题目
题目

BU.232.630.W4.SP25 sample_quiz_3

单项选择题

Consider the following model for the mean of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝛌 + 𝛜 𝑧 𝑡 − 1 + 𝜀 𝑡 where 𝑧 𝑡 − 1 is a predictor of the returns. The model for the volatility is 𝜀 𝑡 = ℎ 𝑡 𝑢 𝑡 ℎ 𝑡 = 𝜇 * + 𝜙 1 * 𝜀 𝑡 − 1 2 + 𝜙 2 * 𝜀 𝑡 − 2 2 + 𝜙 3 * 𝜀 𝑡 − 3 2 𝔌 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔌 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 What is the conditional expected value of the returns 𝔌 𝑡 − 1 ( 𝑟 𝑡 ) ? Choose the best answer below.

选项
A.𝔌 𝑡 − 1 ( 𝑟 𝑡 ) = 𝛌 1 − 𝛜
B.𝔌 𝑡 − 1 ( 𝑟 𝑡 ) = 𝛜 𝑟 𝑡 − 1 + 𝛌
C.𝔌 𝑡 − 1 ( 𝑟 𝑡 ) = 𝛌 + 𝛜 𝑧 𝑡 − 1
D.𝔌 𝑡 − 1 ( 𝑟 𝑡 ) = 𝛜 𝑧 𝑡 − 1
E.𝔌 𝑡 − 1 ( 𝑟 𝑡 ) = 𝑧 𝑡 − 1
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思路分析
The question presents a model for asset returns: r_t = α + β z_{t−1} + ε_t, where z_{t−1} is a predictor of the returns and ε_t is the error term with mean zero given information up to time t−1. The task is to identify the conditional expected value E_{t−1}(r_t). Option 1: E_{t−1}(r_t) = α + 1 − β. This form is incorrect. It treats the expectation as a constant offset of α and subtracts β, but it ignores the actual predictor z_{t−1} and its coefficient, which are essential to the conditional mean. There is no basis in the model for adding a constant 1 minus β;......Login to view full explanation

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类䌌问题

If the conditional variance for tomorrow's return is 0.0004, 𝑉 𝑎 𝑅 𝑡 ( 𝑅 𝑡 + 1 ) = ( 0.02 ) 2 = 0.0004 , then the conditional expectation for tomorrow's return is 2% or -2%.

Consider the following model for the mean of asset returns rt: rt=α+βzt−1+εt where zt−1 is a predictor of the returns. The model for the volatility is εt= √ ht ut ht=ÎŒ*+ϕ * 1 ε 2 t−1 +ϕ * 2 ε 2 t−2 +ϕ * 3 ε 2 t−3 𝔌t−1(ut)=0 𝔌t−1(u 2 t )=1 What is the conditional expected value of the returns 𝔌t−1(rt)? Choose the best answer below.

Consider the following model for the mean and volatility of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝛜 ℎ 𝑡 + 𝜀 𝑡 𝜀 𝑡 = ℎ 𝑡 𝑢 𝑡 ℎ 𝑡 = 𝜇 * + 𝜙 1 * 𝜀 𝑡 − 1 2 + 𝜙 2 * 𝜀 𝑡 − 2 2 + 𝜙 3 * 𝜀 𝑡 − 3 2 𝔌 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔌 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 What is the conditional expectation 𝔌 𝑡 − 1 ( 𝑟 𝑡 ) ?

Consider the following model for the mean and volatility of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝛜 ℎ 𝑡 + 𝜀 𝑡 𝜀 𝑡 = ℎ 𝑡 𝑢 𝑡 ℎ 𝑡 = 𝜇 * + 𝜙 1 * 𝜀 𝑡 − 1 2 + 𝜙 2 * 𝜀 𝑡 − 2 2 + 𝜙 3 * 𝜀 𝑡 − 3 2 𝔌 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔌 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 What is the conditional expectation 𝔌 𝑡 − 1 ( 𝑟 𝑡 ) ?

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