Exercise 10 - exe10 PDF

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Finance 567 Financial Risk Management

Spring 2021 Neil D. Pearson Exercise 10 (5 points)

1. (1 point) Consider the log return defined by Rt = ln(Pt/Pt−1). Suppose that the log return is given by Rt =  + t, where t ~ N(0, 1) and is independent of Pt−1. What is E[Rt | ln(Pt−1)]?

2. (1 point) Suppose instead that Rt = a + b ln(Pt−1)) + et, where et ~ N(0, 2) is a regression residual that is independent of Pt−1. In this case, what is E[Rt | ln(Pt−1)]?

3. (1 point) Write an R or Python script to carry out the simulation in the spreadsheet 2.1_SimpleRegression.xlsm, and compute the average estimate of the slope coefficient. What is the average estimate of the slope coefficient? Please include your R or Python code in the Word or pdf file you upload to the Compass site.

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Finance 567 Financial Risk Management

Spring 2021 Neil D. Pearson

4. (1 point) Consider a time series X0, X1, X2, …, Xt, … Suppose that the time series is weakly stationary (that is, it is covariance stationary) and that the covariance between Xt and Xt+h is given by cov(Xt, Xt+h) = 2. What is the covariance cov(Xt−h , Xt)?

5. (1 point) Please either ask a question or make a comment about the material in one or more of the video lectures (or any earlier part of the course). So in Q3, what I am confused is that, do we need to contain set.seed(seed) function? At first, I didn’t contain it, and the result is different every time. Then I asked my friend who also takes FIN 567, he said we should use set.seed(seed), then we can have a constant number.

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