# How do you measure portfolio performance?

Learn from Mathematical Finance

Measuring portfolio performance is crucial for investors aiming to assess the effectiveness of their investment strategies. Here’s a detailed guide on how to evaluate portfolio performance:

Key Metrics for Portfolio Performance Evaluation

1. Total Return:

- Definition: The percentage increase in the value of the portfolio over a specified period.

- Calculation: \(\text{Total Return} = \frac{\text{Ending Value} - \text{Beginning Value} + \text{Dividends}}{\text{Beginning Value}} \times 100\%\)

- Use: Provides a straightforward measure of how much value the portfolio has gained or lost.

2. Annualized Return:

- Definition: The average yearly return, taking compounding into account.

- Calculation: Use the formula \(\text{Annualized Return} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1\), where \(n\) is the number of years.

- Use: Allows comparison of returns over different periods by standardizing them on an annual basis.

3. Risk-Adjusted Return:

- Definition: Measures returns relative to the risk taken.

- Key Ratios:

- Sharpe Ratio: \(\text{Sharpe Ratio} = \frac{\text{Portfolio Return} - \text{Risk-Free Rate}}{\text{Standard Deviation}}\)

- Sortino Ratio: \(\text{Sortino Ratio} = \frac{\text{Portfolio Return} - \text{Target Return}}{\text{Downside Deviation}}\)

- Use: Helps in evaluating whether the returns justify the risks taken.

4. Alpha:

- Definition: Measures the excess return of the portfolio compared to a benchmark.

- Calculation: \(\text{Alpha} = \text{Actual Return} - (\text{Risk-Free Rate} + \text{Beta} \times (\text{Benchmark Return} - \text{Risk-Free Rate}))\)

- Use: Indicates the portfolio’s performance relative to its expected return based on market risk.

5. Beta:

- Definition: Measures the portfolio’s volatility relative to a benchmark index.

- Calculation: Beta is derived from the correlation between the portfolio’s returns and the benchmark’s returns.

- Use: Assesses how much the portfolio’s value fluctuates in relation to market movements.

6. Standard Deviation:

- Definition: Measures the dispersion of portfolio returns from the average return.

- Calculation: Compute the square root of the variance of portfolio returns.

- Use: Indicates the level of volatility or risk associated with the portfolio.

7. Maximum Drawdown:

- Definition: Measures the largest peak-to-trough decline in portfolio value.

- Calculation: \(\text{Maximum Drawdown} = \frac{\text{Trough Value} - \text{Peak Value}}{\text{Peak Value}}\)

- Use: Helps in understanding the worst-case scenario in terms of portfolio losses.

8. Value at Risk (VaR):

- Definition: Estimates the potential loss in portfolio value over a specified period for a given confidence interval.

- Calculation: VaR can be calculated using historical simulation, variance-covariance method, or Monte Carlo simulation.

- Use: Provides an estimate of the potential downside risk in monetary terms.

9. Tracking Error:

- Definition: Measures how closely the portfolio’s returns follow the returns of a benchmark index.

- Calculation: Standard deviation of the difference between the portfolio’s returns and the benchmark’s returns.

- Use: Assesses the consistency of the portfolio’s performance relative to the benchmark.

Implementing a Performance Evaluation Strategy

1. Set Clear Objectives: Define what you want to achieve with your portfolio, including return targets and acceptable risk levels.

2. Benchmark Selection: Choose appropriate benchmarks that reflect the investment goals and asset allocation.

3. Regular Monitoring: Track performance metrics periodically to ensure alignment with objectives and make necessary adjustments.

4. Use Analytical Tools: Leverage portfolio management software and analytical tools to calculate and visualize performance metrics.

Evaluating portfolio performance using these metrics ensures a comprehensive assessment of how well your investments are performing and helps in making informed decisions to achieve your financial goals.