Advanced Statistics: Bravo Tango
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 | 0.008 | ||||
SD | 0.187 | ||||
Sharpe ratio (Glass type estimate) | 0.044 | ||||
Sharpe ratio (Hedges UMVUE) | 0.043 | ||||
df | 33.000 | ||||
t | 0.074 | ||||
p | 0.471 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -1.121 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.208 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.122 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.207 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | 0.084 | ||||
Upside Potential Ratio | 1.386 | ||||
Upside part of mean | 0.135 | ||||
Downside part of mean | -0.127 | ||||
Upside SD | 0.157 | ||||
Downside SD | 0.097 | ||||
N nonnegative terms | 3.000 | ||||
N negative terms | 31.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 34.000 | ||||
Mean of predictor | 0.457 | ||||
Mean of criterion | 0.008 | ||||
SD of predictor | 0.264 | ||||
SD of criterion | 0.187 | ||||
Covariance | -0.004 | ||||
r | -0.074 | ||||
b (slope, estimate of beta) | -0.052 | ||||
a (intercept, estimate of alpha) | 0.032 | ||||
Mean Square Error | 0.036 | ||||
DF error | 32.000 | ||||
t(b) | -0.420 | ||||
p(b) | 0.661 | ||||
t(a) | 0.255 | ||||
p(a) | 0.400 | ||||
Lowerbound of 95% confidence interval for beta | -0.307 | ||||
Upperbound of 95% confidence interval for beta | 0.202 | ||||
Lowerbound of 95% confidence interval for alpha | -0.225 | ||||
Upperbound of 95% confidence interval for alpha | 0.289 | ||||
Treynor index (mean / b) | -0.156 | ||||
Jensen alpha (a) | 0.032 | ||||
Ratio statistics of excess log return rates | |||||
Statistics related to Sharpe ratio | |||||
Mean | -0.008 | ||||
SD | 0.177 | ||||
Sharpe ratio (Glass type estimate) | -0.043 | ||||
Sharpe ratio (Hedges UMVUE) | -0.042 | ||||
df | 33.000 | ||||
t | -0.072 | ||||
p | 0.528 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -1.207 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.122 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.206 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.123 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | -0.074 | ||||
Upside Potential Ratio | 1.204 | ||||
Upside part of mean | 0.124 | ||||
Downside part of mean | -0.131 | ||||
Upside SD | 0.141 | ||||
Downside SD | 0.103 | ||||
N nonnegative terms | 3.000 | ||||
N negative terms | 31.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 34.000 | ||||
Mean of predictor | 0.416 | ||||
Mean of criterion | -0.008 | ||||
SD of predictor | 0.255 | ||||
SD of criterion | 0.177 | ||||
Covariance | -0.003 | ||||
r | -0.064 | ||||
b (slope, estimate of beta) | -0.045 | ||||
a (intercept, estimate of alpha) | 0.011 | ||||
Mean Square Error | 0.032 | ||||
DF error | 32.000 | ||||
t(b) | -0.363 | ||||
p(b) | 0.641 | ||||
t(a) | 0.093 | ||||
p(a) | 0.463 | ||||
Lowerbound of 95% confidence interval for beta | -0.295 | ||||
Upperbound of 95% confidence interval for beta | 0.206 | ||||
Lowerbound of 95% confidence interval for alpha | -0.230 | ||||
Upperbound of 95% confidence interval for alpha | 0.252 | ||||
Treynor index (mean / b) | 0.170 | ||||
Jensen alpha (a) | 0.011 | ||||
Risk estimates for a one-period unit investment (parametric) | |||||
assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
VaR(95%) | 0.081 | ||||
Expected Shortfall on VaR | 0.101 | ||||
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 | 34.000 | ||||
Minimum | 0.878 | ||||
Quartile 1 | 1.000 | ||||
Median | 1.000 | ||||
Quartile 3 | 1.000 | ||||
Maximum | 1.247 | ||||
Mean of quarter 1 | 0.973 | ||||
Mean of quarter 2 | 1.000 | ||||
Mean of quarter 3 | 1.000 | ||||
Mean of quarter 4 | 1.044 | ||||
Inter Quartile Range | 0.000 | ||||
Number outliers low | 3.000 | ||||
Percentage of outliers low | 0.088 | ||||
Mean of outliers low | 0.918 | ||||
Number of outliers high | 3.000 | ||||
Percentage of outliers high | 0.088 | ||||
Mean of outliers high | 1.131 | ||||
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) | -1.174 | ||||
VaR(95%) (regression method) | 0.090 | ||||
Expected Shortfall (regression method) | 0.120 | ||||
DRAW DOWN STATISTICS | |||||
Quartiles of draw downs | |||||
Number of observations | 2.000 | ||||
Minimum | 0.095 | ||||
Quartile 1 | 0.108 | ||||
Median | 0.121 | ||||
Quartile 3 | 0.134 | ||||
Maximum | 0.147 | ||||
Mean of quarter 1 | 0.095 | ||||
Mean of quarter 2 | NA | ||||
Mean of quarter 3 | NA | ||||
Mean of quarter 4 | 0.147 | ||||
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) | 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) | 0.038 | ||||
Compounded annual return (geometric extrapolation) | 0.037 | ||||
Calmar ratio (compounded annual return / max draw down) | 0.253 | ||||
Compounded annual return / average of 25% largest draw downs | 0.253 | ||||
Compounded annual return / Expected Shortfall lognormal | 0.369 | ||||
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
RATIO STATISTICS | |||||
Ratio statistics of excess return rates | |||||
Statistics related to Sharpe ratio | |||||
Mean | 0.001 | ||||
SD | 0.131 | ||||
Sharpe ratio (Glass type estimate) | 0.008 | ||||
Sharpe ratio (Hedges UMVUE) | 0.007 | ||||
df | 743.000 | ||||
t | 0.013 | ||||
p | 0.495 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -1.156 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.171 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.156 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.171 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | 0.010 | ||||
Upside Potential Ratio | 3.095 | ||||
Upside part of mean | 0.291 | ||||
Downside part of mean | -0.290 | ||||
Upside SD | 0.092 | ||||
Downside SD | 0.094 | ||||
N nonnegative terms | 50.000 | ||||
N negative terms | 694.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 744.000 | ||||
Mean of predictor | 0.479 | ||||
Mean of criterion | 0.001 | ||||
SD of predictor | 0.312 | ||||
SD of criterion | 0.131 | ||||
Covariance | -0.000 | ||||
r | -0.000 | ||||
b (slope, estimate of beta) | -0.000 | ||||
a (intercept, estimate of alpha) | 0.001 | ||||
Mean Square Error | 0.017 | ||||
DF error | 742.000 | ||||
t(b) | -0.012 | ||||
p(b) | 0.505 | ||||
t(a) | 0.014 | ||||
p(a) | 0.495 | ||||
Lowerbound of 95% confidence interval for beta | -0.031 | ||||
Upperbound of 95% confidence interval for beta | 0.030 | ||||
Lowerbound of 95% confidence interval for alpha | -0.153 | ||||
Upperbound of 95% confidence interval for alpha | 0.155 | ||||
Treynor index (mean / b) | -5.260 | ||||
Jensen alpha (a) | 0.001 | ||||
Ratio statistics of excess log return rates | |||||
Statistics related to Sharpe ratio | |||||
Mean | -0.008 | ||||
SD | 0.132 | ||||
Sharpe ratio (Glass type estimate) | -0.058 | ||||
Sharpe ratio (Hedges UMVUE) | -0.058 | ||||
df | 743.000 | ||||
t | -0.098 | ||||
p | 0.539 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -1.221 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.105 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.221 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.105 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | -0.080 | ||||
Upside Potential Ratio | 2.983 | ||||
Upside part of mean | 0.287 | ||||
Downside part of mean | -0.295 | ||||
Upside SD | 0.090 | ||||
Downside SD | 0.096 | ||||
N nonnegative terms | 50.000 | ||||
N negative terms | 694.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 744.000 | ||||
Mean of predictor | 0.430 | ||||
Mean of criterion | -0.008 | ||||
SD of predictor | 0.315 | ||||
SD of criterion | 0.132 | ||||
Covariance | 0.000 | ||||
r | 0.000 | ||||
b (slope, estimate of beta) | 0.000 | ||||
a (intercept, estimate of alpha) | -0.008 | ||||
Mean Square Error | 0.017 | ||||
DF error | 742.000 | ||||
t(b) | 0.008 | ||||
p(b) | 0.497 | ||||
t(a) | -0.098 | ||||
p(a) | 0.539 | ||||
Lowerbound of 95% confidence interval for beta | -0.030 | ||||
Upperbound of 95% confidence interval for beta | 0.030 | ||||
Lowerbound of 95% confidence interval for alpha | -0.162 | ||||
Upperbound of 95% confidence interval for alpha | 0.146 | ||||
Treynor index (mean / b) | -62.424 | ||||
Jensen alpha (a) | -0.008 | ||||
Risk estimates for a one-period unit investment (parametric) | |||||
assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
VaR(95%) | 0.013 | ||||
Expected Shortfall on VaR | 0.017 | ||||
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 | 744.000 | ||||
Minimum | 0.931 | ||||
Quartile 1 | 1.000 | ||||
Median | 1.000 | ||||
Quartile 3 | 1.000 | ||||
Maximum | 1.071 | ||||
Mean of quarter 1 | 0.996 | ||||
Mean of quarter 2 | 1.000 | ||||
Mean of quarter 3 | 1.000 | ||||
Mean of quarter 4 | 1.004 | ||||
Inter Quartile Range | 0.000 | ||||
Number outliers low | 38.000 | ||||
Percentage of outliers low | 0.051 | ||||
Mean of outliers low | 0.981 | ||||
Number of outliers high | 50.000 | ||||
Percentage of outliers high | 0.067 | ||||
Mean of outliers high | 1.017 | ||||
Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
Extreme Value Index (moments method) | -0.246 | ||||
VaR(95%) (moments method) | 0.000 | ||||
Expected Shortfall (moments method) | 0.001 | ||||
Extreme Value Index (regression method) | 0.202 | ||||
VaR(95%) (regression method) | 0.000 | ||||
Expected Shortfall (regression method) | 0.011 | ||||
DRAW DOWN STATISTICS | |||||
Quartiles of draw downs | |||||
Number of observations | 5.000 | ||||
Minimum | 0.001 | ||||
Quartile 1 | 0.002 | ||||
Median | 0.014 | ||||
Quartile 3 | 0.143 | ||||
Maximum | 0.254 | ||||
Mean of quarter 1 | 0.002 | ||||
Mean of quarter 2 | 0.014 | ||||
Mean of quarter 3 | 0.143 | ||||
Mean of quarter 4 | 0.254 | ||||
Inter Quartile Range | 0.141 | ||||
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) | 0.038 | ||||
Compounded annual return (geometric extrapolation) | 0.037 | ||||
Calmar ratio (compounded annual return / max draw down) | 0.146 | ||||
Compounded annual return / average of 25% largest draw downs | 0.146 | ||||
Compounded annual return / Expected Shortfall lognormal | 2.221 | ||||
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 | 0.769 | ||||
Mean of criterion | -0.044 | ||||
SD of predictor | 0.419 | ||||
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 | 0.681 | ||||
Mean of criterion | -0.044 | ||||
SD of predictor | 0.419 | ||||
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) | -8755369067589107.000 | ||||
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) | -636760922601885821230496450871296.000 | ||||
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 |