Advanced Statistics: Prudent Risk
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 | 0.183 | ||||
| SD | 0.297 | ||||
| Sharpe ratio (Glass type estimate) | 0.615 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.602 | ||||
| df | 37.000 | ||||
| t | 1.094 | ||||
| p | 0.141 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.500 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.721 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.508 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.712 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.717 | ||||
| Upside Potential Ratio | 3.984 | ||||
| Upside part of mean | 0.268 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.290 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.566 | ||||
| Mean of criterion | 0.183 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.297 | ||||
| Covariance | -0.003 | ||||
| r | -0.041 | ||||
| b (slope, estimate of beta) | -0.044 | ||||
| a (intercept, estimate of alpha) | 0.207 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.247 | ||||
| p(b) | 0.597 | ||||
| t(a) | 1.055 | ||||
| p(a) | 0.149 | ||||
| Lowerbound of 95% confidence interval for beta | -0.401 | ||||
| Upperbound of 95% confidence interval for beta | 0.314 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.191 | ||||
| Upperbound of 95% confidence interval for alpha | 0.605 | ||||
| Treynor index (mean / b) | -4.193 | ||||
| Jensen alpha (a) | 0.207 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.147 | ||||
| SD | 0.252 | ||||
| Sharpe ratio (Glass type estimate) | 0.582 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.570 | ||||
| df | 37.000 | ||||
| t | 1.036 | ||||
| p | 0.154 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.531 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.687 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.539 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.679 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.083 | ||||
| Upside Potential Ratio | 3.323 | ||||
| Upside part of mean | 0.234 | ||||
| Downside part of mean | -0.087 | ||||
| Upside SD | 0.242 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.517 | ||||
| Mean of criterion | 0.147 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 0.252 | ||||
| Covariance | -0.002 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.026 | ||||
| a (intercept, estimate of alpha) | 0.160 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.164 | ||||
| p(b) | 0.565 | ||||
| t(a) | 0.968 | ||||
| p(a) | 0.170 | ||||
| Lowerbound of 95% confidence interval for beta | -0.348 | ||||
| Upperbound of 95% confidence interval for beta | 0.296 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.175 | ||||
| Upperbound of 95% confidence interval for alpha | 0.495 | ||||
| Treynor index (mean / b) | -5.647 | ||||
| Jensen alpha (a) | 0.160 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.102 | ||||
| Expected Shortfall on VaR | 0.128 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.482 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.087 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.926 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 1.173 | ||||
| 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) | -0.590 | ||||
| VaR(95%) (regression method) | 0.043 | ||||
| Expected Shortfall (regression method) | 0.098 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.144 | ||||
| Quartile 1 | 0.144 | ||||
| Median | 0.144 | ||||
| Quartile 3 | 0.144 | ||||
| Maximum | 0.144 | ||||
| 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) | 0.262 | ||||
| Compounded annual return (geometric extrapolation) | 0.210 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.461 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.636 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.206 | ||||
| SD | 0.349 | ||||
| Sharpe ratio (Glass type estimate) | 0.591 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.591 | ||||
| df | 829.000 | ||||
| t | 1.053 | ||||
| p | 0.146 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.510 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.693 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.511 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.692 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.955 | ||||
| Upside Potential Ratio | 4.497 | ||||
| Upside part of mean | 0.972 | ||||
| Downside part of mean | -0.765 | ||||
| Upside SD | 0.274 | ||||
| Downside SD | 0.216 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 755.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 830.000 | ||||
| Mean of predictor | 0.571 | ||||
| Mean of criterion | 0.206 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.349 | ||||
| Covariance | -0.001 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.212 | ||||
| Mean Square Error | 0.122 | ||||
| DF error | 828.000 | ||||
| t(b) | -0.250 | ||||
| p(b) | 0.599 | ||||
| t(a) | 1.073 | ||||
| p(a) | 0.142 | ||||
| Lowerbound of 95% confidence interval for beta | -0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.064 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.176 | ||||
| Upperbound of 95% confidence interval for alpha | 0.599 | ||||
| Treynor index (mean / b) | -21.937 | ||||
| Jensen alpha (a) | 0.212 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.146 | ||||
| SD | 0.345 | ||||
| Sharpe ratio (Glass type estimate) | 0.425 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.424 | ||||
| df | 829.000 | ||||
| t | 0.756 | ||||
| p | 0.225 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.677 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.526 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.677 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.526 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.648 | ||||
| Upside Potential Ratio | 4.142 | ||||
| Upside part of mean | 0.936 | ||||
| Downside part of mean | -0.790 | ||||
| Upside SD | 0.260 | ||||
| Downside SD | 0.226 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 755.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 830.000 | ||||
| Mean of predictor | 0.517 | ||||
| Mean of criterion | 0.146 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.345 | ||||
| Covariance | -0.001 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.151 | ||||
| Mean Square Error | 0.119 | ||||
| DF error | 828.000 | ||||
| t(b) | -0.251 | ||||
| p(b) | 0.599 | ||||
| t(a) | 0.776 | ||||
| p(a) | 0.219 | ||||
| Lowerbound of 95% confidence interval for beta | -0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.231 | ||||
| Upperbound of 95% confidence interval for alpha | 0.534 | ||||
| Treynor index (mean / b) | -15.995 | ||||
| Jensen alpha (a) | 0.151 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 830.000 | ||||
| Minimum | 0.856 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.184 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 60.000 | ||||
| Percentage of outliers low | 0.072 | ||||
| Mean of outliers low | 0.962 | ||||
| Number of outliers high | 75.000 | ||||
| Percentage of outliers high | 0.090 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -8.991 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.153 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.043 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.212 | ||||
| Maximum | 0.307 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | 0.150 | ||||
| Mean of quarter 4 | 0.261 | ||||
| Inter Quartile Range | 0.169 | ||||
| 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) | -4.264 | ||||
| VaR(95%) (moments method) | 0.288 | ||||
| Expected Shortfall (moments method) | 0.288 | ||||
| Extreme Value Index (regression method) | -0.868 | ||||
| VaR(95%) (regression method) | 0.323 | ||||
| Expected Shortfall (regression method) | 0.340 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.262 | ||||
| Compounded annual return (geometric extrapolation) | 0.210 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.683 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.803 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.946 | ||||
| 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 | 1.079 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.480 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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) | -8732832667606775.000 | ||||
| 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) | 101771608874822661831654551584768.000 | ||||
| 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 | ||||