Advanced Statistics: Strategic Volatility Portfolio
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 | -0.010 | ||||
| SD | 0.290 | ||||
| Sharpe ratio (Glass type estimate) | -0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.035 | ||||
| df | 50.000 | ||||
| t | -0.073 | ||||
| p | 0.529 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.986 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.985 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.916 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.042 | ||||
| Upside Potential Ratio | 1.129 | ||||
| Upside part of mean | 0.272 | ||||
| Downside part of mean | -0.282 | ||||
| Upside SD | 0.156 | ||||
| Downside SD | 0.241 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 27.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.415 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.290 | ||||
| Covariance | 0.006 | ||||
| r | 0.071 | ||||
| b (slope, estimate of beta) | 0.068 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 49.000 | ||||
| t(b) | 0.500 | ||||
| p(b) | 0.310 | ||||
| t(a) | -0.252 | ||||
| p(a) | 0.599 | ||||
| Lowerbound of 95% confidence interval for beta | -0.205 | ||||
| Upperbound of 95% confidence interval for beta | 0.341 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.345 | ||||
| Upperbound of 95% confidence interval for alpha | 0.268 | ||||
| Treynor index (mean / b) | -0.150 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.338 | ||||
| Sharpe ratio (Glass type estimate) | -0.178 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.175 | ||||
| df | 50.000 | ||||
| t | -0.367 | ||||
| p | 0.643 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.129 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.774 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.127 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.776 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.200 | ||||
| Upside Potential Ratio | 0.862 | ||||
| Upside part of mean | 0.259 | ||||
| Downside part of mean | -0.320 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.301 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 27.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.338 | ||||
| Covariance | 0.006 | ||||
| r | 0.057 | ||||
| b (slope, estimate of beta) | 0.067 | ||||
| a (intercept, estimate of alpha) | -0.085 | ||||
| Mean Square Error | 0.116 | ||||
| DF error | 49.000 | ||||
| t(b) | 0.400 | ||||
| p(b) | 0.345 | ||||
| t(a) | -0.480 | ||||
| p(a) | 0.683 | ||||
| Lowerbound of 95% confidence interval for beta | -0.269 | ||||
| Upperbound of 95% confidence interval for beta | 0.402 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.439 | ||||
| Upperbound of 95% confidence interval for alpha | 0.270 | ||||
| Treynor index (mean / b) | -0.902 | ||||
| Jensen alpha (a) | -0.085 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.153 | ||||
| Expected Shortfall on VaR | 0.186 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.120 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 51.000 | ||||
| Minimum | 0.570 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 1.145 | ||||
| Mean of quarter 1 | 0.921 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.083 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.078 | ||||
| Mean of outliers low | 0.803 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 1.119 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.916 | ||||
| VaR(95%) (moments method) | 0.071 | ||||
| Expected Shortfall (moments method) | 0.915 | ||||
| Extreme Value Index (regression method) | 1.449 | ||||
| VaR(95%) (regression method) | 0.061 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.108 | ||||
| Maximum | 0.528 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | 0.057 | ||||
| Mean of quarter 4 | 0.344 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 0.528 | ||||
| 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) | -0.016 | ||||
| Compounded annual return (geometric extrapolation) | -0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.030 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.047 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.087 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.000 | ||||
| SD | 0.305 | ||||
| Sharpe ratio (Glass type estimate) | 0.001 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.001 | ||||
| df | 1114.000 | ||||
| t | 0.002 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.949 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.951 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.949 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.951 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.001 | ||||
| Upside Potential Ratio | 3.009 | ||||
| Upside part of mean | 0.833 | ||||
| Downside part of mean | -0.832 | ||||
| Upside SD | 0.127 | ||||
| Downside SD | 0.277 | ||||
| N nonnegative terms | 542.000 | ||||
| N negative terms | 573.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1115.000 | ||||
| Mean of predictor | 0.406 | ||||
| Mean of criterion | 0.000 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.305 | ||||
| Covariance | 0.021 | ||||
| r | 0.235 | ||||
| b (slope, estimate of beta) | 0.246 | ||||
| a (intercept, estimate of alpha) | -0.100 | ||||
| Mean Square Error | 0.088 | ||||
| DF error | 1113.000 | ||||
| t(b) | 8.050 | ||||
| p(b) | 0.352 | ||||
| t(a) | -0.691 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | 0.186 | ||||
| Upperbound of 95% confidence interval for beta | 0.306 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.383 | ||||
| Upperbound of 95% confidence interval for alpha | 0.183 | ||||
| Treynor index (mean / b) | 0.001 | ||||
| Jensen alpha (a) | -0.100 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.375 | ||||
| Sharpe ratio (Glass type estimate) | -0.161 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.161 | ||||
| df | 1114.000 | ||||
| t | -0.332 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.111 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.789 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.111 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.789 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.171 | ||||
| Upside Potential Ratio | 2.335 | ||||
| Upside part of mean | 0.825 | ||||
| Downside part of mean | -0.885 | ||||
| Upside SD | 0.125 | ||||
| Downside SD | 0.353 | ||||
| N nonnegative terms | 542.000 | ||||
| N negative terms | 573.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1115.000 | ||||
| Mean of predictor | 0.363 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.375 | ||||
| Covariance | 0.024 | ||||
| r | 0.218 | ||||
| b (slope, estimate of beta) | 0.281 | ||||
| a (intercept, estimate of alpha) | -0.162 | ||||
| Mean Square Error | 0.134 | ||||
| DF error | 1113.000 | ||||
| t(b) | 7.454 | ||||
| p(b) | 0.362 | ||||
| t(a) | -0.913 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | 0.207 | ||||
| Upperbound of 95% confidence interval for beta | 0.355 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.511 | ||||
| Upperbound of 95% confidence interval for alpha | 0.187 | ||||
| Treynor index (mean / b) | -0.214 | ||||
| Jensen alpha (a) | -0.162 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1115.000 | ||||
| Minimum | 0.521 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.084 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 83.000 | ||||
| Percentage of outliers low | 0.074 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 97.000 | ||||
| Percentage of outliers high | 0.087 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.801 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | 0.596 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.596 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.131 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 0.225 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.860 | ||||
| VaR(95%) (moments method) | 0.127 | ||||
| Expected Shortfall (moments method) | 0.958 | ||||
| Extreme Value Index (regression method) | 1.441 | ||||
| VaR(95%) (regression method) | 0.127 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.016 | ||||
| Compounded annual return (geometric extrapolation) | -0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.027 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.122 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.344 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.334 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | -1.627 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.617 | ||||
| df | 130.000 | ||||
| t | -1.150 | ||||
| p | 0.550 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.402 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.155 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.396 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.162 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.627 | ||||
| Upside Potential Ratio | 0.197 | ||||
| Upside part of mean | 0.040 | ||||
| Downside part of mean | -0.375 | ||||
| Upside SD | 0.011 | ||||
| Downside SD | 0.206 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 120.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.425 | ||||
| Mean of criterion | -0.334 | ||||
| SD of predictor | 0.575 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | 0.001 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.340 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.130 | ||||
| p(b) | 0.493 | ||||
| t(a) | -1.152 | ||||
| p(a) | 0.564 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.924 | ||||
| Upperbound of 95% confidence interval for alpha | 0.244 | ||||
| Treynor index (mean / b) | -81.582 | ||||
| Jensen alpha (a) | -0.340 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.358 | ||||
| SD | 0.222 | ||||
| Sharpe ratio (Glass type estimate) | -1.612 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.602 | ||||
| df | 130.000 | ||||
| t | -1.140 | ||||
| p | 0.550 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.387 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.170 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.381 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.176 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.612 | ||||
| Upside Potential Ratio | 0.182 | ||||
| Upside part of mean | 0.040 | ||||
| Downside part of mean | -0.398 | ||||
| Upside SD | 0.011 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 120.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.257 | ||||
| Mean of criterion | -0.358 | ||||
| SD of predictor | 0.576 | ||||
| SD of criterion | 0.222 | ||||
| Covariance | 0.001 | ||||
| r | 0.010 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.363 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.113 | ||||
| p(b) | 0.494 | ||||
| t(a) | -1.140 | ||||
| p(a) | 0.563 | ||||
| Lowerbound of 95% confidence interval for beta | -0.063 | ||||
| Upperbound of 95% confidence interval for beta | 0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.992 | ||||
| Upperbound of 95% confidence interval for alpha | 0.267 | ||||
| Treynor index (mean / b) | -93.642 | ||||
| Jensen alpha (a) | -0.363 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| 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 | 0.855 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.005 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 15.000 | ||||
| Percentage of outliers low | 0.115 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.092 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.399 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.222 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.039 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.115 | ||||
| Maximum | 0.153 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.153 | ||||
| Inter Quartile Range | 0.076 | ||||
| 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) | -0.290 | ||||
| Compounded annual return (geometric extrapolation) | -0.269 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.755 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.755 | ||||
| Compounded annual return / Expected Shortfall lognormal | -9.221 | ||||