The variance ratio (VR) can be used to determine whether returns satisfy the efficient market hypothesis...

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The variance ratio (VR) can be used to determine whether returns satisfy the efficient market hypothesis (EMH). Let n = 5 and r5,t be the five period log return at time t, where t = 1,2,..., T. 1. Express (r5,t-F5) in terms of deviations of the relevant one period log returns from their respective means. Denote 75 to be the mean of the five period log return. 2. Factor (r5,t-F5)² as expressed in Q 1 into squares and cross-product terms. 1 3. Using the factorisation of (r5,t - F5)2 in Q 2, provide the expression for s² (5) Σ1 (r5,1 – 75)3 /Τ. = 4. What condition on the expression in Q. 3 is needed to ensure that the factorisation implied by Q1.2 only includes squared terms? What does this imply about the properties of returns? 5. Using the formula in Q 3 for s² (5), deduce that s² (5) = 5s² (1) under the condition in Q. 4. The variance ratio (VR) can be used to determine whether returns satisfy the efficient market hypothesis (EMH). Let n = 5 and r5,t be the five period log return at time t, where t = 1,2,..., T. 1. Express (r5,t-F5) in terms of deviations of the relevant one period log returns from their respective means. Denote 75 to be the mean of the five period log return. 2. Factor (r5,t-F5)² as expressed in Q 1 into squares and cross-product terms. 1 3. Using the factorisation of (r5,t - F5)2 in Q 2, provide the expression for s² (5) Σ1 (r5,1 – 75)3 /Τ. = 4. What condition on the expression in Q. 3 is needed to ensure that the factorisation implied by Q1.2 only includes squared terms? What does this imply about the properties of returns? 5. Using the formula in Q 3 for s² (5), deduce that s² (5) = 5s² (1) under the condition in Q. 4.

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1 15t75 r1t 75 r2t 75 r3t 75 r4t 75 r5t 75 2 15t5 r1t 75 ... View the full answer