Update app.py

app.py

@@ -36,16 +36,22 @@ def plot_efficient_frontier(dataframes, names):
     max_sharpe_return = ret_arr[max_sharpe_idx]
     max_sharpe_volatility = vol_arr[max_sharpe_idx]
 
+    # Find the portfolio with the minimum volatility
+    min_vol_idx = np.argmin(vol_arr)
+    min_vol_return = ret_arr[min_vol_idx]
+    min_vol_volatility = vol_arr[min_vol_idx]
+
     st.write("Optimal Portfolio Weights:")
     optimal_weights = all_weights[max_sharpe_idx]
     for i, name in enumerate(names):
         st.write(f"{name}: {optimal_weights[i]:.4f}")
 
     fig, ax = plt.subplots()
-    scatter = ax.scatter(vol_arr, ret_arr, c=sharpe_arr, cmap='viridis')
+    scatter = ax.scatter(vol_arr, ret_arr, c=sharpe_arr, cmap='Blues')
     colorbar = plt.colorbar(scatter, ax=ax)
     colorbar.set_label('Sharpe Ratio')
-    ax.scatter(max_sharpe_volatility, max_sharpe_return, c='red', s=50, marker='*', label='Optimal Portfolio')
+    ax.scatter(max_sharpe_volatility, max_sharpe_return, c='red', s=200, marker='*', label='Optimal Portfolio - Max Sharpe Ratio')
+    ax.scatter(min_vol_volatility, min_vol_return, c='purple', s=150, edgecolors='black', marker='o', label='Minimum Volatility Portfolio')
     ax.set_xlabel('Volatility')
     ax.set_ylabel('Return')
     ax.set_title('Efficient Frontier')