Questions
BU.232.630.W6.SP25 sample_quiz_3
Single choice
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=μ*+ϕ * 1 ε 2 t−1 +ϕ * 2 ε 2 t−2 +ϕ * 3 ε 2 t−3 𝔼t−1(ut)=0 𝔼t−1(u 2 t )=1 What is the conditional expected value of the returns 𝔼t−1(rt)? Choose the best answer below.
Options
A.𝔼t−1(rt)=βzt−1
B.𝔼t−1(rt)=βrt−1+α
C.𝔼t−1(rt)=α+βzt−1
D.𝔼t−1(rt)=
α
1−β
E.𝔼t−1(rt)=zt−1
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Step-by-Step Analysis
To find the conditional expectation E_{t-1}(r_t), we start from the given mean model r_t = α + β z_{t-1} + ε_t and note that, by construction, the error term ε_t has conditional mean zero given information up to t−1, i.e., E_{t-1}(ε_t) = 0 (since E_{t-1}(u_t) = 0 and ε_t = √h_t u_t with h_t determined by past ......Login to view full explanationLog in for full answers
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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=μ*+ϕ * 1 ε 2 t−1 +ϕ * 2 ε 2 t−2 +ϕ * 3 ε 2 t−3 𝔼t−1(ut)=0 𝔼t−1(u 2 t )=1 What is the conditional expected value of the returns 𝔼t−1(rt)? Choose the best answer below.
Consider the following model for the mean and volatility of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝛽 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 𝔼 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔼 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 What is the conditional expectation 𝔼 𝑡 − 1 ( 𝑟 𝑡 ) ?
Consider the following model for the mean and volatility of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝛽 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 𝔼 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔼 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 What is the conditional expectation 𝔼 𝑡 − 1 ( 𝑟 𝑡 ) ?
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