Advanced Statistics: Dan's Fundamental Options
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 | -0.041 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | -0.493 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.489 | ||||
| df | 91.000 | ||||
| t | -1.364 | ||||
| p | 0.912 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.203 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.220 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.200 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.223 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.849 | ||||
| Upside Potential Ratio | 0.511 | ||||
| Upside part of mean | 0.025 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 92.000 | ||||
| Mean of predictor | 0.230 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.393 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | -0.003 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.036 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 90.000 | ||||
| t(b) | -0.988 | ||||
| p(b) | 0.837 | ||||
| t(a) | -1.179 | ||||
| p(a) | 0.879 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.096 | ||||
| Upperbound of 95% confidence interval for alpha | 0.025 | ||||
| Treynor index (mean / b) | 1.871 | ||||
| Jensen alpha (a) | -0.036 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.554 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.550 | ||||
| df | 91.000 | ||||
| t | -1.534 | ||||
| p | 0.936 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.265 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.160 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.262 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.163 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.873 | ||||
| Upside Potential Ratio | 0.445 | ||||
| Upside part of mean | 0.022 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 92.000 | ||||
| Mean of predictor | 0.158 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.374 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | -0.003 | ||||
| r | -0.109 | ||||
| b (slope, estimate of beta) | -0.023 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 90.000 | ||||
| t(b) | -1.040 | ||||
| p(b) | 0.849 | ||||
| t(a) | -1.397 | ||||
| p(a) | 0.917 | ||||
| Lowerbound of 95% confidence interval for beta | -0.067 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | 0.017 | ||||
| Treynor index (mean / b) | 1.902 | ||||
| Jensen alpha (a) | -0.040 | ||||
| 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 | 0.050 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 92.000 | ||||
| Minimum | 0.891 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.192 | ||||
| Mean of quarter 1 | 0.993 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.022 | ||||
| Mean of outliers low | 0.916 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.011 | ||||
| Mean of outliers high | 1.192 | ||||
| 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) | -1.220 | ||||
| VaR(95%) (regression method) | -0.111 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.161 | ||||
| Quartile 1 | 0.161 | ||||
| Median | 0.161 | ||||
| Quartile 3 | 0.161 | ||||
| Maximum | 0.161 | ||||
| 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 | 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.037 | ||||
| SD | 0.127 | ||||
| Sharpe ratio (Glass type estimate) | -0.291 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.291 | ||||
| df | 2017.000 | ||||
| t | -0.809 | ||||
| p | 0.791 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.998 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.415 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.998 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.415 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.831 | ||||
| Upside Potential Ratio | 1.284 | ||||
| Upside part of mean | 0.057 | ||||
| Downside part of mean | -0.094 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 2013.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2018.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.548 | ||||
| SD of criterion | 0.127 | ||||
| Covariance | -0.003 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 2016.000 | ||||
| t(b) | -2.222 | ||||
| p(b) | 0.987 | ||||
| t(a) | -0.730 | ||||
| p(a) | 0.767 | ||||
| Lowerbound of 95% confidence interval for beta | -0.022 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.123 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 3.234 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.114 | ||||
| Sharpe ratio (Glass type estimate) | -0.386 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.386 | ||||
| df | 2017.000 | ||||
| t | -1.072 | ||||
| p | 0.858 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.093 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.320 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.093 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.320 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.962 | ||||
| Upside Potential Ratio | 1.121 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.046 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 2013.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2018.000 | ||||
| Mean of predictor | 0.165 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.547 | ||||
| SD of criterion | 0.114 | ||||
| Covariance | -0.003 | ||||
| r | -0.050 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 2016.000 | ||||
| t(b) | -2.246 | ||||
| p(b) | 0.988 | ||||
| t(a) | -1.031 | ||||
| p(a) | 0.849 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.123 | ||||
| Upperbound of 95% confidence interval for alpha | 0.038 | ||||
| Treynor index (mean / b) | 4.233 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2018.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.317 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 18.000 | ||||
| Percentage of outliers low | 0.009 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.002 | ||||
| Mean of outliers high | 1.088 | ||||
| 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) | -0.426 | ||||
| VaR(95%) (regression method) | -0.053 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.311 | ||||
| Quartile 1 | 0.311 | ||||
| Median | 0.311 | ||||
| Quartile 3 | 0.311 | ||||
| Maximum | 0.311 | ||||
| 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 | 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.183 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 1.057 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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) | -8724014495350114.000 | ||||
| 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) | 119094722190033680559812481384448.000 | ||||
| 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 | ||||