20.index_steps

20.index_steps - i,i = 1 ··,n(last column as follows C i = σ 2 m ∑ i j =1 ¯ R j-R f β j σ 2 ±j 1 σ 2 m ∑ i j =1 β 2 j σ 2 ±j = σ 2

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University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Constructing the optimal portfolios - Single index model Calculation steps a. Step 1: By regressing the returns of each stock on the returns of the market obtain for each stock: ˆ β, ˆ α, ˆ σ 2 ± and construct the table below: Stock i ˆ α i ˆ β i ¯ R i ˆ σ 2 ±i R i - R f ˆ β i IBM GOOGLE . . . b. Step 2: Sort the table above based on the excess return to beta ratio: ¯ R i - R f β i c. Step 3: Create 5 columns to the right of the sorted table as follows: Stock i ˆ α i ˆ β i ¯ R i ˆ σ 2 ±i R i - R f ˆ β i ( ¯ R i - R f ) ˆ β i ˆ σ 2 ±i i j =1 ( ¯ R j - R f ) ˆ β j ˆ σ 2 ±j ˆ β 2 i ˆ σ 2 ±i i j =1 ˆ β 2 j ˆ σ 2 ±j C i k 1 k 1 l 1 l 1 C 1 k 2 k 1 + k 2 l 2 l 1 + l 2 C 2 k 3 k 1 + k 2 + k 3 l 3 l 1 + l 2 + l 3 C 3 . . . . . . . . . . . . . . . k n k 1 + k 2 + ··· + k n l n l 1 + l 2 + ··· + l n C n Note: Compute all the C
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Unformatted text preview: i ,i = 1 , ··· ,n (last column) as follows: C i = σ 2 m ∑ i j =1 ( ¯ R j-R f ) β j σ 2 ±j 1 + σ 2 m ∑ i j =1 β 2 j σ 2 ±j = σ 2 m × COL2 1 + σ 2 m × COL4 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 β i > C * . In both cases the z i s are computed as follows z i = β i σ 2 ±i ± ¯ R i-R f β i-C * ² and the x i s x i = z i ∑ n i =1 z i...
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This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.

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