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Explanation:

For an MA(1) process defined as $y_t = \varepsilon_t + \theta\varepsilon_{t-1}$ , the autocorrelation at lag 1 is given by:

\rho_1 = \frac{\theta}{1 + \theta^2}

Given $\theta = 0.2$ :

\rho_1 = \frac{0.2}{1 + (0.2)^2} = \frac{0.2}{1 + 0.04} = \frac{0.2}{1.04} = 0.192307... \approx 0.1923

Therefore, the correct answer is 0.1923.

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The first-order moving average MA(1) process has zero mean and constant variance defined as: $ y_t = \varepsilon_t + 0.2\varepsilon_{t-1} $ Based on the above assumption, the autocorrelation can be deduced as: | Financial Risk Manager Part 1 Quiz - LeetQuiz

Financial Risk Manager Part 1

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The first-order moving average MA(1) process has zero mean and constant variance defined as: yt=εt+0.2εt−1y_t = \varepsilon_t + 0.2\varepsilon_{t-1}yt​=εt​+0.2εt−1​ Based on the above assumption, the autocorrelation can be deduced as:

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The first-order moving average MA(1) process has zero mean and constant variance defined as:
$y_t = \varepsilon_t + 0.2\varepsilon_{t-1}$
Based on the above assumption, the autocorrelation can be deduced as: