Advanced Statistics: Market Mood Oscillator
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 | 0.294 | ||||
| SD | 0.760 | ||||
| Sharpe ratio (Glass type estimate) | 0.386 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.382 | ||||
| df | 79.000 | ||||
| t | 0.997 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.377 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.146 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.144 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.892 | ||||
| Upside Potential Ratio | 1.592 | ||||
| Upside part of mean | 0.524 | ||||
| Downside part of mean | -0.231 | ||||
| Upside SD | 0.685 | ||||
| Downside SD | 0.329 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.164 | ||||
| Mean of criterion | 0.294 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.760 | ||||
| Covariance | -0.016 | ||||
| r | -0.088 | ||||
| b (slope, estimate of beta) | -0.287 | ||||
| a (intercept, estimate of alpha) | 0.341 | ||||
| Mean Square Error | 0.581 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.782 | ||||
| p(b) | 0.782 | ||||
| t(a) | 1.131 | ||||
| p(a) | 0.131 | ||||
| Lowerbound of 95% confidence interval for beta | -1.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.443 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.259 | ||||
| Upperbound of 95% confidence interval for alpha | 0.941 | ||||
| Treynor index (mean / b) | -1.024 | ||||
| Jensen alpha (a) | 0.341 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.051 | ||||
| SD | 0.723 | ||||
| Sharpe ratio (Glass type estimate) | 0.071 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.070 | ||||
| df | 79.000 | ||||
| t | 0.183 | ||||
| p | 0.428 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.688 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.830 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.689 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.829 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.092 | ||||
| Upside Potential Ratio | 0.697 | ||||
| Upside part of mean | 0.390 | ||||
| Downside part of mean | -0.338 | ||||
| Upside SD | 0.451 | ||||
| Downside SD | 0.559 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.136 | ||||
| Mean of criterion | 0.051 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.723 | ||||
| Covariance | -0.010 | ||||
| r | -0.061 | ||||
| b (slope, estimate of beta) | -0.187 | ||||
| a (intercept, estimate of alpha) | 0.077 | ||||
| Mean Square Error | 0.527 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.541 | ||||
| p(b) | 0.705 | ||||
| t(a) | 0.269 | ||||
| p(a) | 0.394 | ||||
| Lowerbound of 95% confidence interval for beta | -0.876 | ||||
| Upperbound of 95% confidence interval for beta | 0.501 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.491 | ||||
| Upperbound of 95% confidence interval for alpha | 0.644 | ||||
| Treynor index (mean / b) | -0.274 | ||||
| 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%) | 0.287 | ||||
| Expected Shortfall on VaR | 0.345 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.260 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.575 | ||||
| Mean of quarter 1 | 0.936 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.177 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.113 | ||||
| Mean of outliers low | 0.858 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.138 | ||||
| Mean of outliers high | 1.321 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.093 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.258 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.235 | ||||
| Quartile 3 | 0.534 | ||||
| Maximum | 0.740 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.465 | ||||
| Mean of quarter 4 | 0.740 | ||||
| Inter Quartile Range | 0.529 | ||||
| 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) | 0.133 | ||||
| Compounded annual return (geometric extrapolation) | 0.100 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.135 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.135 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.290 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.229 | ||||
| SD | 2.358 | ||||
| Sharpe ratio (Glass type estimate) | 0.946 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.945 | ||||
| df | 1755.000 | ||||
| t | 2.448 | ||||
| p | 0.463 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.188 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.703 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.187 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.703 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.108 | ||||
| Upside Potential Ratio | 5.054 | ||||
| Upside part of mean | 5.346 | ||||
| Downside part of mean | -3.117 | ||||
| Upside SD | 2.111 | ||||
| Downside SD | 1.058 | ||||
| N nonnegative terms | 145.000 | ||||
| N negative terms | 1611.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1756.000 | ||||
| Mean of predictor | 0.343 | ||||
| Mean of criterion | 2.229 | ||||
| SD of predictor | 0.561 | ||||
| SD of criterion | 2.358 | ||||
| Covariance | 0.029 | ||||
| r | 0.022 | ||||
| b (slope, estimate of beta) | 0.091 | ||||
| a (intercept, estimate of alpha) | 2.198 | ||||
| Mean Square Error | 5.558 | ||||
| DF error | 1754.000 | ||||
| t(b) | 0.909 | ||||
| p(b) | 0.489 | ||||
| t(a) | 2.412 | ||||
| p(a) | 0.471 | ||||
| Lowerbound of 95% confidence interval for beta | -0.106 | ||||
| Upperbound of 95% confidence interval for beta | 0.288 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.411 | ||||
| Upperbound of 95% confidence interval for alpha | 3.985 | ||||
| Treynor index (mean / b) | 24.442 | ||||
| Jensen alpha (a) | 2.198 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.051 | ||||
| SD | 2.075 | ||||
| Sharpe ratio (Glass type estimate) | 0.024 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.024 | ||||
| df | 1755.000 | ||||
| t | 0.063 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.733 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.782 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.733 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.782 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.033 | ||||
| Upside Potential Ratio | 2.668 | ||||
| Upside part of mean | 4.064 | ||||
| Downside part of mean | -4.013 | ||||
| Upside SD | 1.408 | ||||
| Downside SD | 1.523 | ||||
| N nonnegative terms | 145.000 | ||||
| N negative terms | 1611.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1756.000 | ||||
| Mean of predictor | 0.192 | ||||
| Mean of criterion | 0.051 | ||||
| SD of predictor | 0.549 | ||||
| SD of criterion | 2.075 | ||||
| Covariance | -0.009 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.031 | ||||
| a (intercept, estimate of alpha) | 0.057 | ||||
| Mean Square Error | 4.306 | ||||
| DF error | 1754.000 | ||||
| t(b) | -0.345 | ||||
| p(b) | 0.504 | ||||
| t(a) | 0.071 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.208 | ||||
| Upperbound of 95% confidence interval for beta | 0.146 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.516 | ||||
| Upperbound of 95% confidence interval for alpha | 1.629 | ||||
| Treynor index (mean / b) | -1.631 | ||||
| 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%) | 0.190 | ||||
| Expected Shortfall on VaR | 0.231 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1756.000 | ||||
| Minimum | 0.232 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.479 | ||||
| Mean of quarter 1 | 0.953 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.082 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 154.000 | ||||
| Percentage of outliers low | 0.088 | ||||
| Mean of outliers low | 0.866 | ||||
| Number of outliers high | 177.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 1.203 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.136 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.229 | ||||
| Median | 0.509 | ||||
| Quartile 3 | 0.745 | ||||
| Maximum | 0.902 | ||||
| Mean of quarter 1 | 0.083 | ||||
| Mean of quarter 2 | 0.387 | ||||
| Mean of quarter 3 | 0.557 | ||||
| Mean of quarter 4 | 0.849 | ||||
| Inter Quartile Range | 0.516 | ||||
| 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) | -5.366 | ||||
| VaR(95%) (moments method) | 0.887 | ||||
| Expected Shortfall (moments method) | 0.887 | ||||
| Extreme Value Index (regression method) | -1.202 | ||||
| VaR(95%) (regression method) | 0.930 | ||||
| Expected Shortfall (regression method) | 0.942 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.132 | ||||
| Compounded annual return (geometric extrapolation) | 0.099 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.110 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.117 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.430 | ||||
| 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 | 1.920 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.643 | ||||
| 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 | 1.712 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.634 | ||||
| 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) | -8678936999691689.000 | ||||
| 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) | -449072605890745176351446977740800.000 | ||||
| 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 | ||||