Markowitz’s Model, Assumptions, Specific model

Harry Markowitz’s portfolio theory, introduced in his 1952 paper “Portfolio Selection,” revolutionized the way we think about investments and risk. This groundbreaking work laid the foundation for modern portfolio theory (MPT), earning Markowitz the Nobel Prize in Economic Sciences in 1990. His model offers a systematic approach to portfolio construction, emphasizing the importance of diversification and the quantifiable analysis of risk versus return.

Introduction to Markowitz’s Model

Markowitz’s model is predicated on the idea that investors are risk-averse; they prefer a portfolio with the least amount of risk for a given level of expected return. Unlike previous investment strategies that focused on analyzing individual securities in isolation, Markowitz proposed evaluating the performance of securities collectively, based on their overall contribution to portfolio risk and return.

Concept of Diversification

Central to Markowitz’s model is the concept of diversification. By holding a mix of assets that are not perfectly correlated, investors can reduce the overall risk of their portfolio. In essence, the poor performance of some investments can be offset by the good performance of others. Markowitz’s model quantitatively demonstrates how diversification can lead to an efficient frontier of optimal portfolios, offering the best possible expected return for a given level of risk.

Markowitz’s Model Assumptions:

• Rational Investors

Investors are rational and aim to maximize their utility with a given level of risk or minimize risk for a given level of expected return. This assumption posits that investors make decisions based solely on the expected return and variance (or standard deviation) of returns, focusing on the mean-variance efficiency.

• Single–Period Investment Horizon

The model assumes that all investors have the same single-period investment horizon, typically focusing on a single time frame for all investment considerations, without accounting for changing investment strategies or financial needs over time.

• Efficient Markets

Markowitz’s theory implicitly assumes that markets are efficient, meaning that all available information is already reflected in asset prices. Therefore, investors cannot consistently achieve higher returns without accepting higher risk.

• Risk is Quantifiable

The model assumes that risk is measurable and can be quantified by the variance (or standard deviation) of asset returns. This quantification allows for the mathematical modeling of risk in the portfolio context.

• Returns are Normally Distributed

Markowitz assumes that the returns on securities are normally distributed. This normal distribution of returns simplifies calculations and allows for the use of variance and standard deviation as measures of risk.

• Assets are Infinitely Divisible

Investors can buy any fraction of an asset, allowing for precise adjustments to the portfolio composition. This assumption facilitates the optimization process but may not always reflect real-world constraints, such as whole-share purchasing requirements.

• No Taxes or Transaction Costs

The model assumes that there are no taxes or transaction costs associated with buying and selling assets. In reality, these factors can significantly impact investment returns and decisions.

• Investors Have the Same Information and Expectations

It is assumed that all investors have access to the same information and thus have homogeneous expectations regarding the future returns, variances, and covariances of investment assets. This assumption overlooks the potential impacts of asymmetric information and differing investor expectations.

• Unlimited Borrowing and Lending

Investors can lend and borrow unlimited amounts at a risk-free rate of interest. This assumption allows for the creation of the Capital Market Line (CML), further simplifying portfolio selection and optimization.

• Unrestricted Short Selling

The model allows for unrestricted short selling of assets, meaning investors can sell securities they do not own. This flexibility is essential for achieving certain portfolio compositions but may not be feasible or allowed in all market contexts.

Risk, Return, and Correlation

Markowitz introduced the mean-variance analysis, where the expected return (mean) of a portfolio signifies its performance, and the variance measures its risk. He argued that the risk of a portfolio is not just the sum of the individual risks of securities but also depends significantly on the correlation between the returns of those securities. The lower the correlation, or more ideally, if the correlation is negative, the greater the risk reduction through diversification.

The Efficient Frontier

One of the most influential concepts from Markowitz’s model is the efficient frontier. This is a graphical representation of the set of optimal portfolios that offer the highest expected return for a given level of risk or the lowest risk for a given level of expected return. Portfolios that lie on the efficient frontier are considered efficient, and any portfolio not on this frontier is considered inefficient, as it does not provide the best possible expected return for its level of risk.

Portfolio Selection

Markowitz’s model guides investors in selecting a portfolio from the efficient frontier based on their risk tolerance. A risk-averse investor would choose a portfolio closer to the minimum-risk point on the frontier, while a risk-tolerant investor might opt for a portfolio further along the frontier, accepting higher risk for potentially higher returns.

Capital Asset Pricing Model (CAPM)

Building on Markowitz’s groundwork, the Capital Asset Pricing Model (CAPM) was developed to further understand the relationship between risk and return in a market context. CAPM introduces the concept of systemic risk (market risk) and the beta coefficient to measure an investment’s sensitivity to market movements, offering a method to calculate the expected return on an asset based on its risk relative to the market.

Applications and Limitations

Markowitz’s portfolio theory has been widely adopted in the finance industry, informing asset allocation, fund management, and financial advisory services. It provides a rigorous framework for constructing diversified portfolios tailored to an investor’s risk preference.

However, the model also has limitations. It relies on historical data to predict future returns and correlations, which may not always be accurate. The assumption of a single-period investment horizon and normally distributed returns also oversimplifies real market conditions. Furthermore, the model does not account for taxes, transaction costs, or liquidity constraints, which can significantly affect portfolio performance.