Description of H3, H4, H6 and H7 variables, tests and results
| ID | Hypotheses | Tests | Results | ||
|---|---|---|---|---|---|
| H3 | The method most commonly used to determine the covariance matrix is shrinkage | Chi-square statistic | Hypothesis rejected | ||
| H4 | Investment managers use optimization methods more than the simple rule of establishing a maximum concentration limit per asset | Chi-square | Hypothesis not rejected | ||
| H6 | Investment managers use parametric distributions, such as extreme value theory or distributions with higher moments, more than the normal distribution to estimate VaR | Chi-square | Hypothesis rejected | ||
| H7 | Estimation risk management methods are more commonly used than the simple rule of imposing a maximum concentration per asset | Chi-square | Hypothesis rejected | ||
| Tests performed | Hypotheses | p-value | Sig* | Results | |
| T3 | Comparison of the proportions of respondents using shrinkage (θ1) and those using RiskMetrics (θ2) in determining the covariance matrix | H0: θ1 = θ2 h1: θ1 < θ2 | 0.000 | *** | H0 Rejected |
| T4 | Comparison of the proportions of respondents using quantitative optimization (θ1) and those using maximum concentration per asset (θ2) in the construction of portfolios | H0: θ1 = θ2 h1: θ1 > θ2 | 0.253 | H0 Not rejected | |
| T6 | Comparison of the proportions of respondents using extreme value theory or a distribution with upper moments (θ1) and those using the normal distribution (θ2) | H0: θ1 = θ2 h1: θ1 < θ2 | 0.000 | *** | H0 Rejected |
| T7 | Comparison of proportions of respondents using advanced estimation risk management methods (θ1) and those using maximum concentration per asset (θ2) | h0: θ1 = θ2 h1: θ1 < θ2 | 0.000 | *** | H0 Rejected |
| T7b | Same variables as T7. Test performed in the subsample of 43 respondents who perform portfolio optimization | h0: θ1 = θ2 h1: θ1 < θ2 | 0.000 | *** | H0 Rejected |
| ID | Hypotheses | Tests | Results | ||
|---|---|---|---|---|---|
| The method most commonly used to determine the covariance matrix is shrinkage | Chi-square statistic | Hypothesis rejected | |||
| Investment managers use optimization methods more than the simple rule of establishing a maximum concentration limit per asset | Chi-square | Hypothesis not rejected | |||
| Investment managers use parametric distributions, such as extreme value theory or distributions with higher moments, more than the normal distribution to estimate VaR | Chi-square | Hypothesis rejected | |||
| Estimation risk management methods are more commonly used than the simple rule of imposing a maximum concentration per asset | Chi-square | Hypothesis rejected | |||
| Tests performed | Hypotheses | Sig* | Results | ||
| T3 | Comparison of the proportions of respondents using shrinkage (θ1) and those using RiskMetrics (θ2) in determining the covariance matrix | H0: θ1 = θ2 | 0.000 | ||
| T4 | Comparison of the proportions of respondents using quantitative optimization (θ1) and those using maximum concentration per asset (θ2) in the construction of portfolios | H0: θ1 = θ2 | 0.253 | ||
| T6 | Comparison of the proportions of respondents using extreme value theory or a distribution with upper moments (θ1) and those using the normal distribution (θ2) | H0: θ1 = θ2 | 0.000 | ||
| T7 | Comparison of proportions of respondents using advanced estimation risk management methods (θ1) and those using maximum concentration per asset (θ2) | h0: θ1 = θ2 | 0.000 | ||
| T7b | Same variables as T7. Test performed in the subsample of 43 respondents who perform portfolio optimization | h0: θ1 = θ2 | 0.000 | ||
Note:
We reject the null hypothesis at p < 0.01 (
)
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