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hw3_s10

# hw3_s10 - R f = 0 001 a Find the cut-oﬀ point C when...

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University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Homework 3 Exercise 1: Access the data in R as follows: > a <- read.table("http://www.stat.ucla.edu/~nchristo/datac183c283/ statc183c283_10stocks.txt", header=TRUE) These are closing monthly prices for 10 stocks (the ﬁrst 5 are the same as in homework 2) from January 1986 to December 2003. The last column represents the returns on S P 500 for the same period (31-Jan-1986 to 31-Dec-2003). After you convert all the prices into returns (but not the last column - these are already returns), use the single index model to: a. Estimate β , α , and residual risk ( σ ± ) for each stock. b. Estimate the mean, and variance for each stock. Do the same for the returns of the market (ﬁnd the mean and variance of S P 500). c. Use the Vasicek’s technique to adjust the betas. In other words, what betas would you use for the period 2004-09? Exercise 2: Single index model: Use these data (10 stocks) and
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Unformatted text preview: R f = 0 . 001: a. Find the cut-oﬀ point C * when short sales are allowed and when short sales are not allowed. b. Assume short sales are not allowed: Find the composition of the optimum portfolio. c. Assume short sales are allowed: Find the composition of the optimum portfolio. Note: You should submit the table that shows all the necessary steps. Exercise 3: Constant correlation model: Use these data (10 stocks) and R f = 0 . 001: a. Find the cut-oﬀ point C * when short sales are allowed and when short sales are not allowed. You will have to compute the average correlation coeﬃcient ﬁrst by using all the ( 10 2 ) = 45 pairs. So ﬁnd the correlation matrix ﬁrst. b. Assume no short sales are allowed: Find the composition of the optimum portfolio. c. Assume short sales are allowed: Find the composition of the optimum portfolio. Note: You should submit the table that shows all the necessary steps....
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