Problem 45884. Algorithmic Trading - 3 (short selling and leverage)

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It builds on earlier problems 45776 and 45860</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45776-algorithmic-trading-1-optimize-trading-strategy-simple-case\"><w:r><w:t>&lt;https://www.mathworks.com/matlabcentral/cody/problems/45776-algorithmic-trading-1-optimize-trading-strategy-simple-case</w:t></w:r></w:hyperlink><w:r><w:t>&gt;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45860-algorithmic-trading-2-optimize-calmar-ratio\"><w:r><w:t>&lt;https://www.mathworks.com/matlabcentral/cody/problems/45860-algorithmic-trading-2-optimize-calmar-ratio</w:t></w:r></w:hyperlink><w:r><w:t>&gt;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Goal</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Similar to problem 45860, allowing short-selling and leverage. Check</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.sec.gov/answers/shortsale.htm\"><w:r><w:t>&lt;https://www.sec.gov/answers/shortsale.htm</w:t></w:r></w:hyperlink><w:r><w:t>&gt; and</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Leverage_(finance)\"><w:r><w:t>&lt;https://en.wikipedia.org/wiki/Leverage_(finance</w:t></w:r></w:hyperlink><w:r><w:t>)&gt;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Use a fractional trading strategy, allowing short selling and leverage, as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Each day invest fraction</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>E</w:t></w:r><w:r><w:t> of the available funds, with</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>-2 &lt;= E &lt;= 3</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>This is referred as a limit of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>3x</w:t></w:r><w:r><w:t> leverage on long positions, and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>2x</w:t></w:r><w:r><w:t> leverage on short positions</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>You are given</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>P</w:t></w:r><w:r><w:t>, a [n x 1] vector of daily prices of the traded security, at market open (always positive)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>S</w:t></w:r><w:r><w:t>, a [n x 1] vector of trading signals, calculated just ahead of market open (can take any real value)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>These will serve both as training and test set</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Your function should return</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>t</w:t></w:r><w:r><w:t>, a scalar threshold that determines the state of the trading signal S</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>E</w:t></w:r><w:r><w:t>, a 2 x 1 vector of security exposures in each state, i.e.: invest a fraction E(1) of the available equity when</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>S(i) &lt; t</w:t></w:r><w:r><w:t>, and a fraction E(2) when</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>S(i) &gt;= t</w:t></w:r><w:r><w:t>, with</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>-2 &lt;= E(k) &lt;= 3</w:t></w:r><w:r><w:t>, for any k</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Hints</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>The array of daily returns can be calculated by R = D.*E(1+(S(1:end-1)&gt;=t))'</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

This is the third of a series of problems on quant trading. It builds on earlier problems 45776 and 45860<a href = "https://www.mathworks.com/matlabcentral/cody/problems/45776-algorithmic-trading-1-optimize-trading-strategy-simple-case">https://www.mathworks.com/matlabcentral/cody/problems/45776-algorithmic-trading-1-optimize-trading-strategy-simple-case</a><a href = "https://www.mathworks.com/matlabcentral/cody/problems/45860-algorithmic-trading-2-optimize-calmar-ratio">https://www.mathworks.com/matlabcentral/cody/problems/45860-algorithmic-trading-2-optimize-calmar-ratio</a>GoalSimilar to problem 45860, allowing short-selling and leverage.
Check <a href = "https://www.sec.gov/answers/shortsale.htm">https://www.sec.gov/answers/shortsale.htm</a> and <a href = "https://en.wikipedia.org/wiki/Leverage_(finance)">https://en.wikipedia.org/wiki/Leverage_(finance)</a>Use a fractional trading strategy, allowing short selling and leverage, as follows:<ul><li>Each day invest fraction E of the available funds, with -2 &lt;= E &lt;= 3</li><li>This is referred as a limit of 3x leverage on long positions, and 2x leverage on short positions</li></ul>You are given<ul><li>P, a [n x 1] vector of daily prices of the traded security, at market open (always positive)</li><li>S, a [n x 1] vector of trading signals, calculated just ahead of market open (can take any real value)</li><li>These will serve both as training and test set</li></ul>Your function should return<ul><li>t, a scalar threshold that determines the state of the trading signal S</li><li>E, a 2 x 1 vector of security exposures in each state, i.e.: invest a fraction E(1) of the available equity when <tt>S(i) &lt; t</tt>, and a fraction E(2) when <tt>S(i) &gt;= t</tt>, with <tt>-2 &lt;= E(k) &lt;= 3</tt>, for any k</li></ul>Hints<ul><li>The array of daily returns can be calculated by R = D.*E(1+(S(1:end-1)&gt;=t))'</li></ul>

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Problem 45884. Algorithmic Trading - 3 (short selling and leverage)

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