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<h2 class="hd hd-2 unit-title">Portfolio Weights</h2>
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Portfolio Weights
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Consider the following portfolio of stocks. Calculate the portfolio weights.
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<table><thead><tr class="header"><th style="text-align:center">Stock</th><th style="text-align:center">Number of shares</th><th style="text-align:center">Price per share</th></tr></thead><tbody><tr class="odd"><td style="text-align:center">A</td><td style="text-align:center">200</td><td style="text-align:center">$50</td></tr><tr><td style="text-align:center">B</td><td style="text-align:center">1,000</td><td style="text-align:center">$60</td></tr><tr><td style="text-align:center">C</td><td style="text-align:center">750</td><td style="text-align:center">$40</td></tr></tbody></table>
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<h3 class="hd hd-2">Portfolio Weights </h3>
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<h2 class="hd hd-2 unit-title">Three Risky Assets</h2>
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Three Risky Assets
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</style><table><tr><th style="text-align:center"/><th style="text-align:center">Expected Return</th><th style="text-align:center">Standard Deviation</th><th style="text-align:center" colspan="3">Correlations</th></tr><tr><td style="text-align:center"/><td style="text-align:center"/><td style="text-align:center"/><td style="text-align:center;border-bottom:1px solid">A</td><td style="text-align:center;border-bottom:1px solid">B</td><td style="text-align:center;border-bottom:1px solid">C</td></tr><tr><td style="text-align:center">A</td><td style="text-align:center">10%</td><td style="text-align:center">20%</td><td style="text-align:center">1</td><td style="text-align:center">0.2</td><td style="text-align:center">0.1</td></tr><tr><td style="text-align:center">B</td><td style="text-align:center">12%</td><td style="text-align:center">30%</td><td style="text-align:center">0.2</td><td style="text-align:center">1</td><td style="text-align:center">0.4</td></tr><tr><td style="text-align:center">C</td><td style="text-align:center">8%</td><td style="text-align:center">25%</td><td style="text-align:center">0.1</td><td style="text-align:center">0.4</td><td style="text-align:center">1</td></tr></table>
Calculate the expected return and standard deviation of a portfolio of stocks A, B and C. Assume an equal investment in each stock.
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<h2 class="hd hd-2 unit-title">Megafund Example</h2>
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Megafund Example
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Consider a sample of 150 cancer research projects, and assume for simplicity that each project has an expected annual return of 10% and standard deviation of 400% (i.e., with high probability the project is unsuccessful, but a small fraction of projects become blockbuster drugs). If the correlation amongst projects is 0% (i.e., they are uncorrelated), what is the expected value and standard deviation of the portfolio's return where you invest the same amount in each project?
<p><p style="display:inline">\(E[R]=\)</p><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_9ef2dfd8fe354501b0a5b5f055c3cf8b_2_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">\(SD(R)=\)</p><div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_9ef2dfd8fe354501b0a5b5f055c3cf8b_3_1" class=" capa_inputtype inline textline">
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<h3 class="hd hd-2">Megafund Example </h3>
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<h2 class="hd hd-2 unit-title">CAPM Example</h2>
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CAPM Example
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Stock 1 has a standard deviation of 20%, while stock 2 has a standard deviation of 32%. Their correlation with the market portfolio is 0.4 and 0.6, respectively. If the market portfolio has an expected return of 9% and standard deviation of 16%, what is the expected return of a portfolio that has a 50% weight on stock 1, and a 50% weight on stock 2? Assume the risk-free rate is 3%.
<p><p style="display:inline">\(E[R_p] = \)</p><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_cc82cf985ada4fe7abdde8a93df4a919_2_1" class=" capa_inputtype inline textline">
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<h3 class="hd hd-2">CAPM Example </h3>
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