Advanced Statistics: Triple Play
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 | 0.339 | ||||
| SD | 0.417 | ||||
| Sharpe ratio (Glass type estimate) | 0.813 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.795 | ||||
| df | 35.000 | ||||
| t | 1.407 | ||||
| p | 0.084 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.340 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.954 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.352 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.942 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.802 | ||||
| Upside Potential Ratio | 3.680 | ||||
| Upside part of mean | 0.446 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.405 | ||||
| Downside SD | 0.121 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.540 | ||||
| Mean of criterion | 0.339 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.417 | ||||
| Covariance | -0.030 | ||||
| r | -0.237 | ||||
| b (slope, estimate of beta) | -0.330 | ||||
| a (intercept, estimate of alpha) | 0.517 | ||||
| Mean Square Error | 0.169 | ||||
| DF error | 34.000 | ||||
| t(b) | -1.421 | ||||
| p(b) | 0.918 | ||||
| t(a) | 1.926 | ||||
| p(a) | 0.031 | ||||
| Lowerbound of 95% confidence interval for beta | -0.802 | ||||
| Upperbound of 95% confidence interval for beta | 0.142 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 1.063 | ||||
| Treynor index (mean / b) | -1.028 | ||||
| Jensen alpha (a) | 0.517 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.266 | ||||
| SD | 0.358 | ||||
| Sharpe ratio (Glass type estimate) | 0.743 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.727 | ||||
| df | 35.000 | ||||
| t | 1.287 | ||||
| p | 0.103 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.407 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.883 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.417 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.871 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.969 | ||||
| Upside Potential Ratio | 2.815 | ||||
| Upside part of mean | 0.380 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.335 | ||||
| Downside SD | 0.135 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | 0.266 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.358 | ||||
| Covariance | -0.023 | ||||
| r | -0.226 | ||||
| b (slope, estimate of beta) | -0.282 | ||||
| a (intercept, estimate of alpha) | 0.403 | ||||
| Mean Square Error | 0.125 | ||||
| DF error | 34.000 | ||||
| t(b) | -1.354 | ||||
| p(b) | 0.908 | ||||
| t(a) | 1.768 | ||||
| p(a) | 0.043 | ||||
| Lowerbound of 95% confidence interval for beta | -0.706 | ||||
| Upperbound of 95% confidence interval for beta | 0.141 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.060 | ||||
| Upperbound of 95% confidence interval for alpha | 0.867 | ||||
| Treynor index (mean / b) | -0.943 | ||||
| Jensen alpha (a) | 0.403 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.137 | ||||
| Expected Shortfall on VaR | 0.173 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.795 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.571 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.151 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.028 | ||||
| Mean of outliers low | 0.795 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.139 | ||||
| Mean of outliers high | 1.271 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.205 | ||||
| Quartile 1 | 0.205 | ||||
| Median | 0.205 | ||||
| Quartile 3 | 0.205 | ||||
| Maximum | 0.205 | ||||
| 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) | 0.512 | ||||
| Compounded annual return (geometric extrapolation) | 0.364 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.772 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.098 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.301 | ||||
| SD | 0.278 | ||||
| Sharpe ratio (Glass type estimate) | 1.084 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.083 | ||||
| df | 792.000 | ||||
| t | 1.885 | ||||
| p | 0.030 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.044 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.211 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.045 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.211 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.017 | ||||
| Upside Potential Ratio | 5.458 | ||||
| Upside part of mean | 0.815 | ||||
| Downside part of mean | -0.514 | ||||
| Upside SD | 0.235 | ||||
| Downside SD | 0.149 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 728.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 793.000 | ||||
| Mean of predictor | 0.570 | ||||
| Mean of criterion | 0.301 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.278 | ||||
| Covariance | -0.001 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | 0.305 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 791.000 | ||||
| t(b) | -0.254 | ||||
| p(b) | 0.600 | ||||
| t(a) | 1.900 | ||||
| p(a) | 0.029 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.047 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.010 | ||||
| Upperbound of 95% confidence interval for alpha | 0.620 | ||||
| Treynor index (mean / b) | -43.372 | ||||
| Jensen alpha (a) | 0.305 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.263 | ||||
| SD | 0.273 | ||||
| Sharpe ratio (Glass type estimate) | 0.966 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.965 | ||||
| df | 792.000 | ||||
| t | 1.681 | ||||
| p | 0.047 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.162 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.093 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.162 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.093 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.704 | ||||
| Upside Potential Ratio | 5.102 | ||||
| Upside part of mean | 0.788 | ||||
| Downside part of mean | -0.525 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.155 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 728.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 793.000 | ||||
| Mean of predictor | 0.501 | ||||
| Mean of criterion | 0.263 | ||||
| SD of predictor | 0.377 | ||||
| SD of criterion | 0.273 | ||||
| Covariance | -0.001 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | 0.266 | ||||
| Mean Square Error | 0.074 | ||||
| DF error | 791.000 | ||||
| t(b) | -0.210 | ||||
| p(b) | 0.583 | ||||
| t(a) | 1.691 | ||||
| p(a) | 0.046 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.043 | ||||
| Upperbound of 95% confidence interval for alpha | 0.575 | ||||
| Treynor index (mean / b) | -48.634 | ||||
| Jensen alpha (a) | 0.266 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| 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 | 793.000 | ||||
| Minimum | 0.893 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.147 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 55.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 65.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.038 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.511 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.293 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.021 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.055 | ||||
| Median | 0.097 | ||||
| Quartile 3 | 0.110 | ||||
| Maximum | 0.255 | ||||
| Mean of quarter 1 | 0.039 | ||||
| Mean of quarter 2 | 0.066 | ||||
| Mean of quarter 3 | 0.109 | ||||
| Mean of quarter 4 | 0.160 | ||||
| Inter Quartile Range | 0.056 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.255 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.334 | ||||
| VaR(95%) (moments method) | 0.182 | ||||
| Expected Shortfall (moments method) | 0.291 | ||||
| Extreme Value Index (regression method) | 3.946 | ||||
| VaR(95%) (regression method) | 0.305 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.507 | ||||
| Compounded annual return (geometric extrapolation) | 0.360 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.408 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.246 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.854 | ||||
| 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 | 1.094 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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 | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.483 | ||||
| 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) | -8731322317041449.000 | ||||
| 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) | 159233327659657257981839593701376.000 | ||||
| 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 | ||||