Advanced Statistics: Test Stock
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 | 0.002 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | 0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.015 | ||||
| df | 108.000 | ||||
| t | 0.045 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.635 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.665 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.635 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.665 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.020 | ||||
| Upside Potential Ratio | 1.548 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.121 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.079 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 109.000 | ||||
| Mean of predictor | 0.152 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.184 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | -0.001 | ||||
| r | -0.076 | ||||
| b (slope, estimate of beta) | -0.044 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 107.000 | ||||
| t(b) | -0.790 | ||||
| p(b) | 0.548 | ||||
| t(a) | 0.228 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.154 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.080 | ||||
| Treynor index (mean / b) | -0.036 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | -0.038 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.037 | ||||
| df | 108.000 | ||||
| t | -0.113 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.688 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.613 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.688 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.613 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.049 | ||||
| Upside Potential Ratio | 1.467 | ||||
| Upside part of mean | 0.120 | ||||
| Downside part of mean | -0.124 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 109.000 | ||||
| Mean of predictor | 0.134 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.183 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | -0.001 | ||||
| r | -0.046 | ||||
| b (slope, estimate of beta) | -0.027 | ||||
| a (intercept, estimate of alpha) | -0.000 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 107.000 | ||||
| t(b) | -0.475 | ||||
| p(b) | 0.529 | ||||
| t(a) | -0.012 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.138 | ||||
| Upperbound of 95% confidence interval for beta | 0.085 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.071 | ||||
| Treynor index (mean / b) | 0.150 | ||||
| Jensen alpha (a) | -0.000 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 109.000 | ||||
| Minimum | 0.903 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.006 | ||||
| Quartile 3 | 1.016 | ||||
| Maximum | 1.118 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.101 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.055 | ||||
| Mean of outliers high | 1.066 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.293 | ||||
| VaR(95%) (moments method) | 0.020 | ||||
| Expected Shortfall (moments method) | 0.037 | ||||
| Extreme Value Index (regression method) | -0.194 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.043 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.010 | ||||
| Quartile 3 | 0.038 | ||||
| Maximum | 0.337 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.133 | ||||
| Inter Quartile Range | 0.034 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 0.219 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.798 | ||||
| VaR(95%) (moments method) | 0.141 | ||||
| Expected Shortfall (moments method) | 0.713 | ||||
| Extreme Value Index (regression method) | 2.121 | ||||
| VaR(95%) (regression method) | 0.207 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.048 | ||||
| Compounded annual return (geometric extrapolation) | 0.041 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.308 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.662 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.003 | ||||
| SD | 0.120 | ||||
| Sharpe ratio (Glass type estimate) | 0.024 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.024 | ||||
| df | 2400.000 | ||||
| t | 0.072 | ||||
| p | 0.471 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.624 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.671 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.624 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.671 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.035 | ||||
| Upside Potential Ratio | 4.993 | ||||
| Upside part of mean | 0.411 | ||||
| Downside part of mean | -0.408 | ||||
| Upside SD | 0.088 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 1019.000 | ||||
| N negative terms | 1382.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2401.000 | ||||
| Mean of predictor | 0.173 | ||||
| Mean of criterion | 0.003 | ||||
| SD of predictor | 0.203 | ||||
| SD of criterion | 0.120 | ||||
| Covariance | 0.002 | ||||
| r | 0.064 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | -0.004 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 2399.000 | ||||
| t(b) | 3.127 | ||||
| p(b) | 0.001 | ||||
| t(a) | -0.092 | ||||
| p(a) | 0.537 | ||||
| Lowerbound of 95% confidence interval for beta | 0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.082 | ||||
| Upperbound of 95% confidence interval for alpha | 0.074 | ||||
| Treynor index (mean / b) | 0.076 | ||||
| Jensen alpha (a) | -0.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.120 | ||||
| Sharpe ratio (Glass type estimate) | -0.036 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.036 | ||||
| df | 2400.000 | ||||
| t | -0.110 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.684 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.611 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.684 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.611 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.052 | ||||
| Upside Potential Ratio | 4.855 | ||||
| Upside part of mean | 0.407 | ||||
| Downside part of mean | -0.411 | ||||
| Upside SD | 0.086 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 1019.000 | ||||
| N negative terms | 1382.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2401.000 | ||||
| Mean of predictor | 0.152 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.204 | ||||
| SD of criterion | 0.120 | ||||
| Covariance | 0.002 | ||||
| r | 0.066 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | -0.010 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 2399.000 | ||||
| t(b) | 3.222 | ||||
| p(b) | 0.001 | ||||
| t(a) | -0.259 | ||||
| p(a) | 0.602 | ||||
| Lowerbound of 95% confidence interval for beta | 0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.068 | ||||
| Treynor index (mean / b) | -0.112 | ||||
| Jensen alpha (a) | -0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2401.000 | ||||
| Minimum | 0.925 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.105 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 255.000 | ||||
| Percentage of outliers low | 0.106 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 273.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.841 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.034 | ||||
| Extreme Value Index (regression method) | 0.489 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 152.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.008 | ||||
| Maximum | 0.337 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.005 | ||||
| Mean of quarter 4 | 0.035 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 0.061 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.803 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | 0.178 | ||||
| Extreme Value Index (regression method) | 0.868 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.230 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.048 | ||||
| Compounded annual return (geometric extrapolation) | 0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.120 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.157 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.660 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.349 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | -2.194 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.181 | ||||
| df | 130.000 | ||||
| t | -1.551 | ||||
| p | 0.567 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.974 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.595 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.965 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.603 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.810 | ||||
| Upside Potential Ratio | 3.717 | ||||
| Upside part of mean | 0.461 | ||||
| Downside part of mean | -0.810 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.124 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 113.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.416 | ||||
| Mean of criterion | -0.349 | ||||
| SD of predictor | 0.417 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | -0.044 | ||||
| r | -0.666 | ||||
| b (slope, estimate of beta) | -0.254 | ||||
| a (intercept, estimate of alpha) | 0.011 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 129.000 | ||||
| t(b) | -10.142 | ||||
| p(b) | 0.890 | ||||
| t(a) | 0.064 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.304 | ||||
| Upperbound of 95% confidence interval for beta | -0.204 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.329 | ||||
| Upperbound of 95% confidence interval for alpha | 0.351 | ||||
| Treynor index (mean / b) | 1.373 | ||||
| Jensen alpha (a) | 0.011 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.361 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | -2.270 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.257 | ||||
| df | 130.000 | ||||
| t | -1.605 | ||||
| p | 0.570 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.520 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.042 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.529 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.875 | ||||
| Upside Potential Ratio | 3.629 | ||||
| Upside part of mean | 0.456 | ||||
| Downside part of mean | -0.818 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.126 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 113.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.326 | ||||
| Mean of criterion | -0.361 | ||||
| SD of predictor | 0.417 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | -0.044 | ||||
| r | -0.665 | ||||
| b (slope, estimate of beta) | -0.254 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 129.000 | ||||
| t(b) | -10.119 | ||||
| p(b) | 0.890 | ||||
| t(a) | -0.145 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.303 | ||||
| Upperbound of 95% confidence interval for beta | -0.204 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.365 | ||||
| Upperbound of 95% confidence interval for alpha | 0.315 | ||||
| Treynor index (mean / b) | 1.424 | ||||
| Jensen alpha (a) | -0.025 | ||||
| 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 | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.957 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.988 | ||||
| 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 | 32.000 | ||||
| Percentage of outliers low | 0.244 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 19.000 | ||||
| Percentage of outliers high | 0.145 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.562 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.257 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.066 | ||||
| Quartile 1 | 0.090 | ||||
| Median | 0.114 | ||||
| Quartile 3 | 0.138 | ||||
| Maximum | 0.162 | ||||
| Mean of quarter 1 | 0.066 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.162 | ||||
| Inter Quartile Range | 0.048 | ||||
| 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) | -0.293 | ||||
| Compounded annual return (geometric extrapolation) | -0.272 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.678 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.678 | ||||
| Compounded annual return / Expected Shortfall lognormal | -12.690 | ||||