题目
题目

BU.232.630.W6.SP25 Quiz 3 solutions

单项选择题

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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思路分析
To begin, let’s lay out what the model provides and what the conditioning means. - The return is r_t = β h_t + ε_t. - The innovation is ε_t = h_t u_t, with the given conditional facts E_{t-1}(u_t) = 0 and E_{t-1}(u_t^2) = 1. - The conditioning, denoted E_{t-1}(.), refers to information available up to time t−1. Now evaluate E_{t-1}(r_t) by ......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 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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