Review of: ‘Portfolio Selection’ by Harry Markowitz

Why This is an Key Paper for the Finance Industry and Finance Professionals 🚀

A solid map to navigate portfolio construction

Imagine trying to navigate a vast ocean without a map. In the finance world, Markowitz’s is one of the few commonly agreed maps, guiding investors through portfolio selection.

A new approach to asset allocation

Originally published in 1952, this research introduced the brand new concept of modern portfolio theory (MPT), which fundamentally transformed how we think about investment strategies. It highlights that risk and return are not mere afterthoughts but the two sides of the same coin in investment decision-making.

A solid theory to support investors’ intuitions

Investors used to focus primarily on individual stocks, often leading to risk-laden portfolios. However, Markowitz urged us to look at the bigger picture: how assets work together, or rather, how their values interact. By advocating for diversification, he demonstrated that combining a variety of investments can significantly reduce risk without sacrificing returns. This insight is invaluable! It means that financiers can target greater predictability and stability in uncertain markets.

A starting point to build more sophisticated models

Moreover, his mathematical models for calculating the optimal mix of assets have become fundamental in finance education and practice. Even today, Markowitz’s principles underpin the analytical tools that wealth managers and hedge fund strategists use to optimise portfolios.

A new lens for investors

In essence, Markowitz’s work gave us a new lens to view investments, creating a safer, more systematic approach for finance professionals and thereby establishing standards that define today’s investment strategies. His research is not merely of historical significance; its principles continue to shape our everyday financial decisions. Understanding this paper is a stepping stone for anyone committed to excelling in finance.

Starting Point and Key Assumptions

In ‘Portfolio Selection’, Harry Markowitz establishes several key assumptions essential for his framework, which includes:

Investor Rationality: It is assumed that investors are rational and make decisions based on expected return and risk potential rather than emotional or speculative trends.
Markets are Efficient: The paper posits that all investors have access to the same information. Therefore, prices reflect all available information at any given time, making it impossible to consistently achieve excess returns.
Normal Distribution of Returns: Markowitz assumes asset returns follow a normal distribution whereby the mean and variance can sufficiently represent the performance of the assets.
Static Investors’ Horizon: The analysis assumes a single, unchanged investment period. Investors are seen as making decisions based on a fixed time frame, lacking any allowance for dynamics beyond this scope.

These critical assumptions underpin the modern portfolio theory, reflecting a systematic approach to optimise investment portfolios. Understanding these assumptions is paramount for finance professionals as it captures the theoretical essence that shapes investment strategies.

Sélectionner a attributer un poids aux actifs, dans un environnement incertain est un exercice difficile et ambitieux.

Key Formulas

Expected Return

\[ E(R) = w_1 E(R_1) + w_2 E(R_2) + ... + w_n E(R_n) \] This formula calculates the expected return of a portfolio where:

E(R): expected return of the portfolio
w_i: weight of asset i in the portfolio
E(R_i): expected return of asset i

Portfolio Expected Variance (2 assets)

\[ \sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_{1,2} \] This represents the variance of portfolio returns:

sigma_p^2: variance of the portfolio
sigma_i^2: variance of asset i
sigma_{i,j}: covariance between assets i and j

Portfolio Expected Variance (n assets)

\[ V(w) = \sum_{i=1}^{n} w_i^2 V_i + 2 \sum_{i \neq j} w_i w_j Cov_{ij} \] This expression calculates the variance of the portfolio:

V(w): variance of the portfolio
V_i: variance of asset i
w_i: weight of asset i
Cov_{ij}: covariance between assets i and j

Portfolio Expected Return

\[ R(w) = \sum_{i=1}^{n} w_i R_i \] This calculates the weighted return for each asset in a portfolio:

R(w): portfolio return
w_i: weight of the asset
R_i: return of the asset

Efficient Frontier

To find the efficient frontier, we aim to minimize the portfolio’s variance \(\sigma_p^2\) for a given level of expected return \(E(R_p)\). This leads to the following constrained optimization problem:

\[ \text{Minimize: } \sigma_p^2 = \sum_{i=1}^{n} \sum_{j=1}^{n} w_i w_j \sigma_{ij} \]

Subject to: \[ \sum_{i=1}^{n} w_i E(R_i) = E(R_p) \quad \text{(target expected return)} \] \[ \sum_{i=1}^{n} w_i = 1 \quad \text{(sum of portfolio weights equals 1)} \]

Key Outcomes and Academic Impact

Markowitz’s seminal work in ‘Portfolio Selection’ introduces critical intuitions that shaped investment strategies. By integrating the notions of risk and return into a unified framework, he emphasized that:

Risk Is Manageable: Instead of being perceived as a threat, risk can be managed through diversification. The paper laid the foundation for Investors can reduce unsystematic risk by strategically combining assets.
The Significance of Correlation: The relationships between asset returns play a vital role in portfolio performance. Markowitz illustrated how combining negatively correlated assets could lower overall risk, leading to the practice of diversification.
Expected Returns vs. Actual Returns: The concept of expected return establishes that investors must look at potential returns instead of relying on historic performance alone. It emphasises forward thinking.
The Efficient Frontier: A groundbreaking visual representation of optimal portfolios, this concept allows investors to see the balance of risk and returns. This enables the selection of portfolios that maximizes returns for a given risk level.
Broadening Investment Perspectives: The framework encourages investment beyond individual assets; portfolio selection thereby becomes a comprehensive exercise in combining different assets based on their projected performance and risk rarities.

These insights have had lasting implications and have become principles that underpin many modern investment strategies and theories.

Key Takeaways for you as an Investor

Short-Term Strategy: Investors focusing on the short term should familiarize themselves with the risk-return relationship, ensuring they seek diversification across sectors and asset classes. Strategies like sector rotation could leverage Markowitz’s theories while managing risk through varied exposure.
Medium-Term Strategy: Medium-term investors should leverage anticipation of market cycles by strategically adapting their portfolios to capture growth phases. They should continuously adjust their asset allocation based on evolving market conditions while aiming to stay on the efficient frontier.
Long-Term Strategy: For long-term investors, the emphasis should remain on maintaining a balanced and diversified portfolio. Incorporating periodic reviews helps ensure expectations of risk and return align with ongoing investment goals. Adopting an indexed or passively managed portfolio strategy can support steady growth over time, rooted in the principles established in the body of work by Markowitz.

Markowitz’s insights create a framework that empowers investors to make informed decisions, naturally adapting strategies to evolving market environments while managing their risk.

Conclusion

Overall, Harry Markowitz’s ‘Portfolio Selection’ is more than just an academic paper; it is a seminal work that continues to resonate within both academic and practical applications of finance today. The implications of risk management and optimization laid out in the paper serve as a foundation for investors looking to navigate financial markets.