Advanced Statistics: RPH2
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 | 0.061 | ||||
| SD | 0.257 | ||||
| Sharpe ratio (Glass type estimate) | 0.239 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.237 | ||||
| df | 69.000 | ||||
| t | 0.578 | ||||
| p | 0.283 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.574 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.051 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.576 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.049 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.630 | ||||
| Upside Potential Ratio | 1.985 | ||||
| Upside part of mean | 0.194 | ||||
| Downside part of mean | -0.132 | ||||
| Upside SD | 0.236 | ||||
| Downside SD | 0.098 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.270 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.257 | ||||
| Covariance | -0.004 | ||||
| r | -0.076 | ||||
| b (slope, estimate of beta) | -0.087 | ||||
| a (intercept, estimate of alpha) | 0.085 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.626 | ||||
| p(b) | 0.733 | ||||
| t(a) | 0.750 | ||||
| p(a) | 0.228 | ||||
| Lowerbound of 95% confidence interval for beta | -0.363 | ||||
| Upperbound of 95% confidence interval for beta | 0.190 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.141 | ||||
| Upperbound of 95% confidence interval for alpha | 0.311 | ||||
| Treynor index (mean / b) | -0.709 | ||||
| Jensen alpha (a) | 0.085 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.225 | ||||
| Sharpe ratio (Glass type estimate) | 0.152 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.150 | ||||
| df | 69.000 | ||||
| t | 0.366 | ||||
| p | 0.358 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.661 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.963 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.662 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.962 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.330 | ||||
| Upside Potential Ratio | 1.653 | ||||
| Upside part of mean | 0.171 | ||||
| Downside part of mean | -0.137 | ||||
| Upside SD | 0.198 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.243 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.212 | ||||
| SD of criterion | 0.225 | ||||
| Covariance | -0.004 | ||||
| r | -0.084 | ||||
| b (slope, estimate of beta) | -0.089 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.051 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.696 | ||||
| p(b) | 0.756 | ||||
| t(a) | 0.567 | ||||
| p(a) | 0.286 | ||||
| Lowerbound of 95% confidence interval for beta | -0.345 | ||||
| Upperbound of 95% confidence interval for beta | 0.167 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.141 | ||||
| Upperbound of 95% confidence interval for alpha | 0.252 | ||||
| Treynor index (mean / b) | -0.382 | ||||
| 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%) | 0.099 | ||||
| Expected Shortfall on VaR | 0.123 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.845 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.504 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.143 | ||||
| Mean of outliers low | 0.945 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 1.117 | ||||
| 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) | -0.043 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | 0.084 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.027 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.090 | ||||
| Quartile 3 | 0.178 | ||||
| Maximum | 0.266 | ||||
| Mean of quarter 1 | 0.027 | ||||
| Mean of quarter 2 | 0.090 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.266 | ||||
| Inter Quartile Range | 0.120 | ||||
| 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) | 0.099 | ||||
| Compounded annual return (geometric extrapolation) | 0.081 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.305 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.305 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.663 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.051 | ||||
| SD | 0.189 | ||||
| Sharpe ratio (Glass type estimate) | 0.268 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.268 | ||||
| df | 1528.000 | ||||
| t | 0.649 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.543 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.080 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.543 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.080 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.553 | ||||
| Upside Potential Ratio | 4.974 | ||||
| Upside part of mean | 0.456 | ||||
| Downside part of mean | -0.406 | ||||
| Upside SD | 0.165 | ||||
| Downside SD | 0.092 | ||||
| N nonnegative terms | 191.000 | ||||
| N negative terms | 1338.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1529.000 | ||||
| Mean of predictor | 0.275 | ||||
| Mean of criterion | 0.051 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.189 | ||||
| Covariance | 0.002 | ||||
| r | 0.037 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | 0.043 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 1527.000 | ||||
| t(b) | 1.465 | ||||
| p(b) | 0.476 | ||||
| t(a) | 0.543 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.111 | ||||
| Upperbound of 95% confidence interval for alpha | 0.196 | ||||
| Treynor index (mean / b) | 1.708 | ||||
| Jensen alpha (a) | 0.043 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.180 | ||||
| Sharpe ratio (Glass type estimate) | 0.190 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.190 | ||||
| df | 1528.000 | ||||
| t | 0.458 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.622 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.001 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.622 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.001 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.366 | ||||
| Upside Potential Ratio | 4.763 | ||||
| Upside part of mean | 0.444 | ||||
| Downside part of mean | -0.410 | ||||
| Upside SD | 0.153 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 191.000 | ||||
| N negative terms | 1338.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1529.000 | ||||
| Mean of predictor | 0.247 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.239 | ||||
| SD of criterion | 0.180 | ||||
| Covariance | 0.002 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | 0.027 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1527.000 | ||||
| t(b) | 1.484 | ||||
| p(b) | 0.476 | ||||
| t(a) | 0.363 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.173 | ||||
| Treynor index (mean / b) | 1.196 | ||||
| Jensen alpha (a) | 0.027 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1529.000 | ||||
| Minimum | 0.947 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.252 | ||||
| Mean of quarter 1 | 0.994 | ||||
| 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 | 196.000 | ||||
| Percentage of outliers low | 0.128 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 196.000 | ||||
| Percentage of outliers high | 0.128 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.280 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | -0.190 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.072 | ||||
| Quartile 3 | 0.119 | ||||
| Maximum | 0.269 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | 0.096 | ||||
| Mean of quarter 4 | 0.185 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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 | 0.269 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.108 | ||||
| VaR(95%) (moments method) | 0.203 | ||||
| Expected Shortfall (moments method) | 0.268 | ||||
| Extreme Value Index (regression method) | 2.607 | ||||
| VaR(95%) (regression method) | 0.278 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.099 | ||||
| Compounded annual return (geometric extrapolation) | 0.081 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.302 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.439 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.612 | ||||
| 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 | 1.024 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.440 | ||||
| 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 | 0.926 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.439 | ||||
| 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) | -8725256849966746.000 | ||||
| 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) | -429587844690680121587110978256896.000 | ||||
| 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 | ||||