Advanced Statistics: rydex 500
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 | -0.042 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.674 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.668 | ||||
| df | 87.000 | ||||
| t | -1.825 | ||||
| p | 0.964 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.403 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.059 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.399 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.062 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.872 | ||||
| Upside Potential Ratio | 0.427 | ||||
| Upside part of mean | 0.021 | ||||
| Downside part of mean | -0.063 | ||||
| Upside SD | 0.041 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 86.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.200 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | -0.002 | ||||
| r | -0.129 | ||||
| b (slope, estimate of beta) | -0.028 | ||||
| a (intercept, estimate of alpha) | -0.036 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 86.000 | ||||
| t(b) | -1.202 | ||||
| p(b) | 0.884 | ||||
| t(a) | -1.551 | ||||
| p(a) | 0.938 | ||||
| Lowerbound of 95% confidence interval for beta | -0.075 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | 1.487 | ||||
| Jensen alpha (a) | -0.036 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.694 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.688 | ||||
| df | 87.000 | ||||
| t | -1.879 | ||||
| p | 0.968 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.423 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.039 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.419 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.043 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.862 | ||||
| Upside Potential Ratio | 0.388 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 86.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.160 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | -0.002 | ||||
| r | -0.128 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 86.000 | ||||
| t(b) | -1.199 | ||||
| p(b) | 0.883 | ||||
| t(a) | -1.661 | ||||
| p(a) | 0.950 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | 0.008 | ||||
| Treynor index (mean / b) | 1.506 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 88.000 | ||||
| Minimum | 0.880 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.100 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.032 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -40.731 | ||||
| VaR(95%) (moments method) | -16043247863.062 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.934 | ||||
| VaR(95%) (regression method) | -0.011 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.141 | ||||
| Quartile 1 | 0.141 | ||||
| Median | 0.141 | ||||
| Quartile 3 | 0.141 | ||||
| Maximum | 0.141 | ||||
| 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 | -0.041 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.527 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.527 | ||||
| df | 1933.000 | ||||
| t | -1.433 | ||||
| p | 0.521 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.249 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.194 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.249 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.194 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.945 | ||||
| Upside Potential Ratio | 1.652 | ||||
| Upside part of mean | 0.072 | ||||
| Downside part of mean | -0.113 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 1911.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1934.000 | ||||
| Mean of predictor | 0.316 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.528 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | -0.006 | ||||
| r | -0.134 | ||||
| b (slope, estimate of beta) | -0.020 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1932.000 | ||||
| t(b) | -5.938 | ||||
| p(b) | 0.567 | ||||
| t(a) | -1.225 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | -0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | 0.021 | ||||
| Treynor index (mean / b) | 2.081 | ||||
| Jensen alpha (a) | -0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | -0.580 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.580 | ||||
| df | 1933.000 | ||||
| t | -1.575 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.301 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.142 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.301 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.142 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.994 | ||||
| Upside Potential Ratio | 1.576 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 1911.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1934.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.524 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | -0.006 | ||||
| r | -0.138 | ||||
| b (slope, estimate of beta) | -0.020 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1932.000 | ||||
| t(b) | -6.140 | ||||
| p(b) | 0.569 | ||||
| t(a) | -1.461 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | -0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.095 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | 2.195 | ||||
| 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%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| 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 | 1934.000 | ||||
| Minimum | 0.947 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.136 | ||||
| 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 | 61.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 50.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.119 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.010 | ||||
| VaR(95%) (regression method) | -0.007 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.068 | ||||
| Median | 0.104 | ||||
| Quartile 3 | 0.140 | ||||
| Maximum | 0.176 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.176 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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 | 0.000 | ||||
| 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 | 1.133 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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 | 1.007 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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) | -8731845149336169.000 | ||||
| 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) | -116990845680702859980515796058112.000 | ||||
| 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 | ||||