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<h2 class="hd hd-2 unit-title">Returns</h2>
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<h2 class="hd hd-2 unit-title">Exercise: Returns</h2>
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Exercise: Returns
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You have invested $10 million today \(I_0\) in a project that will yield the following returns over the next five years: </p>
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<th style="text-align:left">Year</th>
<th style="text-align:center">1</th>
<th style="text-align:center">2</th>
<th style="text-align:center">3</th>
<th style="text-align:center">4</th>
<th style="text-align:center">5</th>
</tr>
<tr>
<td style="text-align:left">
Returns</td>
<td style="text-align:center">
10% </td>
<td style="text-align:center">
20% </td>
<td style="text-align:center">
25% </td>
<td style="text-align:center">
17% </td>
<td style="text-align:center">
12% </td>
</tr>
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<p>
What are the net return (\(R^{\text{net}}\)) and the annualized return (\(R^{\text{ann}}\)) for this project? (<i>Note</i>: Your answers should be numbers in percentage form. Do not enter '%'.)</p>
<p><p style="display:inline"/> [mathjaxinline]R^{\text{net}}=[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_050f697205de46f48d1cac8d808f2e9e_2_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline"/> [mathjaxinline]R^{\text{ann}}=[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_050f697205de46f48d1cac8d808f2e9e_3_1" class=" capa_inputtype inline textline">
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<h2 class="hd hd-2 unit-title">Risk and Reward</h2>
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Exercise: Sharpe Ratio
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<p>Based on the table below, what is the Sharpe Ratio (\(SR\)) for small stocks? </p>
<p>Note: use the average return on T-Bills as the risk-free rate.</p>
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<img src="/assets/courseware/v1/286a385fc46d7c18f225e7125c305a70/asset-v1:MITx+15.480x+3T2021+type@asset+block/SharpeRatio.png" width="100%"/>
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<p><p style="display:inline"/>\(SR = \) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_617cf67275eb4bcab05527510306c92c_2_1" class=" capa_inputtype inline textline">
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<h2 class="hd hd-2 unit-title">What Does Risk Look Like?</h2>
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<h2 class="hd hd-2 unit-title">Exercise: What Does Risk Look Like?</h2>
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Exercise: What Does Risk Look Like?
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<p>Historically, large stocks have had an average return of 10.0% with a volatility of 20.0%. If you assume that large stock returns have a normal distribution with mean 10.0% and standard deviation 20.0%, what is the probability of observing a return less than &#8211;10%? (<i>Note</i>: Your answer should be a number in percentage form. Do not enter '%'.)</p>
<p>Hint: How many standard deviations away from the mean is &#8211;10%?</p>
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<img src="/assets/courseware/v1/9e7c7e64609a03b00de6c419990b6101/asset-v1:MITx+15.480x+3T2021+type@asset+block/Standard_deviation_diagram.png" width="50%"/>
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