Financial Risk Manager Part 1

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Explanation:

Remember first that when questions ask for volatility, they are referring to the standard deviation.

We first calculate the daily variance, which then needs to be adjusted to an annualized variance; finally, we can take the square root to find the annualized volatility (standard deviation).

Long-run daily variance = $\alpha_0 / (1 - \alpha_1 - \beta)$
Long-run daily variance = $0.00001 / (1 - 0.00048 - 0.87) $Long-run daily variance = `$ 0.000077$ Long-run daily standard deviation = $\sqrt{\text{variance}} = \sqrt{0.000077} = 0.88\%$ Annualized standard deviation = daily standard deviation $\times \sqrt{\text{time}}$ Annualized standard deviation = $0.88`\% \times \sqrt{252} = 13.95\%$

(Book 4, Module 49.3, LO 49.e)

Explanation:

Remember first that when questions ask for volatility, they are referring to the standard deviation.

We first calculate the daily variance, which then needs to be adjusted to an annualized variance; finally, we can take the square root to find the annualized volatility (standard deviation).

(Book 4, Module 49.3, LO 49.e)

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Question 55
A risk manager estimates the daily variance using a GARCH model on daily returns ( $r_t$ ):
$h_t = \alpha_0 + \alpha_1 r_{t-1}^2 + \beta h_{t-1}$
The model parameter values are:
$\alpha_0 = 0.00001$
$\alpha_1 = 0.00048$
$\beta = 0.87$

Using the model, what is the long-run annualized volatility estimate?

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Last updated: July 3, 2026 at 10:47

15.40%

13.95%

24.52%

17.54%