题目
题目

BU.232.630.W6.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.

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思路分析
We begin by restating the problem setup to be clear: the return at time t is modeled as r_t = α + β z_{t-1} + ε_t, with the conditional mean of ε_t given information up to t−1 being zero, i.e., E_{t−1}(ε_t) = 0. The volatility model provides that ε_t = h_t u_t, and E_{t−1}(u_t) = 0, E_{t−1}(u_t^2) = 1, but the key for the conditional mean of r_t is the mean of ε_t conditional on the information set, which is zero by assumption. Option analysis: - Option: E......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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