This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Exam 1 07 May 2010 Name: Problem 1 (20 points) The betas for 10 stocks in two historical periods 20002004 and 20052009 are as follows: beta1 beta2 [1,] 0.9072828 0.7333601 [2,] 1.0874136 1.0096048 [3,] 0.9871119 1.1143148 [4,] 1.0084073 1.1011334 [5,] 0.7606293 0.7711888 [6,] 0.8047901 0.7834646 [7,] 0.9533157 0.9914738 [8,] 0.8036708 1.1083840 [9,] 1.0867607 0.9524100 [10,] 1.0315184 0.8759303 a. Explain how you can obtain an estimate for the beta of stock 8 for the period 20102014 using the Blume’s technique. b. Suppose that for the second period 20052009 the variance of the return of the S & P500 index is σ 2 m = 0 . 00217. Assume that the single index model holds. Find the covariance between stocks 1 and 3 during the same period. c. Explain how you can obtain an estimate for the beta of stock 8 for the period 20102014 using the Vacicek’s technique. d. Suppose that the correlation coefficient between stock A and S & P500 during the period 20052009 is 0.20. The variance of the return of stock A during the same period is 0.0143 and the variance of the return of the S & P500 index was σ 2 m = 0 . 00217. Find the beta of stock A . Problem 2 (20 points) Use the following for questions (a) and (b) below: Stock ¯ R σ A 0.12 0.20 B ??? 0.08 It is also given that ρ AB = 0 . 1. a. What expected return on stock B would result in an optimum portfolio of 1 2 A and 1 2 B ? Assume short sales are allowed and that R f = 0 . 04. b. What expected return on stock B would mean that stock B would not be held? Assume short sales are allowed and that R f = 0 . 04. c. Suppose X and Y represent the returns of two stocks. Show that these two random variables X and Y cannot possibly have the following properties: E ( X ) = 0 . 3 ,E ( Y ) = 0 . 2 ,E ( X 2 ) = 0 . 1 ,E ( Y 2 ) = 0 . 29, and E ( XY ) = 0. Reminder: σ XY = E ( X μ X )( Y μ Y ) = EXY ( EX )( EY ). Problem 3...
View
Full
Document
This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.
 Spring '11
 Nicolas
 Statistics

Click to edit the document details