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<h2 class="hd hd-2 unit-title">Portfolio Optimization Introduction</h2>
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<h2 class="hd hd-2 unit-title">Portfolio Optimization Introduction Exercise</h2>
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Portfolio Optimization Introduction Exercise
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<p>One of the objectives in portfolio optimization is to minimize risk. Which of the following is true?</p>
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A common measure of risk in portfolio optimization is the standard deviation of the portfolio.
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Recall that for Raytheon, the expected five year return was 50% and the standard deviation was 10%. According to the video, there is an approximately 2/3 chance that the 5-year return will be between 40% and 60%.
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<h2 class="hd hd-2 unit-title">Portfolio Optimization Model</h2>
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<h2 class="hd hd-2 unit-title">Portfolio Optimization Model Exercise</h2>
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PART A
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<p>Suppose that \(X\) and \(Y\) are random variables, and \(VAR(X) = 2.25 \times VAR(Y)\). Which one of the following is true:</p>
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\(SD(X) = SD(Y)\)
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\(SD(X) = (81/16) \times SD(Y)\)
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PART B
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<p>Now suppose instead the objective was to maximize the expected return subject to an upper bound on the total variance of the portfolio, \(V_{MAX}\).</p>
<p>Suppose further that returns from \(I, P, R\) are independent, and uncorrelated.</p>
<p>Which of the following is the correct constraint for the variance?</p>
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\( 225 I^2 + 324 P^2 + 100 R^2 + 300 IP -150 IR +120 PR \geq V_{MAX}\)
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\( 225 I^2 + 324 P^2 + 100 R^2 = V_{MAX}\)
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\( -225 I^2 - 324 P^2 - 100 R^2 + 300 IP -150 IR +120 PR \geq V_{MAX}\)
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\( 225 I + 324 P + 100 R \leq V_{MAX}\)
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\( 225 I^2 + 324 P^2 + 100 R^2 \leq V_{MAX}\)
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<h2 class="hd hd-2 unit-title">Portfolio Optimization Analysis</h2>
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<h2 class="hd hd-2 unit-title">Portfolio Optimization Analysis Exercise</h2>
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Portfolio Optimization Analysis Exercise
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<p>Suppose the RHS for the constraint on the minimum expected return is increased by 0.01.
What is the approximate effect on the objective value?</p>
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decrease by \( 1.8580\)
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increase by \( 1.8580\)
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decrease by \( 5.08\)
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decrease by \( 0.0508\)
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increase by \( 0.0508\)
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<h2 class="hd hd-2 unit-title">Convex Sets and Functions Exercise</h2>
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PART A
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<p>Decide whether each function is convex or not.</p>
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Convex
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PART B
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PART C
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Not convex
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Convex
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PART D
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Not convex
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Convex
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PART E
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Not convex
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<h2 class="hd hd-2 unit-title">Local and Global Optimization</h2>
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<h3 class="hd hd-2">Local and Global Optimization</h3>
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<h2 class="hd hd-2 unit-title">Local and Global Optimization Exercise</h2>
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Local and Global Optimization Exercise
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<p>Above is a plot of a nonlinear function \(f(x)\) defined over the interval \([a,b]\) .</p>
<p> The global minimum is located at \( x^4. \) Where are the local minima located?</p>
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<h2 class="hd hd-2 unit-title">Two Applications</h2>
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<h2 class="hd hd-2 unit-title">Two Applications Exercise</h2>
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PART A
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<p>What is the Euclidean distance from the point (8, 2) to the point (5, 6)?</p>
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PART B
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<p>Suppose that the travel cost per mile increased from $1 to $3 and the number of daily truck deliveries doubled for each sales center, and no other data changed. </p>
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<h2 class="hd hd-2 unit-title">SOCP Exercise</h2>
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SOCP Exercise
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<p>Let \(x = x_1, x_2, x_3, x_4.\) Let \(y = y_1, y_2, y_3\). Which of the following constraints are permitted as part of an SOCP? (Select all correct answers.)</p>
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\(||x||_2+||y||_2 \leq 1\)
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\(||x||_2 \geq 1\)
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\(||y||_2 + 10x_1 -5y_2 \leq 100\)
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\(7x_1 - 4y_2 =20\)
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<h2 class="hd hd-2 unit-title">NLP Guidelines</h2>
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