Advanced Statistics: The Barefoot Trader - NASDAQ 100
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 | -0.043 | ||||
| SD | 0.028 | ||||
| Sharpe ratio (Glass type estimate) | -1.523 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.503 | ||||
| df | 57.000 | ||||
| t | -3.348 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.451 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.582 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.436 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.569 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.600 | ||||
| Upside Potential Ratio | 0.421 | ||||
| Upside part of mean | 0.011 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.364 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.028 | ||||
| Covariance | 0.002 | ||||
| r | 0.335 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 56.000 | ||||
| t(b) | 2.664 | ||||
| p(b) | 0.005 | ||||
| t(a) | -4.283 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | -0.030 | ||||
| Treynor index (mean / b) | -1.134 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -1.524 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.504 | ||||
| df | 57.000 | ||||
| t | -3.352 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.453 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.584 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.438 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.571 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.592 | ||||
| Upside Potential Ratio | 0.411 | ||||
| Upside part of mean | 0.011 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.328 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | 0.003 | ||||
| r | 0.363 | ||||
| b (slope, estimate of beta) | 0.042 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 56.000 | ||||
| t(b) | 2.911 | ||||
| p(b) | 0.003 | ||||
| t(a) | -4.379 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | -1.030 | ||||
| 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%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 58.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.028 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1724.001 | ||||
| VaR(95%) (moments method) | -154328266433322690714248585011108316402296593122446434525714480966462895800626574402921084372566191550026083875451559072079470490606473283830432332499848962782692235184952482780735651181257607665995677903916118650970958167253073436578005037801528565729731000611558966477979648.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.364 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.035 | ||||
| Maximum | 0.037 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.037 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.012 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.012 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.021 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.886 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.885 | ||||
| df | 1286.000 | ||||
| t | -1.963 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.771 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.001 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.770 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.112 | ||||
| Upside Potential Ratio | 1.811 | ||||
| Upside part of mean | 0.069 | ||||
| Downside part of mean | -0.112 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 1215.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1287.000 | ||||
| Mean of predictor | 0.399 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.004 | ||||
| r | 0.227 | ||||
| b (slope, estimate of beta) | 0.033 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 1285.000 | ||||
| t(b) | 8.350 | ||||
| p(b) | 0.357 | ||||
| t(a) | -2.626 | ||||
| p(a) | 0.546 | ||||
| Lowerbound of 95% confidence interval for beta | 0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | -0.014 | ||||
| Treynor index (mean / b) | -1.301 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.902 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.901 | ||||
| df | 1286.000 | ||||
| t | -1.999 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.787 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.017 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.786 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.121 | ||||
| Upside Potential Ratio | 1.767 | ||||
| Upside part of mean | 0.069 | ||||
| Downside part of mean | -0.112 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 1215.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1287.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.004 | ||||
| r | 0.246 | ||||
| b (slope, estimate of beta) | 0.035 | ||||
| a (intercept, estimate of alpha) | -0.056 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 1285.000 | ||||
| t(b) | 9.083 | ||||
| p(b) | 0.345 | ||||
| t(a) | -2.622 | ||||
| p(a) | 0.546 | ||||
| Lowerbound of 95% confidence interval for beta | 0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | -0.014 | ||||
| Treynor index (mean / b) | -1.246 | ||||
| Jensen alpha (a) | -0.056 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| 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 | 1287.000 | ||||
| Minimum | 0.943 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.030 | ||||
| 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 | 69.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 89.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.056 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.352 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.058 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.051 | ||||
| Inter Quartile Range | 0.021 | ||||
| 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) | -10.090 | ||||
| VaR(95%) (moments method) | 0.046 | ||||
| Expected Shortfall (moments method) | 0.046 | ||||
| Extreme Value Index (regression method) | -1.364 | ||||
| VaR(95%) (regression method) | 0.067 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.007 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.008 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.067 | ||||
| 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 | 1.054 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.339 | ||||
| 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 | 0.994 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.342 | ||||
| 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) | -8659879182045679.000 | ||||
| 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) | 188154644011433196223439550021632.000 | ||||
| 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 | ||||