Advanced Statistics: Corn Trend
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.287 | ||||
| Sharpe ratio (Glass type estimate) | 0.088 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.086 | ||||
| df | 33.000 | ||||
| t | 0.149 | ||||
| p | 0.441 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.077 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.252 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.078 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.251 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.174 | ||||
| Upside Potential Ratio | 1.392 | ||||
| Upside part of mean | 0.204 | ||||
| Downside part of mean | -0.178 | ||||
| Upside SD | 0.242 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.287 | ||||
| Covariance | -0.011 | ||||
| r | -0.141 | ||||
| b (slope, estimate of beta) | -0.147 | ||||
| a (intercept, estimate of alpha) | 0.105 | ||||
| Mean Square Error | 0.083 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.804 | ||||
| p(b) | 0.786 | ||||
| t(a) | 0.532 | ||||
| p(a) | 0.299 | ||||
| Lowerbound of 95% confidence interval for beta | -0.519 | ||||
| Upperbound of 95% confidence interval for beta | 0.225 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 0.510 | ||||
| Treynor index (mean / b) | -0.173 | ||||
| Jensen alpha (a) | 0.105 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.011 | ||||
| SD | 0.269 | ||||
| Sharpe ratio (Glass type estimate) | -0.041 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.040 | ||||
| df | 33.000 | ||||
| t | -0.070 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.206 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.123 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.205 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.124 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.070 | ||||
| Upside Potential Ratio | 1.123 | ||||
| Upside part of mean | 0.178 | ||||
| Downside part of mean | -0.189 | ||||
| Upside SD | 0.212 | ||||
| Downside SD | 0.159 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.498 | ||||
| Mean of criterion | -0.011 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.269 | ||||
| Covariance | -0.009 | ||||
| r | -0.132 | ||||
| b (slope, estimate of beta) | -0.136 | ||||
| a (intercept, estimate of alpha) | 0.057 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.756 | ||||
| p(b) | 0.772 | ||||
| t(a) | 0.308 | ||||
| p(a) | 0.380 | ||||
| Lowerbound of 95% confidence interval for beta | -0.504 | ||||
| Upperbound of 95% confidence interval for beta | 0.231 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.319 | ||||
| Upperbound of 95% confidence interval for alpha | 0.432 | ||||
| Treynor index (mean / b) | 0.082 | ||||
| Jensen alpha (a) | 0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.121 | ||||
| Expected Shortfall on VaR | 0.148 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.102 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.832 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.301 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.088 | ||||
| Mean of outliers low | 0.871 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.292 | ||||
| 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) | -2.893 | ||||
| VaR(95%) (regression method) | 0.212 | ||||
| Expected Shortfall (regression method) | 0.228 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.059 | ||||
| Quartile 1 | 0.120 | ||||
| Median | 0.180 | ||||
| Quartile 3 | 0.241 | ||||
| Maximum | 0.301 | ||||
| Mean of quarter 1 | 0.059 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.301 | ||||
| Inter Quartile Range | 0.121 | ||||
| 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) | 0.034 | ||||
| Compounded annual return (geometric extrapolation) | 0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.111 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.111 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.225 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.204 | ||||
| Sharpe ratio (Glass type estimate) | 0.044 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.044 | ||||
| df | 760.000 | ||||
| t | 0.075 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.106 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.194 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.106 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.194 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.061 | ||||
| Upside Potential Ratio | 3.207 | ||||
| Upside part of mean | 0.470 | ||||
| Downside part of mean | -0.461 | ||||
| Upside SD | 0.142 | ||||
| Downside SD | 0.147 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 709.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 761.000 | ||||
| Mean of predictor | 0.612 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.365 | ||||
| SD of criterion | 0.204 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 759.000 | ||||
| t(b) | 0.064 | ||||
| p(b) | 0.475 | ||||
| t(a) | 0.068 | ||||
| p(a) | 0.473 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.228 | ||||
| Upperbound of 95% confidence interval for alpha | 0.245 | ||||
| Treynor index (mean / b) | 6.915 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.012 | ||||
| SD | 0.205 | ||||
| Sharpe ratio (Glass type estimate) | -0.058 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.058 | ||||
| df | 760.000 | ||||
| t | -0.099 | ||||
| p | 0.540 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.208 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.092 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.208 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.092 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.079 | ||||
| Upside Potential Ratio | 3.037 | ||||
| Upside part of mean | 0.461 | ||||
| Downside part of mean | -0.473 | ||||
| Upside SD | 0.138 | ||||
| Downside SD | 0.152 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 709.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 761.000 | ||||
| Mean of predictor | 0.546 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.205 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 759.000 | ||||
| t(b) | 0.085 | ||||
| p(b) | 0.466 | ||||
| t(a) | -0.107 | ||||
| p(a) | 0.542 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.250 | ||||
| Upperbound of 95% confidence interval for alpha | 0.225 | ||||
| Treynor index (mean / b) | -6.853 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| 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 | 761.000 | ||||
| Minimum | 0.901 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.078 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 42.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 53.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.026 | ||||
| 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) | 0.001 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.020 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.027 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.077 | ||||
| Maximum | 0.316 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.059 | ||||
| Mean of quarter 4 | 0.282 | ||||
| Inter Quartile Range | 0.050 | ||||
| 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 | 0.222 | ||||
| Mean of outliers high | 0.282 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -54.330 | ||||
| VaR(95%) (moments method) | 0.178 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.319 | ||||
| VaR(95%) (regression method) | 0.449 | ||||
| Expected Shortfall (regression method) | 0.453 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.034 | ||||
| Compounded annual return (geometric extrapolation) | 0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.103 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.115 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.261 | ||||
| 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 | 1.043 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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 | 0.935 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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) | -8731892600719460.000 | ||||
| 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) | -113608529100085304108387133292544.000 | ||||
| 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 | ||||