Free CFA Level II Quantitative Methods Practice Questions

An error correction model is used when variables are cointegrated — they share a long-run equilibrium relationship despite being individually non-stationary. The ECM includes both first-differenced terms (capturing short-run dynamics) and an error correction term (capturing the speed of adjustment back to the long-run equilibrium). This allows the model to incorporate both short-term fluctuations and long-run relationships.

Choice A is incorrect because when all series are stationary, standard regression or VAR models can be applied directly without differencing or error correction. The ECM is specifically designed for the cointegrated (non-stationary but with a stationary linear combination) case.

Choice B is incorrect because the Durbin-Watson test for serial correlation is unrelated to the decision to use an ECM. An ECM is motivated by the cointegration relationship between the variables, not by the serial correlation properties of a particular regression's residuals.

The negative coefficient on Tracking Error (-0.2) means that as tracking error increases by one percentage point, the log-odds of outperformance decrease by 0.2, holding alpha and AUM growth constant. Since the logistic function is monotonically increasing in log-odds, lower log-odds correspond to a lower probability of outperformance. This suggests that funds with more volatile returns relative to their benchmark are less likely to outperform.

Choice A is incorrect because the logistic regression measures association with the probability of outperformance, not causation on absolute returns. The coefficient indicates that higher tracking error is associated with lower outperformance probability, but we cannot claim it causes lower returns without controlling for all confounding factors.

Choice C is incorrect because the z-statistic for Tracking Error is -2.50, which exceeds the typical critical value of 1.96 in absolute value. The p-value would be approximately 0.012, making it significant at the 5% level. The coefficient is both statistically and economically significant.

$R^2 = \frac{RSS}{SST} = \frac{5{,}625}{11{,}625} = 0.4839 \approx 0.484$

Adjusted $R^2 = 1 - \frac{(1 - R^2)(n-1)}{n - k - 1} = 1 - \frac{(1 - 0.4839)(63)}{60} = 1 - \frac{0.5161 \times 63}{60} = 1 - \frac{32.51}{60} = 1 - 0.5419 = 0.458$

B is incorrect because it correctly computes $R^2$ but fails to adjust it. The adjusted $R^2$ is always less than $R^2$ when there are multiple independent variables. Reporting them as equal ignores the degrees-of-freedom penalty.

C is incorrect because $R^2 = 0.516$ would result from using SSE/SST = 6,000/11,625 = 0.516, which is the proportion of unexplained variation ($1 - R^2$), not $R^2$ itself. The numerator for $R^2$ should be RSS (regression sum of squares), not SSE (error sum of squares).