Answered: Let rt be a log return. Suppose that…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 23E

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Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2).
(a) What is the distribution of rt(8) = rt + rt−1 + rt−2 +...+ rt−7?
(b) What is the covariance between r7(3) and r9(3)?
(c) What is the conditional distribution r17(3) given that r16 =0.004

(d) What is the probability that the gross return over the first 10 times periods is at least 1.05?

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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