Feasible portfolio

What Is a Feasible Portfolio?

A feasible portfolio is any combination of assets that an investor can realistically construct given prevailing market conditions and their available capital. In the realm of Portfolio Theory, a feasible portfolio represents a point within the entire set of possible investment combinations, often depicted graphically in a risk-return space. This set of all possible portfolios is known as the feasible region or opportunity set. Unlike an optimal portfolio, which seeks to maximize expected return for a given level of risk, a feasible portfolio simply needs to be achievable, irrespective of its optimality. It takes into account all permissible asset allocation possibilities, considering factors such as liquidity, market accessibility, and investor constraints.

History and Origin

The concept of a feasible portfolio is foundational to Modern Portfolio Theory (MPT), pioneered by Harry Markowitz. In his seminal 1952 paper, "Portfolio Selection," Markowitz introduced a framework for selecting portfolios based on their expected return and variance (a measure of risk). He demonstrated that investors could combine assets to achieve a range of possible risk-return outcomes, forming what he termed the "opportunity set" or feasible region. This groundbreaking work earned him a Nobel Memorial Prize in Economic Sciences in 1990.⁶ Markowitz's insights provided a rigorous mathematical basis for understanding how diversification could improve a portfolio's risk-return profile, moving away from simply evaluating individual securities in isolation.

Key Takeaways

• A feasible portfolio is any combination of assets that can be realistically created by an investor.
• It exists within the "feasible region" or "opportunity set" in a risk-return diagram.
• The concept is fundamental to Modern Portfolio Theory, focusing on what is possible before optimization.
• A feasible portfolio considers all practical constraints, such as available capital and market accessibility.
• Not all feasible portfolios are optimal; many will offer less return for their given risk level compared to those on the efficient frontier.

Interpreting the Feasible Portfolio

Understanding the feasible portfolio involves recognizing the universe of possibilities available to an investor. When plotted on a graph with risk on the x-axis and expected return on the y-axis, the feasible region typically forms a concave shape, bounded by the individual assets and the combinations achievable through varying weights. Every point within this boundary represents a unique feasible portfolio.

The outer edge of this feasible region is known as the efficient frontier. Portfolios lying on the efficient frontier represent the most "efficient" combinations, offering the highest expected return for each level of risk, or the lowest risk for each level of expected return. Any feasible portfolio that falls below the efficient frontier is considered sub-optimal because it is possible to achieve a higher return for the same level of risk, or the same return with lower risk, by reallocating assets to a portfolio on the frontier. The interpretation is crucial for portfolio management as it helps investors identify if their current holdings are underperforming relative to what is achievable given their investment objectives.

Hypothetical Example

Consider an investor, Sarah, with $10,000 to invest. She is considering two assets:

• Asset A: Expected return of 8%, standard deviation of 15%.
• Asset B: Expected return of 4%, standard deviation of 8%.
• The correlation between Asset A and Asset B is 0.3.

Sarah can construct various feasible portfolios by allocating different percentages of her $10,000 between Asset A and Asset B.

Scenario 1: 100% in Asset A

• Expected Return = 8%
• Risk (Standard Deviation) = 15%

Scenario 2: 100% in Asset B

• Expected Return = 4%
• Risk (Standard Deviation) = 8%

Scenario 3: 50% in Asset A, 50% in Asset B
To calculate the portfolio's expected return and standard deviation:
Expected Return ($E(R_P)$) = $(w_A \times E(R_A)) + (w_B \times E(R_B))$
where (w_A) and (w_B) are the weights of Asset A and Asset B, and (E(R_A)) and (E(R_B)) are their expected returns.

Expected Return ($E(R_P)$) = $(0.50 \times 0.08) + (0.50 \times 0.04) = 0.04 + 0.02 = 0.06$ or 6%

Portfolio Variance ($\sigma_P^2$) = $w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \rho_{AB} \sigma_A \sigma_B$
where (\sigma_A) and (\sigma_B) are the standard deviations, and (\rho_{AB}) is the correlation.

Portfolio Variance ($\sigma_P^2$) = $(0.50^2 \times 0.15^2) + (0.50^2 \times 0.08^2) + (2 \times 0.50 \times 0.50 \times 0.3 \times 0.15 \times 0.08)$
$= (0.25 \times 0.0225) + (0.25 \times 0.0064) + (0.12 \times 0.012)$
$= 0.005625 + 0.0016 + 0.00144$
$= 0.008665$

Portfolio Standard Deviation ($\sigma_P$) = $\sqrt{0.008665} \approx 0.0930$ or 9.30%

So, a 50/50 portfolio would have an expected return of 6% and a risk of 9.30%. All these scenarios (100% A, 100% B, 50/50) represent feasible portfolios. By calculating and plotting all possible combinations, Sarah can visualize her feasible region and then identify the efficient portfolios that form the frontier based on her risk tolerance.

Practical Applications

The concept of a feasible portfolio is integral to both theoretical finance and real-world investing. For individual investors, it helps in understanding the range of investment outcomes available to them, considering their capital and the assets accessible in the market. Financial professionals use the feasible region as a starting point for crafting customized portfolios.

Investment advisers, for example, must adhere to strict regulatory guidelines when managing client assets. The Securities and Exchange Commission (SEC) requires registered investment advisers to have written policies and procedures for portfolio management processes, ensuring consistency with client investment objectives and regulatory restrictions.⁵ This involves operating within the bounds of what is feasible and appropriate for each client.

In the institutional world, large asset managers and pension funds also operate within a feasible region dictated by their mandates, liquidity needs, and regulatory constraints. While they often aim for optimal or near-optimal portfolios, their universe of investable assets and permissible strategies defines their feasible set. Understanding the feasible portfolio also informs risk management practices, as it highlights the inherent trade-offs between risk and return that exist for any given set of assets.

Limitations and Criticisms

While fundamental, the concept of a feasible portfolio, particularly within the traditional Markowitz framework, has several limitations. A primary criticism is its reliance on historical data to estimate expected returns, standard deviations, and correlation between assets.⁴ Past performance does not guarantee future results, and market conditions can change, rendering historical data less reliable for future predictions.

Another limitation is the assumption of rational investors who can accurately estimate these inputs. In practice, obtaining precise future expected returns and correlations is challenging, and small variations in these inputs can significantly alter the shape and position of the feasible region and the efficient frontier.³ Furthermore, the standard MPT model, which defines the feasible region, typically assumes that asset returns are normally distributed, which is often not the case in real markets, as returns can exhibit skewness and kurtosis.²

Real-world complexities, such as transaction costs, taxes, and liquidity constraints, are often simplified or excluded in basic theoretical models, which can make a theoretically "feasible" portfolio difficult or expensive to replicate in practice. The spectacular collapse of the highly leveraged hedge fund, Long-Term Capital Management (LTCM), in 1998, serves as a cautionary tale of how even sophisticated models and strategies can fail when market conditions deviate significantly from underlying assumptions.¹ The crisis highlighted the risks of high leverage and concentration, illustrating that what seems feasible in theory can lead to catastrophic outcomes in an unpredictable market.

Feasible Portfolio vs. Efficient Portfolio

The terms "feasible portfolio" and "efficient portfolio" are often discussed together in portfolio theory, but they refer to distinct concepts:

While all efficient portfolios are, by definition, feasible, not all feasible portfolios are efficient. The efficient portfolio represents a subset of the feasible portfolios—those that truly optimize the risk-return relationship. An investor aims to identify an efficient portfolio from the entire set of feasible options that aligns with their specific risk tolerance and return objectives.

FAQs

What is the feasible region in portfolio theory?

The feasible region, also known as the opportunity set, is the entire collection of all possible portfolios that can be constructed from a given set of assets. Each point within this region represents a unique feasible portfolio, plotted on a graph with risk on one axis and expected return on the other.

How does diversification relate to a feasible portfolio?

Diversification is a key strategy for creating feasible portfolios, as it allows investors to combine different assets to achieve various risk and return profiles. By diversifying, investors can often construct portfolios that have lower overall risk than individual assets, expanding the range of feasible options and potentially moving closer to the efficient frontier.

Can a feasible portfolio be bad?

Yes, a feasible portfolio can be "bad" in the sense that it might be sub-optimal. This means that for the same level of risk, a different feasible portfolio could offer a higher expected return, or for the same expected return, another feasible portfolio could have lower risk. Investors typically seek to move from a sub-optimal feasible portfolio towards an efficient portfolio.

How do real-world constraints affect a feasible portfolio?

Real-world constraints such as minimum investment amounts, transaction costs, liquidity issues, and regulatory restrictions can limit the practical construction of certain portfolios, thus narrowing the true feasible region for an investor. For instance, some mutual funds might have minimum investment requirements that prevent smaller investors from including them in their feasible set.

Is the Capital Asset Pricing Model related to feasible portfolios?

Yes, the Capital Asset Pricing Model (CAPM) builds upon the principles of Modern Portfolio Theory and the concept of the efficient frontier. CAPM helps to determine the expected return of an asset or portfolio given its systematic risk, assuming investors select portfolios from the efficient frontier.