A Quantitative Approach To Maximize Portfolio Performance With Optimal Stock Weighting: Monte Carlo Simulation
Sat, 22 Apr 2023 12:00 PM
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As a portfolio manager, our primary goal is to achieve maximal return while taking minimal risks. After picking the right stocks with strong fundamentals, we need to determine the optimal stock weighting for our portfolio. How many percentages should a stock weigh in the portfolio? Why should we own more of one stock than another? Why should GOOGL weigh 7% in the portfolio and not 3%?
There are many possible answers to these questions. One could simply "feel" that way, much like how they feel that it would rain tomorrow. However, relying solely on intuition is not a great way to invest. A more systematic and data-driven approach is required to make informed decisions about stock weightings.
Consider a scenario where a weather forecaster predicts that there is a 30% chance of rain tomorrow. This prediction is not based on a gut feeling but on a thorough analysis of historical data, current weather patterns, and sophisticated models. Similarly, when it comes to managing a portfolio, we can utilize quantitative methods and historical data to optimize our stock weightings, maximizing returns while minimizing risks.
One such approach is the Monte Carlo simulation, a powerful tool for determining the optimal stock weighting in a portfolio. By simulating thousands or even millions of different possible weightings, we can analyze their expected returns and risks, and identify the combination that yields the highest Sharpe ratio, a measure of risk-adjusted return. This way, we can make data-driven decisions about stock allocations, ensuring that our portfolio is well-positioned to deliver the best possible performance.
What is Monte Carlo simulation?
Monte Carlo simulation is a computational technique that uses random sampling to estimate the probability distributions of various outcomes. It was named after the gambling destination in Monaco because just like gambling games such as roulette or dice, chance and random outcomes are central to this modeling technique. It is widely used in various fields, such as finance, engineering, and physics, to model complex systems where exact analytical solutions are not feasible. The key idea is to simulate a large number of scenarios, analyze the results, and make informed decisions based on the aggregated data.
The WIC Flagship Portfolio consists of 23 carefully-selected U.S equities from multiple sectors, have positive cash flow, strong earnings growth, attractive valuation.
Applying Monte Carlo Simulation to Our Portfolio
In the context of our investment portfolio, which consists of 23 carefully-crafted U.S. stocks, we used Monte Carlo simulation to estimate the optimal stock weighting, taking into account expected returns, volatility, and correlations among the individual stocks. We demonstrate the process below.
1. Collect historical data: We gathered historical price data for all the stocks in our portfolio, as well as the benchmark index S&P 500. From there, we calculate their respective returns, volatilities, and correlations. We selected the period from 2000 to now, which encompasses the 2000-2002 Dot-com bubble, the 2007-2009 Global Financial Crisis and most recently the Covid pandemic, and all the volatilities in monetary policies that result from these major events.
2. Generate random portfolios: There are 23 stocks in the portfolio, each with a possibility of receiving an allocation of a non-zero whole-number percentage. As a result, there are approximately 1 x 10^20 (one hundred trillion) possible portfolios. Unfortunately, our programming matrix cannot handle such large number of simulations. We could only simulate 1 million portfolios with varying weights assigned to each stock.
3. Analyze results: We analyzed the performance of each simulated portfolio in terms of its expected return and risk (measured as the standard deviation of returns). This allowed us to create a scatter plot with each data point being a possible portfolio allocation, with expected returns on the y-axis and portfolio risk/ volatility on the x-axis. This plot is known as the "efficient frontier."
4. Identify the optimal allocation: By examining the efficient frontier, we identified the optimal stock weighting that offers the highest return with the lowest relative volatility/risk.
"The Optimal Portfolio"
The optimal stock portfolio that offers the highest return with the lowest relative volatility/risk is identified in the graph with the red circle. Each blue dot is a portfolio. In details, since the turn of the 21st century, this optimal portfolio offers an annual return of 15%, which greatly outperforms the S&P 500's annual return of 6.3% (see benchmark point). Meanwhile, this optimal portfolio experiences an annualized volatility of 20.16%, which is only slightly higher than the 19.82% annualized volatility of the benchmark S&P 500 index (see benchmark point).
The optimal portfolio's Sharpe ratio is 0.57, compared to the benchmark S&P 500 index's Sharpe ratio of 0.14. The Sharpe ratio is a measure of risk-adjusted return used to evaluate the performance of an investment by considering both its return and risk. A higher Sharpe ratio indicates a better risk-adjusted return.
Limitations of Monte Carlo Simulation and the Importance of Ongoing Portfolio Monitoring
It is worthy to remind that up to this point, this optimal portfolio has been constructed based on historical data. While the Monte Carlo simulation is a powerful tool for optimizing stock weightings, it is important to recognize its limitations. Specifically, the simulation relies on the assumption that historical patterns and relationships will persist in the future, which may not always be the case. Market conditions, economic factors, and individual stock performance can change rapidly, making it necessary to continuously monitor and adjust the portfolio to maintain its optimal risk-adjusted return.
To address the limitations of relying solely on historical data, we also consider additional approaches such as sensitivity and scenario analyses to assess the impact of changing assumptions and potential future market conditions on the portfolio. Additionally, we review portfolio performance regularly and rebalance as needed. Lastly, while at the beginning we made fun of managers running money based on feelings, we understand the importance of incorporating qualitative factors, such as assessing a company's management team, competitive advantages and industry strengths.
Conclusion
Achieving maximal returns while taking minimal risks is the primary goal of a portfolio manager. Utilizing data-driven approaches like the Monte Carlo simulation can significantly enhance the decision-making process when determining optimal stock weightings. While the Monte Carlo simulation has its limitations, such as relying on historical data and patterns, it remains a powerful tool for optimizing stock allocations in a portfolio. By supplementing this quantitative approach with sensitivity and scenario analyses, regular performance reviews, rebalancing, and qualitative assessments of individual stocks, we can build and maintain a resilient, high-performing investment portfolio. This holistic approach to portfolio management ensures that we are well-equipped to navigate the dynamic and ever-changing financial markets, ultimately delivering the best possible risk-adjusted returns for our investors.
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