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class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="Breadcrumbs"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="Home page" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_OVgt"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/sdk/reference"><span itemprop="name">SDK Reference</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/sdk/reference/portfolio"><span itemprop="name">portfolio</span></a><meta itemprop="position" content="2"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/sdk/reference/portfolio/po"><span itemprop="name">po</span></a><meta itemprop="position" content="3"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">herc</span><meta itemprop="position" content="4"></li></ul></nav><div class="theme-doc-markdown markdown"><h1>herc</h1><p>Optimize with Hierarchical Equal Risk Contribution (HERC) method.</p><p>Source Code: [<a href="https://github.com/OpenBB-finance/OpenBBTerminal/tree/main/openbb_terminal/portfolio/portfolio_optimization/po_model.py#L1793" target="_blank" rel="noopener noreferrer">link</a>]</p><div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code style="white-space:pre-wrap;overflow-wrap:anywhere" class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">portfolio</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">po</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">herc</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">portfolio_engine</span><span class="token punctuation" style="color:rgb(212, 212, 212)">:</span><span class="token plain"> portfolio_optimization</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">po_engine</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">PoEngine </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> </span><span class="token boolean">None</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> kwargs</span><span class="token punctuation" style="color:rgb(212, 212, 212)">:</span><span class="token plain"> Any</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 24"><path d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><hr><h2 class="anchor anchorWithStickyNavbar_LWe7" id="parameters">Parameters<a class="hash-link" href="#parameters" title="Direct link to heading">​</a></h2><table><thead><tr><th>Name</th><th>Type</th><th>Description</th><th>Default</th><th>Optional</th></tr></thead><tbody><tr><td>portfolio_engine</td><td>PoEngine</td><td>Portfolio optimization engine, by default None<br>Use <code>portfolio.po.load</code> to load a portfolio engine</td><td>None</td><td>True</td></tr><tr><td>interval</td><td>str</td><td>Interval to get data, by default &#x27;3y&#x27;</td><td>None</td><td>True</td></tr><tr><td>start_date</td><td>str</td><td>If not using interval, start date string (YYYY-MM-DD), by default &quot;&quot;</td><td>None</td><td>True</td></tr><tr><td>end_date</td><td>str</td><td>If not using interval, end date string (YYYY-MM-DD). If empty use last weekday, by default &quot;&quot;</td><td>None</td><td>True</td></tr><tr><td>log_returns</td><td>bool</td><td>If True use log returns, else arithmetic returns, by default False</td><td>None</td><td>True</td></tr><tr><td>freq</td><td>str</td><td>Frequency of returns, by default &#x27;D&#x27;. Options: &#x27;D&#x27; for daily, &#x27;W&#x27; for weekly, &#x27;M&#x27; for monthly</td><td>None</td><td>True</td></tr><tr><td>maxnan</td><td>float</td><td>Maximum percentage of NaNs allowed in the data, by default 0.05</td><td>None</td><td>True</td></tr><tr><td>threshold</td><td>float</td><td>Value used to replace outliers that are higher than threshold, by default 0.0</td><td>None</td><td>True</td></tr><tr><td>method</td><td>str</td><td>Method used to fill nan values, by default &#x27;time&#x27;<br>For more information see <code>interpolate &lt;https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.interpolate.html&gt;</code>__.</td><td>None</td><td>True</td></tr><tr><td>value</td><td>float</td><td>Amount to allocate to portfolio in long positions, by default 1.0</td><td>None</td><td>True</td></tr><tr><td>objective</td><td>str</td><td>Objective function of the optimization model, by default &#x27;MinRisk&#x27;<br>Possible values are:<br><br>- &#x27;MinRisk&#x27;: Minimize the selected risk measure.<br>- &#x27;Utility&#x27;: Maximize the risk averse utility function.<br>- &#x27;Sharpe&#x27;: Maximize the risk adjusted return ratio based on the selected risk measure.<br>- &#x27;MaxRet&#x27;: Maximize the expected return of the portfolio.</td><td>None</td><td>True</td></tr><tr><td>risk_measure</td><td>str</td><td>The risk measure used to optimize the portfolio, by default &#x27;MV&#x27;<br>If model is &#x27;NCO&#x27;, the risk measures available depends on the objective function.<br>Possible values are:<br><br>- &#x27;MV&#x27;: Variance.<br>- &#x27;MAD&#x27;: Mean Absolute Deviation.<br>- &#x27;MSV&#x27;: Semi Standard Deviation.<br>- &#x27;FLPM&#x27;: First Lower Partial Moment (Omega Ratio).<br>- &#x27;SLPM&#x27;: Second Lower Partial Moment (Sortino Ratio).<br>- &#x27;VaR&#x27;: Value at Risk.<br>- &#x27;CVaR&#x27;: Conditional Value at Risk.<br>- &#x27;TG&#x27;: Tail Gini.<br>- &#x27;EVaR&#x27;: Entropic Value at Risk.<br>- &#x27;WR&#x27;: Worst Realization (Minimax).<br>- &#x27;RG&#x27;: Range of returns.<br>- &#x27;CVRG&#x27;: CVaR range of returns.<br>- &#x27;TGRG&#x27;: Tail Gini range of returns.<br>- &#x27;MDD&#x27;: Maximum Drawdown of uncompounded cumulative returns (Calmar Ratio).<br>- &#x27;ADD&#x27;: Average Drawdown of uncompounded cumulative returns.<br>- &#x27;DaR&#x27;: Drawdown at Risk of uncompounded cumulative returns.<br>- &#x27;CDaR&#x27;: Conditional Drawdown at Risk of uncompounded cumulative returns.<br>- &#x27;EDaR&#x27;: Entropic Drawdown at Risk of uncompounded cumulative returns.<br>- &#x27;UCI&#x27;: Ulcer Index of uncompounded cumulative returns.<br>- &#x27;MDD_Rel&#x27;: Maximum Drawdown of compounded cumulative returns (Calmar Ratio).<br>- &#x27;ADD_Rel&#x27;: Average Drawdown of compounded cumulative returns.<br>- &#x27;DaR_Rel&#x27;: Drawdown at Risk of compounded cumulative returns.<br>- &#x27;CDaR_Rel&#x27;: Conditional Drawdown at Risk of compounded cumulative returns.<br>- &#x27;EDaR_Rel&#x27;: Entropic Drawdown at Risk of compounded cumulative returns.<br>- &#x27;UCI_Rel&#x27;: Ulcer Index of compounded cumulative returns.</td><td>None</td><td>True</td></tr><tr><td>risk_free_rate</td><td>float</td><td>Risk free rate, annualized. Used for &#x27;FLPM&#x27; and &#x27;SLPM&#x27; and Sharpe objective function, by default 0.0</td><td>None</td><td>True</td></tr><tr><td>risk_aversion</td><td>float</td><td>Risk aversion factor of the &#x27;Utility&#x27; objective function, by default 1.0</td><td>None</td><td>True</td></tr><tr><td>alpha</td><td>float</td><td>Significance level of VaR, CVaR, EDaR, DaR, CDaR, EDaR, Tail Gini of losses, by default 0.05</td><td>None</td><td>True</td></tr><tr><td>a_sim</td><td>float</td><td>Number of CVaRs used to approximate Tail Gini of losses, by default 100</td><td>None</td><td>True</td></tr><tr><td>beta</td><td>float</td><td>Significance level of CVaR and Tail Gini of gains. If None it duplicates alpha value, by default None</td><td>None</td><td>True</td></tr><tr><td>b_sim</td><td>float</td><td>Number of CVaRs used to approximate Tail Gini of gains. If None it duplicates a_sim value, by default None</td><td>None</td><td>True</td></tr><tr><td>covariance</td><td>str</td><td>The method used to estimate the covariance matrix, by default &#x27;hist&#x27;<br>Possible values are:<br><br>- &#x27;hist&#x27;: use historical estimates.<br>- &#x27;ewma1&#x27;: use ewma with adjust=True. For more information see <code>EWM &lt;https://pandas.pydata.org/pandas-docs/stable/user_guide/window.html#exponentially-weighted-window&gt;</code><strong>.<br>- &#x27;ewma2&#x27;: use ewma with adjust=False. For more information see <code>EWM &lt;https://pandas.pydata.org/pandas-docs/stable/user_guide/window.html#exponentially-weighted-window&gt;</code></strong>.<br>- &#x27;ledoit&#x27;: use the Ledoit and Wolf Shrinkage method.<br>- &#x27;oas&#x27;: use the Oracle Approximation Shrinkage method.<br>- &#x27;shrunk&#x27;: use the basic Shrunk Covariance method.<br>- &#x27;gl&#x27;: use the basic Graphical Lasso Covariance method.<br>- &#x27;jlogo&#x27;: use the j-LoGo Covariance method. For more information see: <code>a-jLogo</code>.<br>- &#x27;fixed&#x27;: denoise using fixed method. For more information see chapter 2 of <code>a-MLforAM</code>.<br>- &#x27;spectral&#x27;: denoise using spectral method. For more information see chapter 2 of <code>a-MLforAM</code>.<br>- &#x27;shrink&#x27;: denoise using shrink method. For more information see chapter 2 of <code>a-MLforAM</code>.</td><td>None</td><td>True</td></tr><tr><td>d_ewma</td><td>float</td><td>The smoothing factor of ewma methods, by default 0.94</td><td>None</td><td>True</td></tr><tr><td>codependence</td><td>str</td><td>The codependence or similarity matrix used to build the distance<br>metric and clusters. The default is &#x27;pearson&#x27;. Possible values are:<br><br>- &#x27;pearson&#x27;: pearson correlation matrix. Distance formula:<br> .. math:: D<em>{i,j} = \sqrt{0.5(1-\rho^{pearson}</em>{i,j})}<br>- &#x27;spearman&#x27;: spearman correlation matrix. Distance formula:<br> .. math:: D<em>{i,j} = \sqrt{0.5(1-\rho^{spearman}</em>{i,j})}<br>- &#x27;abs<em>pearson&#x27;: absolute value pearson correlation matrix. Distance formula:<br> .. math:: D</em>{i,j} = \sqrt{(1-</td><td>\rho^{pearson}_{i,j}</td><td>)}<br>- &#x27;abs<em>spearman&#x27;: absolute value spearman correlation matrix. Distance formula:<br> .. math:: D</em>{i,j} = \sqrt{(1-</td></tr><tr><td>linkage</td><td>str</td><td>Linkage method of hierarchical clustering. For more information see <code>linkage &lt;https://docs.scipy.org/doc/scipy/reference/generated/scipy.&lt;br/&gt;cluster.hierarchy.linkage.html?highlight=linkage#scipy.cluster.hierarchy.linkage&gt;</code>__.<br>The default is &#x27;single&#x27;. Possible values are:<br><br>- &#x27;single&#x27;.<br>- &#x27;complete&#x27;.<br>- &#x27;average&#x27;.<br>- &#x27;weighted&#x27;.<br>- &#x27;centroid&#x27;.<br>- &#x27;median&#x27;.<br>- &#x27;ward&#x27;.<br>- &#x27;dbht&#x27;: Direct Bubble Hierarchical Tree.</td><td>None</td><td>True</td></tr><tr><td>k</td><td>int</td><td>Number of clusters. This value is took instead of the optimal number<br>of clusters calculated with the two difference gap statistic, by default None</td><td>None</td><td>True</td></tr><tr><td>max_k</td><td>int</td><td>Max number of clusters used by the two difference gap statistic<br>to find the optimal number of clusters, by default 10</td><td>None</td><td>True</td></tr><tr><td>bins_info</td><td>str</td><td>Number of bins used to calculate variation of information, by default &#x27;KN&#x27;.<br>Possible values are:<br><br>- &#x27;KN&#x27;: Knuth&#x27;s choice method. For more information see <code>knuth_bin_width &lt;https://docs.astropy.org/en/stable/api/astropy.stats.knuth_bin_width.html&gt;</code><strong>.<br>- &#x27;FD&#x27;: Freedman–Diaconis&#x27; choice method. For more information see <code>freedman_bin_width &lt;https://docs.astropy.org/en/stable/api/astropy.stats.freedman_bin_width.html&gt;</code></strong>.<br>- &#x27;SC&#x27;: Scotts&#x27; choice method. For more information see <code>scott_bin_width &lt;https://docs.astropy.org/en/stable/api/astropy.stats.scott_bin_width.html&gt;</code>__.<br>- &#x27;HGR&#x27;: Hacine-Gharbi and Ravier&#x27; choice method.</td><td>None</td><td>True</td></tr><tr><td>alpha_tail</td><td>float</td><td>Significance level for lower tail dependence index, by default 0.05</td><td>None</td><td>True</td></tr><tr><td>leaf_order</td><td>bool</td><td>Indicates if the cluster are ordered so that the distance between<br>successive leaves is minimal, by default True</td><td>None</td><td>True</td></tr></tbody></table><hr><h2 class="anchor anchorWithStickyNavbar_LWe7" id="returns">Returns<a class="hash-link" href="#returns" title="Direct link to heading">​</a></h2><table><thead><tr><th>Type</th><th>Description</th></tr></thead><tbody><tr><td>Tuple<!-- -->[pd.DataFrame, Dict]</td><td>Tuple with weights and performance dictionary</td></tr></tbody></table><hr><h2 class="anchor anchorWithStickyNavbar_LWe7" id="examples">Examples<a class="hash-link" href="#examples" title="Direct link to heading">​</a></h2><div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token keyword" style="color:rgb(86, 156, 214)">from</span><span class="token plain"> openbb_terminal</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">sdk </span><span class="token keyword" style="color:rgb(86, 156, 214)">import</span><span class="token plain"> openbb</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">d </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(212, 212, 212)">{</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 24"><path d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-text codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">&quot;SECTOR&quot;: {</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;AAPL&quot;: &quot;INFORMATION TECHNOLOGY&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;MSFT&quot;: &quot;INFORMATION TECHNOLOGY&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;AMZN&quot;: &quot;CONSUMER DISCRETIONARY&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> },</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;CURRENCY&quot;: {</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;AAPL&quot;: &quot;USD&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;MSFT&quot;: &quot;USD&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;AMZN&quot;: &quot;USD&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> },</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;CURRENT_INVESTED_AMOUNT&quot;: {</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;AAPL&quot;: &quot;100000.0&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;MSFT&quot;: &quot;200000.0&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> &quot;AMZN&quot;: &quot;300000.0&quot;,</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> },</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> }</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 24"><path d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">p </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">portfolio</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">po</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">load</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">symbols_categories</span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain">d</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">weights</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> performance </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">portfolio</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">po</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">herc</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">portfolio_engine</span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain">p</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg class="copyButtonIcon_y97N" viewBox="0 0 24 24"><path d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg class="copyButtonSuccessIcon_LjdS" viewBox="0 0 24 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