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# tutorial1 - zero in DS and 10 percent in FS How should an...

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TUTORIAL 1 – WEEK 2 ECON3107/5106 – Economics of Finance 1. Find the inverse of the following matrix: X = 0 . 1 0 . 1 0 0 . 9 0 . 8 0 . 2 0 . 1 0 0 0 . 4 0 . 5 0 0 . 1 0 . 3 0 . 4 0 . 1 2. Show that the three columns in the matrix A below are linearly dependent A = 1 0 3 2 - 3 9 4 1 11 . 3. Let a ij denote the element in the i - th row and j - th column of a matrix A . The determinant of a 3 × 3 matrix is calculated as follows: | A | = a 11 a 22 a 33 + a 12 a 23 a 31 + a 13 a 21 a 32 - a 13 a 22 a 31 - a 12 a 21 a 33 - a 11 a 23 a 32 Calculate the determinant for the matrix in question 2. Explain. 4. Suppose the columns in the matrix in question 1 describe the allocations over four asset classes [domestic bonds (DB), foreign bonds (FB), domestic stocks (DS), foreign stocks (FS)] of four mutual funds denoted by MF1, MF2, MF3, MF4. For example, MF1 holds 10 percent of its assets in DB, 80 percent in FB,
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Unformatted text preview: zero in DS, and 10 percent in FS. How should an investor allocate her wealth between the four funds to obtain the following asset mixes: (i) DB = 0 . 2 ,FB = 0 . 4 ,DS = 0 . 2 ,FS = 0 . 4 (ii) DB = 0 . 3 ,FB = 0 . 3 ,DS = 0 . 2 ,FS = 0 . 2 (iii) DB = 1 ,FB = 0 ,DS = 0 ,FS = 0 (iv) DB = 0 ,FB = 1 ,DS = 0 ,FS = 0 (v) DB = 0 ,FB = 0 ,DS = 1 ,FS = 0 (vi) DB = 0 ,FB = 0 ,DS = 0 ,FS = 1 Note: (iii), (iv), (v) and (vi) are referred to as pure asset plays. Notes: Do not submit this tutorial assignment, since it will not be marked. MATLAB should be used to make the calculations. 1...
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