Advanced Statistics: SilverRock TS
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 | 0.010 | ||||
| SD | 0.062 | ||||
| Sharpe ratio (Glass type estimate) | 0.163 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.160 | ||||
| df | 42.000 | ||||
| t | 0.308 | ||||
| p | 0.380 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.874 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.198 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.876 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.196 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.379 | ||||
| Upside Potential Ratio | 2.479 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.423 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.062 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.011 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 41.000 | ||||
| t(b) | -0.027 | ||||
| p(b) | 0.511 | ||||
| t(a) | 0.284 | ||||
| p(a) | 0.389 | ||||
| Lowerbound of 95% confidence interval for beta | -0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | 0.086 | ||||
| Treynor index (mean / b) | -9.375 | ||||
| Jensen alpha (a) | 0.011 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.008 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | 0.136 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.133 | ||||
| df | 42.000 | ||||
| t | 0.257 | ||||
| p | 0.399 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.901 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.171 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.902 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.169 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.306 | ||||
| Upside Potential Ratio | 2.397 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.387 | ||||
| Mean of criterion | 0.008 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | 0.000 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 41.000 | ||||
| t(b) | 0.052 | ||||
| p(b) | 0.479 | ||||
| t(a) | 0.207 | ||||
| p(a) | 0.419 | ||||
| Lowerbound of 95% confidence interval for beta | -0.079 | ||||
| Upperbound of 95% confidence interval for beta | 0.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | 0.080 | ||||
| Treynor index (mean / b) | 3.958 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.975 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.076 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.140 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.233 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.587 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -1.175 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.040 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.040 | ||||
| Inter Quartile Range | 0.013 | ||||
| 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) | 0.057 | ||||
| Compounded annual return (geometric extrapolation) | 0.054 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.327 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.327 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.537 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | 0.147 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.147 | ||||
| df | 958.000 | ||||
| t | 0.282 | ||||
| p | 0.389 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.877 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.172 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.877 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.172 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.269 | ||||
| Upside Potential Ratio | 4.755 | ||||
| Upside part of mean | 0.159 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 866.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 959.000 | ||||
| Mean of predictor | 0.473 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | 0.002 | ||||
| r | 0.078 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | 0.002 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 957.000 | ||||
| t(b) | 2.409 | ||||
| p(b) | 0.008 | ||||
| t(a) | 0.075 | ||||
| p(a) | 0.470 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.060 | ||||
| Upperbound of 95% confidence interval for alpha | 0.065 | ||||
| Treynor index (mean / b) | 0.644 | ||||
| Jensen alpha (a) | 0.002 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.007 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | 0.118 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.118 | ||||
| df | 958.000 | ||||
| t | 0.225 | ||||
| p | 0.411 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.907 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.142 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.907 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.142 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.212 | ||||
| Upside Potential Ratio | 4.682 | ||||
| Upside part of mean | 0.158 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.034 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 866.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 959.000 | ||||
| Mean of predictor | 0.416 | ||||
| Mean of criterion | 0.007 | ||||
| SD of predictor | 0.338 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | 0.002 | ||||
| r | 0.078 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 957.000 | ||||
| t(b) | 2.430 | ||||
| p(b) | 0.008 | ||||
| t(a) | 0.041 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.061 | ||||
| Upperbound of 95% confidence interval for alpha | 0.064 | ||||
| Treynor index (mean / b) | 0.508 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 959.000 | ||||
| Minimum | 0.973 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 198.000 | ||||
| Percentage of outliers low | 0.206 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 207.000 | ||||
| Percentage of outliers high | 0.216 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.430 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.218 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.010 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.060 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.016 | ||||
| Mean of quarter 4 | 0.047 | ||||
| Inter Quartile Range | 0.026 | ||||
| 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) | -5.698 | ||||
| VaR(95%) (moments method) | 0.052 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | -1.008 | ||||
| VaR(95%) (regression method) | 0.065 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.056 | ||||
| Compounded annual return (geometric extrapolation) | 0.053 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.881 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.116 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.827 | ||||
| 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 | 0.991 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.484 | ||||
| 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 | 0.873 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.483 | ||||
| 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) | -8744961819943820.000 | ||||
| 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) | 282158014157000073182420100186112.000 | ||||
| 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 | ||||