Advanced Statistics: HT-TradingAdvice
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 | -0.055 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | -0.665 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.657 | ||||
| df | 66.000 | ||||
| t | -1.571 | ||||
| p | 0.939 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.499 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.175 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.494 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.180 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.781 | ||||
| Upside Potential Ratio | 0.725 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.180 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | -0.002 | ||||
| r | -0.084 | ||||
| b (slope, estimate of beta) | -0.025 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 65.000 | ||||
| t(b) | -0.681 | ||||
| p(b) | 0.751 | ||||
| t(a) | -1.408 | ||||
| p(a) | 0.918 | ||||
| Lowerbound of 95% confidence interval for beta | -0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.122 | ||||
| Upperbound of 95% confidence interval for alpha | 0.021 | ||||
| Treynor index (mean / b) | 2.155 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.084 | ||||
| Sharpe ratio (Glass type estimate) | -0.694 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.686 | ||||
| df | 66.000 | ||||
| t | -1.640 | ||||
| p | 0.947 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.529 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.146 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.524 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.151 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.801 | ||||
| Upside Potential Ratio | 0.684 | ||||
| Upside part of mean | 0.050 | ||||
| Downside part of mean | -0.108 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.142 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.084 | ||||
| Covariance | -0.002 | ||||
| r | -0.071 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 65.000 | ||||
| t(b) | -0.574 | ||||
| p(b) | 0.716 | ||||
| t(a) | -1.526 | ||||
| p(a) | 0.934 | ||||
| Lowerbound of 95% confidence interval for beta | -0.099 | ||||
| Upperbound of 95% confidence interval for beta | 0.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | 0.017 | ||||
| Treynor index (mean / b) | 2.638 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 67.000 | ||||
| Minimum | 0.911 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.059 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.179 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.224 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.036 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.073 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.046 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.044 | ||||
| Quartile 1 | 0.047 | ||||
| Median | 0.053 | ||||
| Quartile 3 | 0.097 | ||||
| Maximum | 0.216 | ||||
| Mean of quarter 1 | 0.044 | ||||
| Mean of quarter 2 | 0.047 | ||||
| Mean of quarter 3 | 0.058 | ||||
| Mean of quarter 4 | 0.216 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.216 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.065 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.065 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.264 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.242 | ||||
| Sharpe ratio (Glass type estimate) | -0.119 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.119 | ||||
| df | 1478.000 | ||||
| t | -0.284 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.944 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.944 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.706 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.174 | ||||
| Upside Potential Ratio | 3.505 | ||||
| Upside part of mean | 0.582 | ||||
| Downside part of mean | -0.611 | ||||
| Upside SD | 0.176 | ||||
| Downside SD | 0.166 | ||||
| N nonnegative terms | 168.000 | ||||
| N negative terms | 1311.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1479.000 | ||||
| Mean of predictor | 0.430 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.629 | ||||
| SD of criterion | 0.242 | ||||
| Covariance | -0.025 | ||||
| r | -0.161 | ||||
| b (slope, estimate of beta) | -0.062 | ||||
| a (intercept, estimate of alpha) | -0.002 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 1477.000 | ||||
| t(b) | -6.269 | ||||
| p(b) | 0.602 | ||||
| t(a) | -0.023 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.081 | ||||
| Upperbound of 95% confidence interval for beta | -0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.200 | ||||
| Upperbound of 95% confidence interval for alpha | 0.195 | ||||
| Treynor index (mean / b) | 0.467 | ||||
| Jensen alpha (a) | -0.002 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.242 | ||||
| Sharpe ratio (Glass type estimate) | -0.240 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.240 | ||||
| df | 1478.000 | ||||
| t | -0.571 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.065 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.065 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.585 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.338 | ||||
| Upside Potential Ratio | 3.299 | ||||
| Upside part of mean | 0.567 | ||||
| Downside part of mean | -0.625 | ||||
| Upside SD | 0.170 | ||||
| Downside SD | 0.172 | ||||
| N nonnegative terms | 168.000 | ||||
| N negative terms | 1311.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1479.000 | ||||
| Mean of predictor | 0.237 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.618 | ||||
| SD of criterion | 0.242 | ||||
| Covariance | -0.024 | ||||
| r | -0.160 | ||||
| b (slope, estimate of beta) | -0.063 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 1477.000 | ||||
| t(b) | -6.241 | ||||
| p(b) | 0.602 | ||||
| t(a) | -0.430 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | -0.082 | ||||
| Upperbound of 95% confidence interval for beta | -0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.240 | ||||
| Upperbound of 95% confidence interval for alpha | 0.154 | ||||
| Treynor index (mean / b) | 0.927 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1479.000 | ||||
| Minimum | 0.874 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.128 | ||||
| Mean of quarter 1 | 0.991 | ||||
| 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 | 241.000 | ||||
| Percentage of outliers low | 0.163 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 275.000 | ||||
| Percentage of outliers high | 0.186 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.508 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| 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 | 9.000 | ||||
| Minimum | 0.030 | ||||
| Quartile 1 | 0.072 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.109 | ||||
| Maximum | 0.217 | ||||
| Mean of quarter 1 | 0.054 | ||||
| Mean of quarter 2 | 0.073 | ||||
| Mean of quarter 3 | 0.095 | ||||
| Mean of quarter 4 | 0.187 | ||||
| Inter Quartile Range | 0.038 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.217 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.972 | ||||
| VaR(95%) (moments method) | 0.180 | ||||
| Expected Shortfall (moments method) | 0.181 | ||||
| Extreme Value Index (regression method) | -0.618 | ||||
| VaR(95%) (regression method) | 0.239 | ||||
| Expected Shortfall (regression method) | 0.264 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.013 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.064 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.075 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.457 | ||||
| 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 | 1.952 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.781 | ||||
| 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 | 1.628 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.814 | ||||
| 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) | -8732949246089436.000 | ||||
| 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) | 343677270464145145105906443223040.000 | ||||
| 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 | ||||