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26.rho_steps - ρ = ∑ n i =1 ∑ n j =1,j 6 = i ρ ij n...

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University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Constructing the optimal portfolios - Constant correlation model Calculation steps a. Step 1: Compute the historical mean return, standard deviation for each stock. You will also need the correlation coefficients for all pairs of stocks (step 2). Construct the table below: Stock i ¯ R i ¯ R i - R f σ i R i - R f σ i IBM GOOGLE . . . b. Step 2: Sort the table above based on the excess return to standard deviation ratio: ¯ R i - R f σ i c. Step 3: Create 3 columns to the right of the sorted table as follows: Stock i ¯ R i ¯ R i - R f σ i R i - R f σ i ρ 1 - ρ + i j =1 ¯ R j - R f σ j C i Note: ρ is the average correlation. It is equal to:
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Unformatted text preview: ρ = ∑ n i =1 ∑ n j =1 ,j 6 = i ρ ij n ( n-1) Note: Compute all the C i ,i = 1 , ··· ,n (last column) as follows: C i = ρ 1-ρ + iρ j X i =1 ¯ R j-R f σ j = COL 1 × COL 2 . Once the C i s are calculated we find the C * as follows: If short sales are allowed, C * is the last element in the last column. If short sales are not allowed, C * is the element in the last column for which ¯ R i-R f σ i > C * . In both cases the z i s are computed as follows z i = 1 (1-ρ ) σ i ± ¯ R i-R f σ i-C * ² and the x i s x i = z i ∑ n i =1 z i...
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