Math Problem Statement
Asset 1 Asset 2 Asset 3 Estimated Mean 2.1675 -1.8883 3.0712 Asset 1 Asset 2 Asset 3 3.3875 -0.5608 1.2428 -0.5186 4.7057 -0.6986 -2.5194 1.5773 -3.184 -1.3959 1.4225 3.0923 Estimated Covariance matrix -2.7264 1.0408 -0.0131 Asset 1 Asset 2 Asset 3 0.7832 1.2914 -2.0597 Asset 1 0.0056 -0.0020 0.0037 3.9749 -0.2969 2.0496 Asset 2 -0.0020 0.0022 -0.0022 -3.3869 0.6602 -0.585 Asset 3 0.0037 -0.0022 0.0074 -0.1714 0.2207 0.6504 0.5439 0.3632 1.0962 Asset 1 Asset 2 Asset 3 1.0913 0.103 2.7193 Volatility 7.48 4.69 8.60 -1.0361 -0.5964 -0.8361 -0.871 2.2177 -4.2316 Interest rate 1 1.0377 0.2439 1.624 -2.7236 2.7658 -3.2315 Excess return -1.52 3.71 -1.70 2.7485 -1.4885 7.4063 -0.8348 -1.3056 0.3338 Porfolio x1 x2 x3 x0 -1.2728 2.2504 -4.3389 0.00 = 1.00 -0.5232 1.8409 1.5357 0.1174 0.9127 -1.2732 Rate of return (%) 0.0000 1.1843 1.6094 -0.208 0.6003 -0.1249 -0.6808 Volatility (%) #VALUE! <= 5.00 -0.5785 -0.2565 1.451 -1.8834 0.5511 -1.5372 1.0666 -0.555 -1.0502 3.7147 0.2948 3.36 -0.3213 0.8969 -0.3788 1.3712 -0.6688 -0.1197 -0.7987 -0.0603 -0.1823 0.949 -0.0582 -0.1217 -2.5322 3.4582 -4.8028 0.4613 1.0112 -0.5589 -1.6205 0.7624 -0.5277 4.7482 -2.1118 3.0093 1.6551 0.6686 1.0955 -5.1563 1.286 -2.0927 -1.0738 0.5736 0.7881 -1.2798 -0.3968 -1.4555 -0.7793 -0.6159 2.2117 -0.3613 -2.5366 2.9634 0.1896 0.889 -3.5207 -2.6047 1.2735 -4.4262 -3.1645 1.264 -4.5345 -0.6066 1.6454 0.1385 0.8595 0.1415 -3.6547 3.642 -0.3455 2.8741 0.6684 1.9907 -0.0495 1.5556 -1.1351 0.9447 1.4717 -1.3031 1.3656 -2.6414 0.9842 1.7807 -1.6742 2.6791 -1.7593 1.5918 -0.6697 0.9009 -1.4625 -2.1408 -2.0389 0.0491 0.656 0.1216 -0.2674 0.0338 4.0254 1.0214 1.0945 2.3588 1.0679 0.9726 0.7781 -5.4239 3.2911 -4.9794 0.4125 0.2005 0.2146 4.9665 -2.4944 -0.2641
-0.51864 4.70574 -0.69862 Compute an estimated efficient portfolio with 5% volatility. What is the estimated return on this portfolio?
Solution
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Math Problem Analysis
Mathematical Concepts
Portfolio Optimization
Markowitz Portfolio Theory
Volatility
Covariance Matrix
Excess Returns
Formulas
Covariance Matrix: Σ = [[0.0056, -0.0020, 0.0037], [-0.0020, 0.0022, -0.0022], [0.0037, -0.0022, 0.0074]]
Volatility Constraint: x^T Σ x = (0.05)^2
Excess Returns: μ = [-1.52, 3.71, -1.70]
Portfolio Return: μ_p = x^T (μ - r_f)
Theorems
Markowitz Efficient Frontier
Quadratic Optimization
Suitable Grade Level
Undergraduate Finance/Economics
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