence interval for alpha | -16.826 | ||||
| Upperbound of 95% confidence interval for alpha | 2.110 | ||||
| Treynor index (mean / b) | -0.212 | ||||
| Jensen alpha (a) | -7.358 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.991 | ||||
| Expected Shortfall on VaR | 0.996 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.228 | ||||
| Expected Shortfall on VaR | 0.483 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 56859.000 | ||||
| Mean of quarter 1 | 0.744 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 4375.834 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.140 | ||||
| Mean of outliers low | 0.525 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.160 | ||||
| Mean of outliers high | 7110.105 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.534 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 0.867 | ||||
| Median | 0.911 | ||||
| Quartile 3 | 0.956 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.823 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.089 | ||||
| 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) | -0.240 | ||||
| Compounded annual return (geometric extrapolation) | -0.890 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.890 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.890 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.894 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 13620.483 | ||||
| SD | 27812.163 | ||||
| Sharpe ratio (Glass type estimate) | 0.490 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.489 | ||||
| df | 1094.000 | ||||
| t | 1.001 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.469 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.449 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.470 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.448 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 9723.834 | ||||
| Upside Potential Ratio | 9726.344 | ||||
| Upside part of mean | 13623.999 | ||||
| Downside part of mean | -3.516 | ||||
| Upside SD | 27812.193 | ||||
| Downside SD | 1.401 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 1015.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1095.000 | ||||
| Mean of predictor | 0.590 | ||||
| Mean of criterion | 13620.483 | ||||
| SD of predictor | 0.408 | ||||
| SD of criterion | 27812.163 | ||||
| Covariance | 958.031 | ||||
| r | 0.084 | ||||
| b (slope, estimate of beta) | 5751.294 | ||||
| a (intercept, estimate of alpha) | 10229.537 | ||||
| Mean Square Error | 768709132.723 | ||||
| DF error | 1093.000 | ||||
| t(b) | 2.800 | ||||
| p(b) | 0.446 | ||||
| t(a) | 0.751 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | 1721.389 | ||||
| Upperbound of 95% confidence interval for beta | 9781.199 | ||||
| Lowerbound of 95% confidence interval for alpha | -16486.882 | ||||
| Upperbound of 95% confidence interval for alpha | 36945.957 | ||||
| Treynor index (mean / b) | 2.368 | ||||
| Jensen alpha (a) | 10229.537 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.248 | ||||
| SD | 10.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.221 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.221 | ||||
| df | 1094.000 | ||||
| t | -0.451 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.180 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.738 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.179 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.738 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.279 | ||||
| Upside Potential Ratio | 1.008 | ||||
| Upside part of mean | 8.129 | ||||
| Downside part of mean | -10.377 | ||||
| Upside SD | 6.203 | ||||
| Downside SD | 8.065 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 1015.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1095.000 | ||||
| Mean of predictor | 0.507 | ||||
| Mean of criterion | -2.248 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 10.178 | ||||
| Covariance | 0.070 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.426 | ||||
| a (intercept, estimate of alpha) | -2.464 | ||||
| Mean Square Error | 103.660 | ||||
| DF error | 1093.000 | ||||
| t(b) | 0.559 | ||||
| p(b) | 0.489 | ||||
| t(a) | -0.493 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | -1.068 | ||||
| Upperbound of 95% confidence interval for beta | 1.919 | ||||
| Lowerbound of 95% confidence interval for alpha | -12.265 | ||||
| Upperbound of 95% confidence interval for alpha | 7.338 | ||||
| Treynor index (mean / b) | -5.280 | ||||
| Jensen alpha (a) | -2.464 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.648 | ||||
| Expected Shortfall on VaR | 0.722 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1095.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 56859.000 | ||||
| Mean of quarter 1 | 0.947 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 208.810 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 99.000 | ||||
| Percentage of outliers low | 0.090 | ||||
| Mean of outliers low | 0.853 | ||||
| Number of outliers high | 99.000 | ||||
| Percentage of outliers high | 0.090 | ||||
| Mean of outliers high | 576.152 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.070 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| 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 | 19.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.084 | ||||
| Median | 0.217 | ||||
| Quartile 3 | 0.898 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.053 | ||||
| Mean of quarter 2 | 0.136 | ||||
| Mean of quarter 3 | 0.650 | ||||
| Mean of quarter 4 | 0.946 | ||||
| Inter Quartile Range | 0.814 | ||||
| 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) | 0.335 | ||||
| VaR(95%) (moments method) | 0.963 | ||||
| Expected Shortfall (moments method) | 1.005 | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.239 | ||||
| Compounded annual return (geometric extrapolation) | -0.890 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.890 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.940 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.232 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 113711.956 | ||||
| SD | 80409.377 | ||||
| Sharpe ratio (Glass type estimate) | 1.414 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.406 | ||||
| df | 130.000 | ||||
| t | 1.000 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.366 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.189 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.371 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 56847.375 | ||||
| Upside Potential Ratio | 56849.397 | ||||
| Upside part of mean | 113716.000 | ||||
| Downside part of mean | -4.044 | ||||
| Upside SD | 80409.354 | ||||
| Downside SD | 2.000 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.372 | ||||
| Mean of criterion | 113711.956 | ||||
| SD of predictor | 0.601 | ||||
| SD of criterion | 80409.377 | ||||
| Covariance | 7281.611 | ||||
| r | 0.151 | ||||
| b (slope, estimate of beta) | 20187.751 | ||||
| a (intercept, estimate of alpha) | 65827.378 | ||||
| Mean Square Error | 6367650410.301 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.732 | ||||
| p(b) | 0.404 | ||||
| t(a) | 0.567 | ||||
| p(a) | 0.468 | ||||
| Lowerbound of 95% confidence interval for beta | -2868.550 | ||||
| Upperbound of 95% confidence interval for beta | 43244.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -164050.740 | ||||
| Upperbound of 95% confidence interval for alpha | 295705.496 | ||||
| Treynor index (mean / b) | 5.633 | ||||
| Jensen alpha (a) | 65827.378 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -21.941 | ||||
| SD | 26.886 | ||||
| Sharpe ratio (Glass type estimate) | -0.816 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.811 | ||||
| df | 130.000 | ||||
| t | -0.577 | ||||
| p | 0.525 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.588 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.959 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.585 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.962 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.002 | ||||
| Upside Potential Ratio | 1.000 | ||||
| Upside part of mean | 21.896 | ||||
| Downside part of mean | -43.837 | ||||
| Upside SD | 15.483 | ||||
| Downside SD | 21.897 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.189 | ||||
| Mean of criterion | -21.941 | ||||
| SD of predictor | 0.586 | ||||
| SD of criterion | 26.886 | ||||
| Covariance | 0.161 | ||||
| r | 0.010 | ||||
| b (slope, estimate of beta) | 0.469 | ||||
| a (intercept, estimate of alpha) | -22.967 | ||||
| Mean Square Error | 728.411 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.116 | ||||
| p(b) | 0.493 | ||||
| t(a) | -0.586 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | -7.528 | ||||
| Upperbound of 95% confidence interval for beta | 8.466 | ||||
| Lowerbound of 95% confidence interval for alpha | -100.487 | ||||
| Upperbound of 95% confidence interval for alpha | 54.552 | ||||
| Treynor index (mean / b) | -46.781 | ||||
| Jensen alpha (a) | -22.967 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.940 | ||||
| Expected Shortfall on VaR | 0.965 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 56859.000 | ||||
| Mean of quarter 1 | 0.939 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1723.970 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.000 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 56859.000 | ||||
| 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 | 2.000 | ||||
| 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 | NA | ||||
| Mean of quarter 3 | NA | ||||
| 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 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) | -2.000 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.000 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.036 | ||||