Advanced Statistics: TimerSignals - SPY
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 | -0.017 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.349 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.343 | ||||
| df | 44.000 | ||||
| t | -0.677 | ||||
| p | 0.749 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.362 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.667 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.358 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.671 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.511 | ||||
| Upside Potential Ratio | 1.515 | ||||
| Upside part of mean | 0.050 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.424 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | -0.000 | ||||
| r | -0.001 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.004 | ||||
| p(b) | 0.502 | ||||
| t(a) | -0.599 | ||||
| p(a) | 0.724 | ||||
| Lowerbound of 95% confidence interval for beta | -0.059 | ||||
| Upperbound of 95% confidence interval for beta | 0.058 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.040 | ||||
| Treynor index (mean / b) | 152.192 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.373 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.367 | ||||
| df | 44.000 | ||||
| t | -0.723 | ||||
| p | 0.763 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.386 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.644 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.382 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.648 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.538 | ||||
| Upside Potential Ratio | 1.478 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.388 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.000 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 43.000 | ||||
| t(b) | 0.060 | ||||
| p(b) | 0.476 | ||||
| t(a) | -0.671 | ||||
| p(a) | 0.747 | ||||
| Lowerbound of 95% confidence interval for beta | -0.060 | ||||
| Upperbound of 95% confidence interval for beta | 0.064 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.074 | ||||
| Upperbound of 95% confidence interval for alpha | 0.037 | ||||
| Treynor index (mean / b) | -9.674 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.967 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.036 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.156 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -9.334 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.942 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.039 | ||||
| Maximum | 0.083 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.083 | ||||
| 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 | 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) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.320 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.320 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.903 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.016 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | -0.210 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.209 | ||||
| df | 1001.000 | ||||
| t | -0.410 | ||||
| p | 0.659 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.212 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.793 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.212 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.304 | ||||
| Upside Potential Ratio | 4.001 | ||||
| Upside part of mean | 0.204 | ||||
| Downside part of mean | -0.220 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 123.000 | ||||
| N negative terms | 879.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1002.000 | ||||
| Mean of predictor | 0.472 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | 0.003 | ||||
| r | 0.119 | ||||
| b (slope, estimate of beta) | 0.028 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1000.000 | ||||
| t(b) | 3.801 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.759 | ||||
| p(a) | 0.776 | ||||
| Lowerbound of 95% confidence interval for beta | 0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.046 | ||||
| Treynor index (mean / b) | -0.556 | ||||
| Jensen alpha (a) | -0.029 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | -0.247 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.247 | ||||
| df | 1001.000 | ||||
| t | -0.483 | ||||
| p | 0.685 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.249 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.756 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.249 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.756 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.354 | ||||
| Upside Potential Ratio | 3.928 | ||||
| Upside part of mean | 0.203 | ||||
| Downside part of mean | -0.221 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 123.000 | ||||
| N negative terms | 879.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1002.000 | ||||
| Mean of predictor | 0.421 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | 0.003 | ||||
| r | 0.118 | ||||
| b (slope, estimate of beta) | 0.027 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1000.000 | ||||
| t(b) | 3.770 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.789 | ||||
| p(a) | 0.785 | ||||
| Lowerbound of 95% confidence interval for beta | 0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.104 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -0.667 | ||||
| Jensen alpha (a) | -0.030 | ||||
| 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 | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1002.000 | ||||
| Minimum | 0.959 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.046 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 122.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 133.000 | ||||
| Percentage of outliers high | 0.133 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.477 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.254 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.034 | ||||
| Maximum | 0.145 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.075 | ||||
| Inter Quartile Range | 0.031 | ||||
| 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 | 0.077 | ||||
| Mean of outliers high | 0.145 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.621 | ||||
| VaR(95%) (moments method) | 0.085 | ||||
| Expected Shortfall (moments method) | 0.223 | ||||
| Extreme Value Index (regression method) | 2.686 | ||||
| VaR(95%) (regression method) | 0.136 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.180 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.347 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.748 | ||||
| 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 | 1.128 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.513 | ||||
| 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 | 0.993 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.521 | ||||
| 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) | -8738899433655984.000 | ||||
| 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) | 117410857355077581788402174394368.000 | ||||
| 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 | ||||