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Explanation:
A is correct. In practice, the return distributions of many assets (and other financial variables) are observed to have fatter tails than a normal distribution. In a model where the return is conditionally normal, the return distribution is normal each day, while the standard deviation of the return varies throughout time. This leads to an unconditional distribution with fat tails.
B is incorrect. Stochastic mean combined with stochastic volatility can give rise to a non-symmetrical distribution.
C is incorrect. This describes an unconditionally normal model.
D is incorrect. This does not describe a conditionally normal model.
Learning Objective: Distinguish between conditional and unconditional distributions and describe regime switching. Explain reasons for fat tails in a return distribution and describe their implications.
Reference: Global Association of Risk Professionals. Valuation and Risk Models. New York, NY: Pearson, 2023. Chapter 3. Measuring and Monitoring Volatility [VRM-3]
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Question 9
A risk analyst for an equity hedge fund is modeling the returns of a group of stocks. In order to reflect the non-normal properties empirically observed in distributions of asset returns, the analyst employs a conditionally normal model. Which of the following is correct regarding such a model?
A
Daily stock returns are normally distributed, but the distribution's standard deviation varies throughout time, causing the distribution of returns over time to be non-normal.
B
Daily stock returns are normally distributed, but the distribution's mean differs each day, causing the distribution of returns over time to be non-normal.
C
Daily stock returns are normally distributed with a standard deviation that is constant throughout time, causing the distribution of returns over time to be normally distributed.
D
Daily stock returns are not normally distributed, but the distribution of returns over time tends toward a normal distribution due to the central limit theorem.