Advanced Statistics: NoReply
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 | -0.037 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | -0.347 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.342 | ||||
| df | 53.000 | ||||
| t | -0.735 | ||||
| p | 0.767 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.271 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.581 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.268 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.585 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.438 | ||||
| Upside Potential Ratio | 1.190 | ||||
| Upside part of mean | 0.100 | ||||
| Downside part of mean | -0.137 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.382 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.016 | ||||
| r | 0.519 | ||||
| b (slope, estimate of beta) | 0.190 | ||||
| a (intercept, estimate of alpha) | -0.110 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 52.000 | ||||
| t(b) | 4.379 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.366 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | 0.103 | ||||
| Upperbound of 95% confidence interval for beta | 0.278 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.202 | ||||
| Upperbound of 95% confidence interval for alpha | -0.017 | ||||
| Treynor index (mean / b) | -0.193 | ||||
| Jensen alpha (a) | -0.110 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.108 | ||||
| Sharpe ratio (Glass type estimate) | -0.394 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.388 | ||||
| df | 53.000 | ||||
| t | -0.836 | ||||
| p | 0.797 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.319 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.535 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.315 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.538 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.484 | ||||
| Upside Potential Ratio | 1.117 | ||||
| Upside part of mean | 0.098 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.339 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.108 | ||||
| Covariance | 0.014 | ||||
| r | 0.491 | ||||
| b (slope, estimate of beta) | 0.202 | ||||
| a (intercept, estimate of alpha) | -0.111 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 52.000 | ||||
| t(b) | 4.067 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.328 | ||||
| p(a) | 0.988 | ||||
| Lowerbound of 95% confidence interval for beta | 0.102 | ||||
| Upperbound of 95% confidence interval for beta | 0.302 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.207 | ||||
| Upperbound of 95% confidence interval for alpha | -0.015 | ||||
| Treynor index (mean / b) | -0.210 | ||||
| Jensen alpha (a) | -0.111 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 54.000 | ||||
| Minimum | 0.894 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.100 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.899 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.037 | ||||
| Mean of outliers high | 1.080 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.550 | ||||
| VaR(95%) (moments method) | 0.035 | ||||
| Expected Shortfall (moments method) | 0.086 | ||||
| Extreme Value Index (regression method) | 0.457 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.072 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.236 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.015 | ||||
| Mean of quarter 4 | 0.126 | ||||
| Inter Quartile Range | 0.007 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.236 | ||||
| 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) | 0.002 | ||||
| Compounded annual return (geometric extrapolation) | 0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.007 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.013 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.025 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.028 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | -0.265 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.265 | ||||
| df | 1190.000 | ||||
| t | -0.565 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.184 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.654 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.184 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.654 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.353 | ||||
| Upside Potential Ratio | 5.507 | ||||
| Upside part of mean | 0.437 | ||||
| Downside part of mean | -0.465 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.079 | ||||
| N nonnegative terms | 576.000 | ||||
| N negative terms | 615.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1191.000 | ||||
| Mean of predictor | 0.392 | ||||
| Mean of criterion | -0.028 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.005 | ||||
| r | 0.181 | ||||
| b (slope, estimate of beta) | 0.069 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 1189.000 | ||||
| t(b) | 6.352 | ||||
| p(b) | 0.385 | ||||
| t(a) | -1.127 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | 0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.151 | ||||
| Upperbound of 95% confidence interval for alpha | 0.041 | ||||
| Treynor index (mean / b) | -0.405 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | -0.316 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.316 | ||||
| df | 1190.000 | ||||
| t | -0.674 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.235 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.603 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.235 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.603 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.414 | ||||
| Upside Potential Ratio | 5.347 | ||||
| Upside part of mean | 0.434 | ||||
| Downside part of mean | -0.468 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.081 | ||||
| N nonnegative terms | 576.000 | ||||
| N negative terms | 615.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1191.000 | ||||
| Mean of predictor | 0.353 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.005 | ||||
| r | 0.184 | ||||
| b (slope, estimate of beta) | 0.070 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 1189.000 | ||||
| t(b) | 6.437 | ||||
| p(b) | 0.384 | ||||
| t(a) | -1.187 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | 0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.092 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 0.038 | ||||
| Treynor index (mean / b) | -0.479 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1191.000 | ||||
| Minimum | 0.916 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.073 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 53.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 51.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.431 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.012 | ||||
| Extreme Value Index (regression method) | 0.302 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 29.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.012 | ||||
| Maximum | 0.244 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.061 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.138 | ||||
| Mean of outliers high | 0.091 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.650 | ||||
| VaR(95%) (moments method) | 0.050 | ||||
| Expected Shortfall (moments method) | 0.161 | ||||
| Extreme Value Index (regression method) | 0.784 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | 0.293 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.043 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.173 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.771 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.124 | ||||
| SD | 0.145 | ||||
| Sharpe ratio (Glass type estimate) | -0.855 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.850 | ||||
| df | 130.000 | ||||
| t | -0.605 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.628 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.920 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.624 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.923 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.956 | ||||
| Upside Potential Ratio | 3.978 | ||||
| Upside part of mean | 0.517 | ||||
| Downside part of mean | -0.642 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.130 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.062 | ||||
| Mean of criterion | -0.124 | ||||
| SD of predictor | 0.460 | ||||
| SD of criterion | 0.145 | ||||
| Covariance | 0.027 | ||||
| r | 0.402 | ||||
| b (slope, estimate of beta) | 0.127 | ||||
| a (intercept, estimate of alpha) | -0.259 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.983 | ||||
| p(b) | 0.251 | ||||
| t(a) | -1.358 | ||||
| p(a) | 0.575 | ||||
| Lowerbound of 95% confidence interval for beta | 0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.177 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.637 | ||||
| Upperbound of 95% confidence interval for alpha | 0.118 | ||||
| Treynor index (mean / b) | -0.979 | ||||
| Jensen alpha (a) | -0.259 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.135 | ||||
| SD | 0.150 | ||||
| Sharpe ratio (Glass type estimate) | -0.904 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.899 | ||||
| df | 130.000 | ||||
| t | -0.639 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.676 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.872 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.673 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.875 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.001 | ||||
| Upside Potential Ratio | 3.817 | ||||
| Upside part of mean | 0.515 | ||||
| Downside part of mean | -0.650 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.135 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.955 | ||||
| Mean of criterion | -0.135 | ||||
| SD of predictor | 0.461 | ||||
| SD of criterion | 0.150 | ||||
| Covariance | 0.028 | ||||
| r | 0.400 | ||||
| b (slope, estimate of beta) | 0.130 | ||||
| a (intercept, estimate of alpha) | -0.259 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.956 | ||||
| p(b) | 0.252 | ||||
| t(a) | -1.321 | ||||
| p(a) | 0.573 | ||||
| Lowerbound of 95% confidence interval for beta | 0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.647 | ||||
| Upperbound of 95% confidence interval for alpha | 0.129 | ||||
| Treynor index (mean / b) | -1.042 | ||||
| Jensen alpha (a) | -0.259 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.019 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.916 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.017 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.916 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.599 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.021 | ||||
| Extreme Value Index (regression method) | 0.309 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.040 | ||||
| Median | 0.072 | ||||
| Quartile 3 | 0.103 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.135 | ||||
| Inter Quartile Range | 0.063 | ||||
| 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) | -0.089 | ||||
| Compounded annual return (geometric extrapolation) | -0.087 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.645 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.645 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.496 | ||||