Advanced Statistics: Commodities P/X (Test System)
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 | -0.019 | ||||
| SD | 0.213 | ||||
| Sharpe ratio (Glass type estimate) | -0.088 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.087 | ||||
| df | 99.000 | ||||
| t | -0.254 | ||||
| p | 0.600 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.767 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.591 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.766 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.592 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.126 | ||||
| Upside Potential Ratio | 0.768 | ||||
| Upside part of mean | 0.114 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.151 | ||||
| Downside SD | 0.149 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 92.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 100.000 | ||||
| Mean of predictor | 0.188 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.213 | ||||
| Covariance | 0.014 | ||||
| r | 0.233 | ||||
| b (slope, estimate of beta) | 0.174 | ||||
| a (intercept, estimate of alpha) | -0.051 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 98.000 | ||||
| t(b) | 2.367 | ||||
| p(b) | 0.010 | ||||
| t(a) | -0.701 | ||||
| p(a) | 0.758 | ||||
| Lowerbound of 95% confidence interval for beta | 0.028 | ||||
| Upperbound of 95% confidence interval for beta | 0.320 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.197 | ||||
| Upperbound of 95% confidence interval for alpha | 0.094 | ||||
| Treynor index (mean / b) | -0.107 | ||||
| Jensen alpha (a) | -0.051 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.221 | ||||
| Sharpe ratio (Glass type estimate) | -0.190 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.189 | ||||
| df | 99.000 | ||||
| t | -0.549 | ||||
| p | 0.708 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.869 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.490 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.868 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.491 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.242 | ||||
| Upside Potential Ratio | 0.598 | ||||
| Upside part of mean | 0.104 | ||||
| Downside part of mean | -0.146 | ||||
| Upside SD | 0.135 | ||||
| Downside SD | 0.174 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 92.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 100.000 | ||||
| Mean of predictor | 0.146 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.221 | ||||
| Covariance | 0.017 | ||||
| r | 0.270 | ||||
| b (slope, estimate of beta) | 0.208 | ||||
| a (intercept, estimate of alpha) | -0.072 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 98.000 | ||||
| t(b) | 2.776 | ||||
| p(b) | 0.003 | ||||
| t(a) | -0.966 | ||||
| p(a) | 0.832 | ||||
| Lowerbound of 95% confidence interval for beta | 0.059 | ||||
| Upperbound of 95% confidence interval for beta | 0.357 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.221 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | -0.202 | ||||
| Jensen alpha (a) | -0.072 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.103 | ||||
| Expected Shortfall on VaR | 0.126 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 100.000 | ||||
| Minimum | 0.686 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.291 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.039 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.100 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.110 | ||||
| Mean of outliers high | 1.089 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19.611 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.052 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | 0.115 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.239 | ||||
| Maximum | 0.370 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.016 | ||||
| Mean of quarter 4 | 0.342 | ||||
| Inter Quartile Range | 0.239 | ||||
| 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) | 0.002 | ||||
| Compounded annual return (geometric extrapolation) | 0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.005 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.006 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.015 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.042 | ||||
| SD | 0.419 | ||||
| Sharpe ratio (Glass type estimate) | 0.100 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.100 | ||||
| df | 2193.000 | ||||
| t | 0.290 | ||||
| p | 0.386 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.577 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.778 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.577 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.777 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.165 | ||||
| Upside Potential Ratio | 1.964 | ||||
| Upside part of mean | 0.498 | ||||
| Downside part of mean | -0.456 | ||||
| Upside SD | 0.333 | ||||
| Downside SD | 0.254 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 2101.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2194.000 | ||||
| Mean of predictor | 0.314 | ||||
| Mean of criterion | 0.042 | ||||
| SD of predictor | 0.562 | ||||
| SD of criterion | 0.419 | ||||
| Covariance | 0.073 | ||||
| r | 0.311 | ||||
| b (slope, estimate of beta) | 0.232 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.159 | ||||
| DF error | 2192.000 | ||||
| t(b) | 15.321 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.223 | ||||
| p(a) | 0.588 | ||||
| Lowerbound of 95% confidence interval for beta | 0.202 | ||||
| Upperbound of 95% confidence interval for beta | 0.261 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.301 | ||||
| Upperbound of 95% confidence interval for alpha | 0.239 | ||||
| Treynor index (mean / b) | 0.181 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.409 | ||||
| Sharpe ratio (Glass type estimate) | -0.103 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.103 | ||||
| df | 2193.000 | ||||
| t | -0.298 | ||||
| p | 0.617 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.780 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.574 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.780 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.575 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.144 | ||||
| Upside Potential Ratio | 1.545 | ||||
| Upside part of mean | 0.453 | ||||
| Downside part of mean | -0.495 | ||||
| Upside SD | 0.285 | ||||
| Downside SD | 0.293 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 2101.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2194.000 | ||||
| Mean of predictor | 0.155 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.565 | ||||
| SD of criterion | 0.409 | ||||
| Covariance | 0.072 | ||||
| r | 0.310 | ||||
| b (slope, estimate of beta) | 0.225 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.151 | ||||
| DF error | 2192.000 | ||||
| t(b) | 15.270 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.572 | ||||
| p(a) | 0.716 | ||||
| Lowerbound of 95% confidence interval for beta | 0.196 | ||||
| Upperbound of 95% confidence interval for beta | 0.253 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.341 | ||||
| Upperbound of 95% confidence interval for alpha | 0.187 | ||||
| Treynor index (mean / b) | -0.187 | ||||
| Jensen alpha (a) | -0.077 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| 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 | 2194.000 | ||||
| Minimum | 0.686 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.458 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 112.000 | ||||
| Percentage of outliers low | 0.051 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 122.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.201 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 26.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.120 | ||||
| Maximum | 0.370 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.016 | ||||
| Mean of quarter 4 | 0.297 | ||||
| Inter Quartile Range | 0.120 | ||||
| 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 | 0.192 | ||||
| Mean of outliers high | 0.332 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -23.970 | ||||
| VaR(95%) (moments method) | 0.271 | ||||
| Expected Shortfall (moments method) | 0.271 | ||||
| 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) | 0.005 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.007 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.038 | ||||
| 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 | 1.199 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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 | 1.081 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.482 | ||||
| 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) | -8715921576995464.000 | ||||
| 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) | 80782867552757779949641449603072.000 | ||||
| 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 | ||||