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Unformatted text preview: ji. Example 2: Matrix Multiplication f 2 0] 4 1 3 NM=L 7 2~~ ~ = [4.2 + 1·5 +3·1 4·0+ 1.3+3.6] 1·2+7·5+2·1 1·0+7·3+2·6 = [16 21] 39 33 Note that matrix multiplication is not, in general, commutative: MN * NM. The Market Portfolio (with N risky assets) • Note that when we multiply the matrices w'R we get a single number. • To see this, note that the dimension ofw' is 1 x n and the dimension ofR is n x 1. So the product is I x 1 (a scalar). • Note that when we multiply the matrices w':Ew we get a single number. • To see this, look first at the product w'E. Since w' is I x"n and E is n x n, the product has dimension I x n. When we multiply this product times w which is n x I we get a final product which is I x I (a scalar). Risk and Return IV L The Market Portfolio (with N risky assets) • Key Question: How do we find the market portfolio? • By choosing asset weights w that maximize the Sharpe Ratio: w 'R -R Max S = f p .)W'LW subject to the constraint that the weights sum to I ....
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- Fall '10
- Capital Asset Pricing Model, risky assets, systematic risk, Market Portfolio, The Market Portfolio, measuring systematic risk