Advanced Statistics: China Market Timing
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 | 0.070 | ||||
| SD | 0.193 | ||||
| Sharpe ratio (Glass type estimate) | 0.361 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.357 | ||||
| df | 60.000 | ||||
| t | 0.814 | ||||
| p | 0.209 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.512 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.231 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.515 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.228 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.623 | ||||
| Upside Potential Ratio | 3.204 | ||||
| Upside part of mean | 0.137 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.187 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.401 | ||||
| Mean of criterion | 0.070 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.193 | ||||
| Covariance | 0.007 | ||||
| r | 0.138 | ||||
| b (slope, estimate of beta) | 0.108 | ||||
| a (intercept, estimate of alpha) | 0.026 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.068 | ||||
| p(b) | 0.145 | ||||
| t(a) | 0.278 | ||||
| p(a) | 0.391 | ||||
| Lowerbound of 95% confidence interval for beta | -0.094 | ||||
| Upperbound of 95% confidence interval for beta | 0.310 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.163 | ||||
| Upperbound of 95% confidence interval for alpha | 0.215 | ||||
| Treynor index (mean / b) | 0.644 | ||||
| Jensen alpha (a) | 0.026 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.054 | ||||
| SD | 0.172 | ||||
| Sharpe ratio (Glass type estimate) | 0.312 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.308 | ||||
| df | 60.000 | ||||
| t | 0.702 | ||||
| p | 0.243 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.561 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.181 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.563 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.179 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.215 | ||||
| Upside Potential Ratio | 2.770 | ||||
| Upside part of mean | 0.122 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.165 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | 0.054 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.172 | ||||
| Covariance | 0.006 | ||||
| r | 0.144 | ||||
| b (slope, estimate of beta) | 0.106 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.121 | ||||
| p(b) | 0.133 | ||||
| t(a) | 0.176 | ||||
| p(a) | 0.430 | ||||
| Lowerbound of 95% confidence interval for beta | -0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.296 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.153 | ||||
| Upperbound of 95% confidence interval for alpha | 0.182 | ||||
| Treynor index (mean / b) | 0.505 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.074 | ||||
| Expected Shortfall on VaR | 0.093 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.931 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.298 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.047 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.236 | ||||
| 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) | -0.779 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.044 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.062 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.065 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.069 | ||||
| Mean of quarter 1 | 0.062 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.069 | ||||
| Inter Quartile Range | 0.003 | ||||
| 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) | 0.126 | ||||
| Compounded annual return (geometric extrapolation) | 0.102 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.494 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.494 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.101 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.098 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | 0.322 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.322 | ||||
| df | 1339.000 | ||||
| t | 0.729 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.545 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.189 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.545 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.189 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.525 | ||||
| Upside Potential Ratio | 3.096 | ||||
| Upside part of mean | 0.578 | ||||
| Downside part of mean | -0.480 | ||||
| Upside SD | 0.240 | ||||
| Downside SD | 0.187 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 1274.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1340.000 | ||||
| Mean of predictor | 0.447 | ||||
| Mean of criterion | 0.098 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | 0.036 | ||||
| r | 0.351 | ||||
| b (slope, estimate of beta) | 0.318 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.081 | ||||
| DF error | 1338.000 | ||||
| t(b) | 13.713 | ||||
| p(b) | 0.324 | ||||
| t(a) | -0.350 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 0.273 | ||||
| Upperbound of 95% confidence interval for beta | 0.364 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.293 | ||||
| Upperbound of 95% confidence interval for alpha | 0.204 | ||||
| Treynor index (mean / b) | 0.308 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.053 | ||||
| SD | 0.299 | ||||
| Sharpe ratio (Glass type estimate) | 0.177 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.177 | ||||
| df | 1339.000 | ||||
| t | 0.400 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.690 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.044 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.690 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.044 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.269 | ||||
| Upside Potential Ratio | 2.800 | ||||
| Upside part of mean | 0.552 | ||||
| Downside part of mean | -0.499 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 1274.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1340.000 | ||||
| Mean of predictor | 0.391 | ||||
| Mean of criterion | 0.053 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.299 | ||||
| Covariance | 0.035 | ||||
| r | 0.346 | ||||
| b (slope, estimate of beta) | 0.308 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 0.079 | ||||
| DF error | 1338.000 | ||||
| t(b) | 13.500 | ||||
| p(b) | 0.327 | ||||
| t(a) | -0.541 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.263 | ||||
| Upperbound of 95% confidence interval for beta | 0.352 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.311 | ||||
| Upperbound of 95% confidence interval for alpha | 0.177 | ||||
| Treynor index (mean / b) | 0.172 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1340.000 | ||||
| Minimum | 0.858 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.204 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 58.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 66.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.045 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.328 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.206 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.046 | ||||
| Median | 0.104 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.186 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | 0.080 | ||||
| Mean of quarter 3 | 0.121 | ||||
| Mean of quarter 4 | 0.161 | ||||
| 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 | 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) | -0.827 | ||||
| VaR(95%) (moments method) | 0.178 | ||||
| Expected Shortfall (moments method) | 0.186 | ||||
| Extreme Value Index (regression method) | -0.437 | ||||
| VaR(95%) (regression method) | 0.177 | ||||
| Expected Shortfall (regression method) | 0.189 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.126 | ||||
| Compounded annual return (geometric extrapolation) | 0.102 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.547 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.633 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.739 | ||||
| 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 | 1.354 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.360 | ||||
| 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 | 1.286 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.360 | ||||
| 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) | -8591955368523205.000 | ||||
| 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) | -73958965323552278542024469118976.000 | ||||
| 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 | ||||