### Extracted Code Segments

#### **File: `portfolio_optimizer.py`**

#### **Segment 1: `display_portfolio_vs_benchmark` Function**
- **Relevance:** This function is directly related to the problem described, as it contains the line causing the `ValueError: Unknown format code 'f' for object of type 'str'`.
- **Context:** The function is responsible for displaying the backtest results of a portfolio versus a benchmark. It formats various metrics, including the "Max Drawdown".

```python
def display_portfolio_vs_benchmark(results):
    """
    Enhanced display function for Portfolio vs Benchmark comparison with improved visualizations and UX.
    """
    # Extract data from results
    returns = results['returns']
    cum_returns = results['cum_returns']
    weights = results['weights']
    price_data = results['price_data']
    available_selected = results['available_selected']
    metrics = results['metrics']
    benchmark_metrics = results['benchmark_metrics']
    benchmark_returns = results['benchmark_returns']
    benchmark_cum_returns = results['benchmark_cum_returns']

    # Define a consistent theme for all plots
    THEMES = {
        'plotly_dark': 'plotly_dark',
        'plotly_light': 'plotly_white'
    }
    selected_theme = THEMES.get('plotly_light')  # Change as needed

    # Create tabs for better organization
    main_tab, metrics_tab, risk_tab, analysis_tab, insights_tab = st.tabs([
        "📈 Main Charts", "📊 Performance Metrics", "🎯 Risk Analysis", "🔍 Deep Analysis", "🧠 Metric-Based Insights"
    ])

    with main_tab:
        st.header("🔹 Portfolio vs Benchmark Overview")
        col1, col2 = st.columns([2, 1])
        with col1:
            st.subheader("Portfolio Composition")
            fig_composition = px.pie(
                values=weights,
                names=price_data.columns,
                title="Current Portfolio Allocation",
                template=selected_theme,
                hole=0.4
            )
            fig_composition.update_traces(textinfo='percent+label')
            st.plotly_chart(fig_composition, use_container_width=True)

        with col2:
            st.subheader("Key Performance Indicators")
            metrics_display = {
                "Total Return": f"{(cum_returns.iloc[-1] - 1) * 100:.2f}%",
                "Annualized Return": f"{metrics.get('Annualized Return (CAGR)', 0) * 100:.2f}%" if metrics.get('Annualized Return (CAGR)', 0) else "N/A",
                "Sharpe Ratio": metrics.get('Sharpe Ratio', 'N/A'),
                "Max Drawdown": f"{metrics.get('Maximum Drawdown', 0):.2f}%"  # This line is causing the error
            }
            for metric, value in metrics_display.items():
                st.metric(metric, value)

        # Enhanced Cumulative Returns Plot with Interactive Features
        st.subheader("Cumulative Returns Comparison")
        fig_returns = go.Figure()
        fig_returns.add_trace(go.Scatter(
            x=cum_returns.index,
            y=cum_returns,
            name="Portfolio",
            line=dict(color='cyan', width=2),
            hovertemplate='%{y:.2f}'
        ))
        fig_returns.add_trace(go.Scatter(
            x=benchmark_cum_returns.index,
            y=benchmark_cum_returns,
            name="Benchmark",
            line=dict(color='orange', width=2, dash='dash'),
            hovertemplate='%{y:.2f}'
        ))
        fig_returns.update_layout(
            template=selected_theme,
            hovermode='x unified',
            height=500,
            xaxis_title='Date',
            yaxis_title='Cumulative Returns',
            legend=dict(x=0.01, y=0.99)
        )
        st.plotly_chart(fig_returns, use_container_width=True)

        # Interactive Summary Recommendations
        create_summary_recommendations('overview', metrics=metrics)
```

#### **Segment 2: `calculate_metrics` Function**
- **Relevance:** This function calculates various performance metrics, including the "Max Drawdown". The value returned by this function is used in the `display_portfolio_vs_benchmark` function.
- **Context:** The function ensures that metrics are calculated correctly and handles cases where data might be missing or invalid.

```python
def calculate_metrics(
    returns: pd.Series, 
    cum_returns: pd.Series, 
    rf: float = 0.02, 
    benchmark_returns: pd.Series = None
) -> dict:
    metrics = {}
    metrics['Start Balance'] = "$10,000.00"
    if not cum_returns.empty and not returns.empty:
        end_balance = 10000 * cum_returns.iloc[-1]
        years = (cum_returns.index[-1] - cum_returns.index[0]).days / 365.25
        try:
            cagr = (end_balance / 10000) ** (1 / years) - 1 if years > 0 else np.nan
        except:
            cagr = np.nan
        metrics.update({
            'End Balance': end_balance if not np.isnan(end_balance) else np.nan,
            'Annualized Return (CAGR)': cagr if not np.isnan(cagr) else np.nan,
            'Best Year': f"{returns.resample('Y').apply(lambda x: (1 + x).prod() - 1).max() * 100:.2f}%" if not returns.empty else "N/A",
            'Worst Year': f"{returns.resample('Y').apply(lambda x: (1 + x).prod() - 1).min() * 100:.2f}%" if not returns.empty else "N/A",
            'Arithmetic Mean (Monthly)': returns.mean() * 100,
            'Arithmetic Mean (Annualized)': returns.mean() * 252 * 100,
            'Geometric Mean (Monthly)': (np.exp(np.log1p(returns).mean()) - 1) if not returns.empty else "N/A",
            'Geometric Mean (Annualized)': (np.exp(np.log1p(returns).mean() * 252) - 1) if not returns.empty else "N/A",
            'Standard Deviation (Monthly)': returns.std() * 100,
            'Standard Deviation (Annualized)': returns.std() * np.sqrt(252) * 100,
            'Downside Deviation (Monthly)': f"{returns[returns < 0].std() * 100:.2f}%" if not returns.empty else "N/A",
            'Maximum Drawdown': f"{drawdown(cum_returns) * 100:.2f}%" if not cum_returns.empty else "N/A",  # This line calculates the "Max Drawdown"
            'Sharpe Ratio': f"{calculate_sharpe_ratio(returns, rf):.2f}" if not cum_returns.empty else "N/A",
            'Sortino Ratio': f"{calculate_sortino_ratio(returns, rf):.2f}" if not cum_returns.empty else "N/A",
            'Gain/Loss Ratio': f"{calculate_gain_loss_ratio(returns):.2f}" if not cum_returns.empty else "N/A",
            'Skewness': f"{skew(returns):.2f}" if not returns.empty else "N/A",
            'Excess Kurtosis': f"{kurtosis(returns):.2f}" if not returns.empty else "N/A",
            'Safe Withdrawal Rate': f"{calculate_safe_withdrawal_rate(returns):.4f}%" if not returns.empty else "N/A",
            'Perpetual Withdrawal Rate': f"{calculate_perpetual_withdrawal_rate(returns):.4f}%" if not returns.empty else "N/A",
            'Positive Periods': calculate_positive_periods(returns) if not returns.empty else "N/A"
        })
    else:
        # Assign "N/A" to all metrics if cum_returns or returns are empty
        metrics.update({
            'End Balance': "N/A",
            'Annualized Return (CAGR)': "N/A",
            'Best Year': "N/A",
            'Worst Year': "N/A",
            'Arithmetic Mean (Monthly)': "N/A",
            'Arithmetic Mean (Annualized)': "N/A",
            'Geometric Mean (Monthly)': "N/A",
            'Geometric Mean (Annualized)': "N/A",
            'Standard Deviation (Monthly)': "N/A",
            'Standard Deviation (Annualized)': "N/A",
            'Downside Deviation (Monthly)': "N/A",
            'Maximum Drawdown': "N/A",
            'Sharpe Ratio': "N/A",
            'Sortino Ratio': "N/A",
            'Gain/Loss Ratio': "N/A",
            'Skewness': "N/A",
            'Excess Kurtosis': "N/A",
            'Safe Withdrawal Rate': "N/A",
            'Perpetual Withdrawal Rate': "N/A",
            'Positive Periods': "N/A"
        })
    
    if benchmark_returns is not None and not benchmark_returns.empty:
        # Calculate benchmark-relative metrics
        correlation = returns.corr(benchmark_returns)
        beta = calculate_beta(returns, benchmark_returns)
        alpha = calculate_alpha(returns, benchmark_returns, rf)
        r2 = calculate_r_squared(returns, benchmark_returns)
        treynor = calculate_treynor_ratio(returns, benchmark_returns, rf)
        calmar = calculate_calmar_ratio(returns, cum_returns)
        m2 = calculate_modigliani_miller(returns, benchmark_returns, rf)
        info_ratio = calculate_information_ratio(returns, benchmark_returns)
        tracking_error = calculate_tracking_error(returns, benchmark_returns)
        active_return = calculate_active_return(returns, benchmark_returns)
        upside_capture = calculate_capture_ratio(returns, benchmark_returns, upside=True)
        downside_capture = calculate_capture_ratio(returns, benchmark_returns, upside=False)
        
        metrics.update({
            'Benchmark Correlation': f"{correlation:.2f}" if not np.isnan(correlation) else "N/A",
            'Beta': f"{beta:.2f}" if not np.isnan(beta) else "N/A",
            'Alpha (annualized)': f"{alpha * 100:.2f}%" if not np.isnan(alpha) else "N/A",
            'R2': f"{r2 * 100:.2f}%" if not np.isnan(r2) else "N/A",
            'Treynor Ratio': f"{treynor:.2f}" if not np.isnan(treynor) else "N/A",
            'Calmar Ratio': f"{calmar:.2f}" if not np.isnan(calmar) else "N/A",
            'Modigliani–Modigliani Measure': f"{m2 * 100:.2f}%" if not np.isnan(m2) else "N/A",
            'Information Ratio': f"{info_ratio:.2f}" if not np.isnan(info_ratio) else "N/A",
            'Tracking Error': f"{tracking_error * 100:.2f}%" if not np.isnan(tracking_error) else "N/A",
            'Active Return': f"{active_return:.2f}%" if not np.isnan(active_return) else "N/A",
            'Upside Capture Ratio': f"{upside_capture:.2f}%" if not np.isnan(upside_capture) else "N/A",
            'Downside Capture Ratio': f"{downside_capture:.2f}%" if not np.isnan(downside_capture) else "N/A"
        })
    else:
        # Assign "N/A" to all benchmark metrics
        metrics.update({
            'Benchmark Correlation': "N/A",
            'Beta': "N/A",
            'Alpha (annualized)': "N/A",
            'R2': "N/A",
            'Treynor Ratio': "N/A",
            'Calmar Ratio': "N/A",
            'Modigliani–Modigliani Measure': "N/A",
            'Information Ratio': "N/A",
            'Tracking Error': "N/A",
            'Active Return': "N/A",
            'Upside Capture Ratio': "N/A",
            'Downside Capture Ratio': "N/A"
        })
    
    return metrics
```

### Summary
- **Segment 1 (`display_portfolio_vs_benchmark`)**: This function is where the error occurs. Specifically, the line `"Max Drawdown": f"{metrics.get('Maximum Drawdown', 0):.2f}%"` is causing the `ValueError`. This line attempts to format the "Max Drawdown" metric, which is retrieved from the `metrics` dictionary.
- **Segment 2 (`calculate_metrics`)**: This function calculates the "Max Drawdown" metric and other performance metrics. The value returned by this function is used in the `display_portfolio_vs_benchmark` function.

### Key Points
- The error is likely due to the `metrics.get('Maximum Drawdown', 0)` returning a string instead of a numeric value, which cannot be formatted using `:.2f`.
- The `calculate_metrics` function should ensure that the "Max Drawdown" metric is always a numeric value (e.g., a float) to avoid this error.

problem: ValueError: Unknown format code 'f' for object of type 'str'
Traceback:
File "/usr/local/lib/python3.10/dist-packages/streamlit/runtime/scriptrunner/exec_code.py", line 88, in exec_func_with_error_handling
    result = func()
File "/usr/local/lib/python3.10/dist-packages/streamlit/runtime/scriptrunner/script_runner.py", line 579, in code_to_exec
    exec(code, module.__dict__)
File "/content/portfolio_optimizer.py", line 4434, in <module>
    display_backtest_results(result["backtest_results"], comparison_type, portfolio1)
File "/content/portfolio_optimizer.py", line 609, in display_backtest_results
    display_portfolio_vs_benchmark(results)
File "/content/portfolio_optimizer.py", line 662, in display_portfolio_vs_benchmark
    "Max Drawdown": f"{metrics.get('Maximum Drawdown', 0):.2f}%"

if the segments code need update, please return the full updated segments code, no need import or other stuff, only the full version of the updated segment