Update app.py

app.py

@@ -18,6 +18,56 @@ It simulates various market scenarios to analyze the dependencies between differ
 Users can assess potential outcomes in terms of best, worst, and mean case scenarios.
 """)
 
+with st.expander("Methodology", expanded=False):
+    st.markdown("## Simulating Market Drop Scenarios: Best, Worst, and Mean Cases")
+    #st.markdown("## Transforming Returns")
+    st.markdown("""
+    To prepare the returns for copula modeling, we transform them to a uniform distribution using quantile transformation. 
+    This is to ensure that the data fits within the range required by the copula model.
+    """)
+    st.latex(r"""
+    u_i = \frac{\text{rank}(R_i)}{n + 1}
+    """)
+
+    #st.markdown("## Fitting the Copula Model")
+    st.markdown("""
+    Next, we fit a multivariate Student-t copula to the transformed data. The copula model captures the dependencies between the stock returns to understand the joint behavior of the assets.
+    """)
+    st.latex(r"""
+    C_{\nu}(u_1, u_2, \ldots, u_d) = t_{\nu, \Sigma}(t_{\nu}^{-1}(u_1), t_{\nu}^{-1}(u_2), \ldots, t_{\nu}^{-1}(u_d))
+    """)
+
+    #st.markdown("## Simulating Scenarios")
+    st.markdown("""
+    Using the fitted copula model, we simulate a large number of return scenarios. This simulation helps us explore potential future outcomes 
+    and assess the portfolio's risk under various market conditions.
+    """)
+
+    #st.markdown("## Market Drop Scenarios")
+    st.markdown("""
+    We identify scenarios where the specified ticker drops by the given percentage. By analyzing these scenarios, we can evaluate how the portfolio performs under stress.
+    """)
+
+    #st.markdown("## Portfolio Returns")
+    st.markdown("""
+    For each identified scenario, we calculate the portfolio returns. The portfolio return is a weighted sum of the individual stock returns.
+    """)
+    st.latex(r"""
+    R_p = \sum_{i=1}^{n} w_i R_i
+    """)
+
+    #st.markdown("## Visualizing Results")
+    st.markdown("""
+    We visualize the simulated portfolio returns using histograms, cumulative distribution functions, and kernel density estimates. 
+    These visualizations help us understand the distribution and characteristics of potential returns.
+    """)
+
+    #st.markdown("## Portfolio Price Trajectory")
+    st.markdown("""
+    Finally, we visualize the portfolio's price trajectory under the worst-case, best-case, and mean scenarios. 
+    This helps in understanding the potential impact of market drops on the portfolio value.
+    """)
+
 st.sidebar.title("Input Parameters")
 
 # Sidebar: How to Use (closed by default)
@@ -62,58 +112,7 @@ run_button = st.sidebar.button("Run Analysis")
 if run_button and len(portfolio_tickers) == len(portfolio_weights):
 
     # Explanation of the Simulation and Copula Models
-    st.markdown("## Simulating Market Drop Scenarios: Best, Worst, and Mean Cases")
-    st.markdown("This section explores how the portfolio performs under simulated market drop scenarios using copula models.")
-
-    with st.expander("Methodology", expanded=False):
-        st.markdown("## Simulating Market Drop Scenarios: Best, Worst, and Mean Cases")
-        #st.markdown("## Transforming Returns")
-        st.markdown("""
-        To prepare the returns for copula modeling, we transform them to a uniform distribution using quantile transformation. 
-        This is to ensure that the data fits within the range required by the copula model.
-        """)
-        st.latex(r"""
-        u_i = \frac{\text{rank}(R_i)}{n + 1}
-        """)
-    
-        #st.markdown("## Fitting the Copula Model")
-        st.markdown("""
-        Next, we fit a multivariate Student-t copula to the transformed data. The copula model captures the dependencies between the stock returns to understand the joint behavior of the assets.
-        """)
-        st.latex(r"""
-        C_{\nu}(u_1, u_2, \ldots, u_d) = t_{\nu, \Sigma}(t_{\nu}^{-1}(u_1), t_{\nu}^{-1}(u_2), \ldots, t_{\nu}^{-1}(u_d))
-        """)
-    
-        #st.markdown("## Simulating Scenarios")
-        st.markdown("""
-        Using the fitted copula model, we simulate a large number of return scenarios. This simulation helps us explore potential future outcomes 
-        and assess the portfolio's risk under various market conditions.
-        """)
-    
-        #st.markdown("## Market Drop Scenarios")
-        st.markdown("""
-        We identify scenarios where the specified ticker drops by the given percentage. By analyzing these scenarios, we can evaluate how the portfolio performs under stress.
-        """)
-    
-        #st.markdown("## Portfolio Returns")
-        st.markdown("""
-        For each identified scenario, we calculate the portfolio returns. The portfolio return is a weighted sum of the individual stock returns.
-        """)
-        st.latex(r"""
-        R_p = \sum_{i=1}^{n} w_i R_i
-        """)
-    
-        #st.markdown("## Visualizing Results")
-        st.markdown("""
-        We visualize the simulated portfolio returns using histograms, cumulative distribution functions, and kernel density estimates. 
-        These visualizations help us understand the distribution and characteristics of potential returns.
-        """)
-    
-        #st.markdown("## Portfolio Price Trajectory")
-        st.markdown("""
-        Finally, we visualize the portfolio's price trajectory under the worst-case, best-case, and mean scenarios. 
-        This helps in understanding the potential impact of market drops on the portfolio value.
-        """)
+    #st.markdown("## Simulating Market Drop Scenarios: Best, Worst, and Mean Cases")
 
     # Define the portfolio and allocation
     portfolio_allocation = dict(zip(portfolio_tickers, portfolio_weights))