# The Power of Long-Term Investments and Dynamic Programming

Hatched by Alessio Frateily

Apr 10, 2024

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### Introduction:

Investing wisely and solving complex problems often require a similar mindset - one that values patience, perseverance, and a long-term perspective. In this article, we will explore the common threads between long-term investments and the concept of dynamic programming. We will delve into the benefits of holding onto assets, the importance of rebalancing, and the fascinating world of recursive relationships. Let's explore how these seemingly distinct topics intersect and offer valuable insights for success.

### The Longest Common Subsequence Problem:

To understand the power of recursion and dynamic programming, let's consider the longest common subsequence problem. This algorithmic challenge involves finding the longest subsequence that appears in both given strings, S and T. The characters of the subsequence do not have to appear consecutively in the original strings. For example, given the strings "ABCDE" and "DACACBE," the longest common subsequence is "ACE."

The recursive nature of this problem highlights how straightforward and elegant recursive relationships can be. Dynamic programming, also known as DP, is a technique that proves invaluable for solving such counting and optimization problems. If a problem statement includes phrases like "how many," "minimum," "maximum," "shortest," or "longest," chances are high that it is a DP problem. However, to grasp DP fully, one must first have a solid understanding of recursion.

For those who find recursion daunting, it is essential to practice and embrace it. By writing a few for-loops and gradually immersing oneself in recursive thinking, the fear of recursion can be overcome. The ability to recognize and utilize recursive relationships is a valuable asset in both problem-solving and long-term investments.

### The Power of Holding On:

In the realm of investments, the adage "just keep buying" holds true. Selling your investments should only be done for the purpose of rebalancing or during retirement. Capitalism, at its core, is about acquiring capital and building wealth for the future. Selling out is, quite literally, selling out your potential for future wealth.

One critical metric to consider when evaluating stocks is the price-to-earnings (P/E) ratio. This measurement indicates how expensive a stock is relative to its current earnings. Interestingly, there is a negative relationship between the P/E ratio and future real returns. As stocks become more expensive, the expected real return decreases.

However, over longer periods of time, these negative returns tend to diminish, making way for positive real returns. Holding onto your investments for extended periods allows you to ride out market fluctuations and benefit from the long-term upward trend of the economy. By resisting the urge to sell during downturns and maintaining a balanced portfolio, you position yourself for greater wealth accumulation over time.

• 1. Embrace recursive thinking: Challenge yourself to understand and utilize recursive relationships in problem-solving. Start by practicing with simple examples and gradually tackle more complex scenarios. The ability to think recursively will enhance your problem-solving skills and open doors to more efficient solutions.
• 2. Adopt a long-term investment strategy: Resist the temptation to time the market or make impulsive selling decisions. Instead, focus on acquiring and holding onto assets for extended periods. Rebalance your portfolio annually or quarterly to maintain a healthy asset allocation, but avoid unnecessary selling that may hinder future wealth accumulation.
• 3. Understand the power of compounding: Compounding is the magical force that allows your investments to grow exponentially over time. By reinvesting dividends and letting your investments compound, you harness the power of time and exponential growth. Keep reinvesting and let compounding work its wonders for your long-term financial goals.

### Conclusion:

In conclusion, the worlds of long-term investments and dynamic programming intersect in intriguing ways. Both require a patient, long-term perspective, a willingness to embrace recursive relationships, and the ability to resist impulsive actions. By recognizing the power of holding onto assets, understanding the negative relationship between P/E ratios and future returns, and adopting a long-term investment strategy, you position yourself for financial success. Embrace recursive thinking, practice patience, and let the power of compounding work its magic. Your future self will thank you.

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