As investors, we participate in the market for decades, making countless investment decisions. The most important goal in this journey is to survive in the market without suffering significant capital losses. In a previous post, we discussed how reducing the frequency and magnitude of losses is key to survival. In this article, we will delve into a more concrete method—asset allocation. While numerous asset allocation strategies have been widely popularized, this article focuses on the foundational portfolio theory that underpins all these approaches, along with its mathematical basis and inherent limitations. Understanding these core principles is crucial because they not only form the backbone of effective asset allocation strategies but also empower you to balance risk and reward in a systematic manner, ultimately helping you make more informed investment decisions.

---

What Is Asset Allocation?

Asset allocation refers to the strategy of diversifying an investment portfolio across various asset classes (e.g., stocks, bonds, real estate, commodities, etc.). While it may seem like a simple concept, it is an exception to the investment adage "There is no free lunch"—meaning that proper asset allocation can reduce risk while maintaining the same level of returns. This principle aligns with the well-known saying, "Don't put all your eggs in one basket."

---

If You Could Only Choose One Asset?

Let's start with a simple question: if you could only invest in one asset for your entire life, which one would you choose?

Imagine that from now until retirement you’re allowed to invest in just a single asset—and at retirement, you cash out everything you've invested. Some might lean towards stocks, others might opt for the security of a savings account, while a few bold investors could even consider Bitcoin. However, for most people, the safer bet would likely be a savings account or an index fund like the S&P 500, thanks to their relative stability and lower risk.

Why?

Because of risk considerations. While stocks and Bitcoin have the potential for high returns, their price volatility makes them a risky choice for long-term stability.

Let's compare the Compound Annual Growth Rate (CAGR) of four major assets: the S&P 500 index, Apple, Intel, and Bitcoin.

Note: Bitcoin, despite its short history, boasts the highest CAGR at around 67%. However, most investors hesitate to commit to Bitcoin for a lifetime due to its volatility. Apple and Intel also show higher returns than index funds, but because individual stocks like Intel can be highly volatile, investing in an index fund may be a more stable choice—unless one can accurately pick winning stocks like Apple.

Now that we've explored the idea of investing in a single asset, let's examine how we can measure the risk associated with these investments.

---

Risk and the Sharpe Ratio

Reflecting on our earlier discussion, we learned that when choosing an asset, two main factors come into play: expected return and risk. Now, let's introduce the Sharpe Ratio, a valuable metric that helps us assess how efficiently an asset generates returns relative to the risk it takes on.

High volatility generally means higher risk, whereas lower volatility suggests greater stability. However, low volatility alone doesn't guarantee a good investment. We need a way to balance both aspects. This is where the Sharpe Ratio comes in:

[ \text{Sharpe Ratio} = \frac{\text{Expected Return of Asset} - \text{Risk-Free Rate}}{\text{Volatility}} ]

• Risk-Free Rate: Represents the theoretical return of an investment with zero risk (typically the yield on highly reliable government bonds such as U.S. Treasury bonds). It is the minimum return an investor can expect without taking on any risk.
• A higher Sharpe Ratio indicates a more efficient asset, meaning it delivers higher returns for the level of risk taken.

Comparing the Sharpe Ratios (assuming a 3% risk-free rate):

• Bitcoin: 0.93
• Apple: 0.37
• S&P 500: 0.33
• Intel: 0.20

Despite Bitcoin’s high Sharpe Ratio, its unsystematic risks (which we will discuss later) make it less reliable as a long-term investment.

---

Portfolio Theory and the Markowitz Model

In our previous discussion, we explored the idea of investing in a single asset. However, in the real world, combining multiple assets can create a more robust portfolio. Two key factors in asset selection are return and volatility. These ideas are formalized in Modern Portfolio Theory (MPT), developed by economist Harry Markowitz—who was awarded a Nobel Prize for his pioneering work.

To visualize these concepts, we can plot them on a graph using recent five-year data for selected S&P 500 stocks.

• The horizontal axis represents volatility (standard deviation).
• The vertical axis represents CAGR (annual compounded return).

In general:

• Assets positioned higher on the graph are more attractive due to higher returns.
• Assets located further left are preferable because they exhibit lower volatility.

Investors can use this visualization to compare different assets and construct a portfolio that balances high returns with low risk.

---

Portfolio Construction and the Efficient Frontier

Markowitz’s model aims to maximize expected return while minimizing risk by identifying the optimal asset allocation strategy. This is where the concept of the Efficient Frontier comes into play.

• Efficient Frontier: A curve that represents the best possible portfolio combinations offering the highest expected return for a given level of risk. Portfolios below this curve are considered inefficient because they fail to maximize returns relative to risk.

Let’s take a closer look at a concrete example:

An Example:

• Assume an investment in Walmart and Coca-Cola:

  • When you mix these two assets in ratios ranging from 0% to 100%, the resulting curve is known as the Portfolio Frontier (depicted as a red solid line).
  • Among this curve, the combination that offers the maximum return for a given level of risk is identified as the Efficient Frontier (shown as a magenta dotted line).
  • Additionally, the portfolio with the smallest risk (represented by the black dot) is referred to as the Minimum Variance Portfolio.

But that's not all. In addition to this pair, we can also create another Efficient Frontier by combining assets such as NVIDIA and Walmart:

• By selecting the two portfolios with the lowest volatility from both the Walmart-NVIDIA Efficient Frontier and the Walmart-Coca-Cola Efficient Frontier, we can draw a new Efficient Frontier (represented by a magenta-colored curve). This new frontier is positioned further to the left, meaning it achieves lower volatility, and among portfolios with the same volatility, it enables higher returns.

By combining various assets and portfolios in this manner, investors can iteratively construct portfolios that maximize returns while minimizing risk.

This process allows for the design of an optimal asset allocation strategy tailored to individual risk tolerance and return objectives.

Advanced (Optional): Markowitz emphasized the importance of the correlation between assets rather than just individual asset risk. If two assets have a correlation of 1, their combination forms a straight line on the risk-return graph. However, if the correlation is lower, the combination produces a curve, enabling greater risk reduction relative to return reduction, which often leads to portfolios with higher Sharpe Ratios.

In summary, by intelligently combining assets, you not only reduce your overall risk but also position your portfolio for better returns.

---

The Meaning and Limitations of Asset Allocation

The primary goal of asset allocation is to reduce volatility, thereby minimizing the frequency and magnitude of losses. Investing in a single asset exposes investors to significant losses from market shocks, while diversifying across multiple assets reduces the impact of individual asset volatility on the overall portfolio.

Benefits:

• Reduces Volatility: Helps in minimizing losses.
• Diversification: Protects against market shocks in any single asset.

Limitations:

• Dependence on Historical Data:

  • Portfolio allocation decisions often rely on past performance, assuming that historical trends will continue. However, market conditions can change, and past performance may not always predict future behavior.

• Systematic vs. Unsystematic Risk:

  • Systematic Risk: Market-wide risks that asset allocation can help reduce.
  • Unsystematic Risk: Risks unique to individual assets. For example, despite Bitcoin’s high Sharpe Ratio, it faces:
    • Regulatory risk: Potential for stricter cryptocurrency regulations.
    • Technological risk: Possibility of security vulnerabilities in blockchain technology.
    • Liquidity risk: Difficulty in quickly converting Bitcoin into cash during market downturns.

• Trade-Off Between Stability and Growth:

  • While reducing volatility minimizes losses, it can also limit the potential for high returns. Investors must balance the need for risk management with the desire for growth.

---

Conclusion

Modern Portfolio Theory provides a crucial framework for long-term investing. While asset allocation is key to reducing volatility and safeguarding against significant losses, it is not without its limitations. By understanding both the strengths and weaknesses of asset allocation, investors can better tailor their portfolios to meet their individual risk and return goals.

In this post, we explored the core ideas behind Portfolio Theory and asset allocation. In the next post, we will delve into practical asset allocation strategies derived from this theory and further discuss their limitations.

Thank you for reading!