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Backtesting Brilliance: Navigating the Investment Labyrinth with Modern Portfolio Theory
Backtesting Brilliance: Navigating the Investment Labyrinth with Modern Portfolio Theory
Diving Deep into Investment Simulations Powered by Python.
Background
Background
The inspiration for this project began this summer with my father asking me to sit down with him to take a look over the performance of his retirement account. I took him up on this offer but I had to set some ground rules for myself before I got started. To start, I am not a financial advisor so I wanted to make sure that all the information that I gave my father was factual rather than opinion based. Additionally, I had to understand the gravity my suggestions would hold. The performance of a retirement account can have a high impact on how flexible families can be financially in a period of reduced income.
The inspiration for this project began this summer with my father asking me to sit down with him to take a look over the performance of his retirement account. I took him up on this offer but I had to set some ground rules for myself before I got started. To start, I am not a financial advisor so I wanted to make sure that all the information that I gave my father was factual rather than opinion based. Additionally, I had to understand the gravity my suggestions would hold. The performance of a retirement account can have a high impact on how flexible families can be financially in a period of reduced income.
When I reviewed my father's account there were two things that stood out to me right away. First I noticed the steep fees he was being charged, upwards of 1% annually for an actively managed account with a well-known asset management firm. The second thing that stood out to me was that the managed portfolio he invested in underperformed compared to a simple total stock market benchmark. This insight into my father's investment situation, in addition to the knowledge of portfolio management gained so far with my finance degree, prompted me to look deeper into this situation to see how I could help. It also sparked my interest to look into how underperforming actively managed portfolios with high fees affect families in similar situations across the nation. Through this brainstorming session I envisioned a tool that was straightforward and insightful, even for those new to the world of investing. I also understood that there is no magic 8 ball that can tell you to pick which stocks are going to go up or down. Therefore, my goal was a portfolio that tracked common investment benchmarks rather than playing "casino" with my father's retirement account.
When I reviewed my father's account there were two things that stood out to me right away. First I noticed the steep fees he was being charged, upwards of 1% annually for an actively managed account with a well-known asset management firm. The second thing that stood out to me was that the managed portfolio he invested in underperformed compared to a simple total stock market benchmark. This insight into my father's investment situation, in addition to the knowledge of portfolio management gained so far with my finance degree, prompted me to look deeper into this situation to see how I could help. It also sparked my interest to look into how underperforming actively managed portfolios with high fees affect families in similar situations across the nation. Through this brainstorming session I envisioned a tool that was straightforward and insightful, even for those new to the world of investing. I also understood that there is no magic 8 ball that can tell you to pick which stocks are going to go up or down. Therefore, my goal was a portfolio that tracked common investment benchmarks rather than playing "casino" with my father's retirement account.
Notice: Before I get into the project I want you to understand that I am not a financial advisor. The information in this article and the tool I have built is purely educational and not a substitute for professional investment advice. Always consult with a financial advisor before making investment choices.
Planning
Planning
As I started to work towards an initial plan, I settled on three fundamental elements I wanted this tool to achieve. First, I wanted the tool to be based upon highly regarded and conservative financial theory. Second, I wanted to have simple user inputs with a low learning curve for increased adoption. Lastly, I wanted a straightforward plan outputted to the user that is easy to understand and execute upon.
1: What financial theories am I going to use to in this project and why?
The vision was set, but the path wasn't. As I got my journey underway the first thing I needed to figure out is which financial theories I was going to use for this project and why. For this I reached back to my financial management class where we learned about Nobel Prize Winner Harry Markowitz and his Modern Portfolio Theory. MPT is a framework that emphasizes the power of diversification by showing it's not just individual assets but their collective harmony that crafts an optimal portfolio. For better visualization of this concept I have provided a graphic below. (Photo by Forbes Advsior: source)
The Efficient Frontier emerged as a guiding light for this project's development. This concept highlights portfolios that provide the highest returns for a given level of risk (represented by the blue line in the image above). Another segment of finance that I drew inspiration from was the relationship between a portfolio's return and it's standard deviation. Let's say that you have a two fund portfolio of Asset A and Asset B. Let's say that Asset A has a return of 10% and a standard deviation of 10%. Additionally, Asset B has a return of 20% and a standard deviation of 20%. The average return of these two assets will be 15% but for the standard deviation we need to dig a little deeper. To start, we need to know the correlation: how these two assets move together. Assuming a correlation of 0.5, and that the two assets are 50/50 split in the portfolio, we now have all of our variables to calculate portfolio standard deviation using the formula below:
As we can see in the calculation above the standard deviation of the portfolio (13.23%) is actually less than the weighted average of the two assets' standard deviation (15%). This difference can be attributed to a factor called "diversification benefit". In summary, if assets in the portfolio are not perfectly correlated, combining them can result in a total portfolio standard deviation that is lower than the weighted average of the individual asset standard deviations, thereby optimizing the risk-return tradeoff.
The Image above is a visual representation of diversification reducing volatility. (The assets above have a correlation of 0.) (source)
2: What is the importance of a easy to use interface?
My goal in the creation of this project was to make investment decisions easier to understand and visualize for families in a similar situation to mine. One of my inspirations for this project is an online tool that I use frequently to judge the historical performance of a portfolio called Portfolio Visualizer. This is a great tool and I enjoy using it but requires too many inputs for beginners. For example if you are interested in a portfolio with eight assets you would need to enter 29 different variables, including finding the assets you would like to invest in. For my tool it only needs 4–6 specified inputs: age, risk tolerance (1/10), investment amount, duration, and the option for periodic reinvestment.
Continuing the idea of ease of use I wanted the user just to focus on inputing information they already have, rather than stressing about picking the correct stocks. Another thing the user does not have to worry about is the optimal weighting of each stock. Below in the “Building” section I will get into how python is able to simulate random portfolios for us to use in our very Efficient Frontier.
3: What do I want the user to take way from this experience?
The third big goal I had with the creation of this project was for the user to have a positive experience, and to be best equipped to act upon the results of their input. To ensure a positive experience I made sure to have a responsive web based platform that is easy to access and easy to use. Additionally I wanted all graphs and text outputs to be easy to understand.
The second part of this goal is for the user to be able to take action on the data presented. For this I created a PDF output that brings all the key statistics into one document that can be printed out and taken wherever needed. On this document you can also find what I like to call a "Stock Shopping List". This section on the document lets you know what stock to buy, and uses your initial investment to determine how much to buy.
Development
Before diving too deep into building a full web-interface tool, it was important to verify the feasibility of implementing all these financial tools in python. To start, all of the data used in this project is obtained using the yfinance python package. From there the data was cleaned with pandas dataframes so it could be organized efficiently. Then the script will use this data and construct random portfolios, simulating a multitude of investment combinations. After, the portfolio's standard deviation is calculated and stored aswell as the rest of the details from the generated portfolio. Below is a code snippet that shows how this is done. (Full code at Github).
After simulating numerous portfolios, the next step was to graphically represent them to identify the optimal portfolio based on the user's risk preference. To achieve this, I incorporated the Efficient Frontier, as previously mentioned in this article. Furthermore, I aimed to depict the Capital Market Line on the same graph. This line is plotted using the risk-free return rate as the y-intercept, and its slope is determined by the stock with the highest Sharpe ratio (a measure of risk to reward). Essentially, the closer a portfolio is to this line, the better the return for its associated risk.
To determine the user's target portfolio, I first compute their risk score using the formula: (118−age) × (0.5) + (risk × 10) × (0.5). For instance, a 30-year-old user with a risk tolerance of 6/10 would have a risk score of 74/100. I would then examine the portfolios in the 72nd to 76th percentile range and select the one with the highest return. This calculation is represented in the code below:
Culmination
With this code done, the focus then shifted to setting up the user interface. For my user interface I chose to build a streamlit app. (Side note: If you are a python coder I would strongly recommend streamlit. With streamlit you are able to build front end applications fully in python without any knowledge of html, JavaScript, or other coding languages). The application is split into two different sections, inputs and outputs. As discussed in the "Planning" section of this article the user is prompted to enter 4–6 different input variables: their age and risk (to calculate the risk score), initial investment, duration, and any recurring investment information. The second portion of the application is output. I will cover each output individually below:
Portfolio Outlook (Line chart): To show the portfolio's performance over the user specified duration. To help understand the returns I added a feature that compares the main portfolio's growth with two others. The first being a purely stock-driven portfolio, the second, a balanced mix of 75% stocks and 25% bonds. This lets users see how their portfolio might grow over time compared to other popular investment portfolios over the same timeframe.
Portfolio Comparison (Stats): The subsequent item to display was a "stats" section that compared the generated portfolio against the benchmarks specified above. Displayed in the chart you can see the return (compound annual growth rate), risk (standard deviation), sharpe ratio, the ending balance, as well as the minimum and maximum balance.
Portfolio Allocation (Pie chart): Following the performance of the portfolio, a pie chart is displayed. This pie chart shows the user all of the asset classes that their portfolio comprises and their corresponding allocation. If you open the PDF report you can see which asset class corresponds to which ETF to purchase.
Efficient Frontier (Scatter plot): This is the first output in the "Advanced Stats" section. This scatter plot has every individual simulated portfolio graphed, with the portfolio details when you hover over it. Additionally the target portfolio is represented by a gold star, with the two other benchmark portfolios represented as diamonds. Additionally the CML line is graphed to display the portfolio with the greatest sharpe ratio.
Correlation Matrix (Dataframe): The correlation matrix output is there for advanced users to see how well the different assets of the portfolio correlate with one another. You can find the correlation by identifying the intersection of the column and row of your two desired assets.
These outputs are great but I wanted to provide an exceptional experience. In order to go past expectations I needed to provide something that was tangible and actionable. This understanding culminated in the creation of a PDF report generation feature that can be found near the bottom of the website after you submit your inputs. This comprehensive document encapsulated the tool's relevant insights in addition to the actional plan mentioned previously in this article, the "Stock Shopping List". This consolidated output transformed the tool from an informational website, to a resource that is easy to use, take with you, and act upon.
Conclusion
In reflecting on this journey, it's clear that the driving force behind this project was a genuine desire to provide reliable, factual information to those keen on optimizing their investments - especially when it pertains to something as vital as retirement. My initial encounter with my father's investment account was the catalyst, illuminating the pressing need for a user-friendly tool that not only educates but also empowers individuals across age groups.
The creation of this tool was guided by a foundational principle: simplicity. It was significant to keep user interactions minimal, ensuring that all users are not overwhelmed. After all, the world of investing can be very daunting, the last thing I want is a tool that adds to that complexity. Additionally, by offering insights grounded in Modern Portfolio Theory and presenting them in an accessible manner, it bridges the gap between detailed financial concepts and everyday investment decisions.
Looking ahead, the potential for enhancement in the software is appealing. I am looking into developing a Version 2.0, with some exciting features lined up. For this upgrade I am considering integrating a Monte Carlo Simulation tailored for retirement investments. Furthermore, the next update will be focused on flexibility and more advanced stats. For flexibility the goal is to allow for the user input custom stock variables and set custom benchmarks. As far as advanced stats I am looking to include metrics such as the Geometric Mean, Downside Deviation, and annual max drawdowns to help explain the portfolio to those investors looking to take the next step. Lastly I am working towards extending the investment duration beyond 22 years, the key for this is finding accurate data outside of the yfinance package. Each of these additions is not just a feature but a step toward making investment knowledge more comprehensive and accessible.
In summary, this project started from something I went through personally but I believe it can help a lot of people, reaching far beyond the impact it has had in my household. I've had a lot of fun making this tool and I hope that you have enjoyed the process with me. If you have any questions or would like to reachout, headover to the "Contact Me" page on this website to get in contact. Thank you for your time and support!
Below is an embedded version of my Portfolio Backtest tool. For best performace open the tool in a new tab with the "Fullscreen" button in the bottom of the embed. Once you press "Calculate Results" it may take a minute to output your results.
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