Markowitz Model – Applications in Portfolio Management

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Written By
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Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.

The Markowitz Model, the basis behind Modern Portfolio Theory, was developed by Harry Markowitz in 1952.

This groundbreaking work introduced the concept of portfolio optimization and earned Markowitz the Nobel Prize in Economics in 1990.

The Markowitz Model enables investors to create an optimal portfolio by maximizing returns for each unit of risk.

This article looks at the assumptions, advantages, and limitations of the Markowitz Model, as well as its implications for portfolio construction, asset allocation, and diversification strategies.


Key Takeaways – Markowitz Model

  • The Markowitz Model, developed by Harry Markowitz, introduced the concept of portfolio optimization and earned him the Nobel Prize in Economics. It enables traders/investors to create an optimal portfolio by maximizing returns for each unit of risk they take on.
  • The Markowitz Model assumes rational and risk-averse investors, normally distributed expected returns, complete information availability, no transaction costs or taxes, and unlimited borrowing and lending at the risk-free rate.
  • The model’s advantages include systematic (less discretionary) portfolio construction, emphasis on diversification, and risk-return trade-off consideration.
  • Nonetheless, it has limitations such as reliance on historical data, volatility as the sole measure of risk, and the assumption of normal distribution. It also ignores transaction costs and taxes.


Markowitz Model Assumptions

The Markowitz Model is based on a number of key assumptions that underpin its theoretical framework.

These assumptions include:

Investors are rational and risk-averse

The model assumes that investors prefer higher returns with lower risk.

They make their investment decisions based on the expected returns and standard deviation (which is considered risk) of their portfolios.

Expected returns are normally distributed

The model assumes that asset returns follow a normal distribution, simplifying calculations and enabling portfolio optimization.

(In reality, financial returns tend to be more fat-tailed.)

Investors have access to complete information

It is assumed that investors possess all relevant information about the assets in their portfolio, including expected returns, risk, and correlations.

No transaction costs or taxes

The model assumes that investors face no transaction costs or taxes when trading assets, allowing them to rebalance their portfolios freely.

Unlimited borrowing and lending at the risk-free rate

The model assumes that investors can borrow or lend an unlimited amount of funds at the risk-free rate, facilitating portfolio optimization.


Markowitz Model Advantages and Limitations


  • The Markowitz Model provides a systematic, quantitative approach to portfolio construction, enabling investors to optimize their portfolios based on their risk tolerance and return objectives.
  • It emphasizes the importance of diversification by considering the correlations between different assets, reducing overall portfolio risk.


  • The model relies on historical data to estimate expected returns and asset correlations, which may not accurately predict future performance.
  • It uses volatility as risk. (Volatility is a form of risk and not all volatility is necessarily bad.)
  • It assumes that asset returns follow a normal distribution, which may not hold true for all assets, leading to inaccurate risk assessments.
  • The model ignores transaction costs, taxes, and other real-world factors that can significantly impact investment performance.


Markowitz Model Efficient Frontier

The Efficient Frontier represents the set of optimal portfolios that offer the highest expected return for a given level of risk or the lowest risk for a given expected return.

By plotting the expected return against the standard deviation of different portfolios, the Efficient Frontier is formed as the upper boundary of the feasible set.

Portfolios on the Efficient Frontier are considered optimal because they provide the best risk-return trade-off.


The Efficient Frontier


Markowitz Model & Modern Portfolio Construction and Asset Allocation

The Markowitz Model has had a profound impact on modern portfolio construction and asset allocation.

It has shifted the focus from individual asset selection to constructing a well-diversified portfolio that maximizes returns for a given level of risk.

This is the basis behind modern strategies like risk parity and risk parity variants.

By incorporating the risk-return trade-off and correlations between assets, investors can make more informed decisions when allocating capital across various asset classes, such as stocks, bonds, and commodities.


Markowitz Diversification Model

Diversification is a central tenet of the Markowitz Model, as it enables investors to reduce portfolio risk without sacrificing returns.

By combining assets with low/zero correlations (negative correlations is even better, assuming positive returns), investors can reduce the overall volatility of their portfolio, as the positive and negative price movements of different assets tend to offset each other.

This concept, known as the Markowitz Diversification Model, highlights the importance of asset selection and allocation in achieving optimal portfolio performance.


FAQs – Markowitz Model

How is the risk of a portfolio measured in the Markowitz Model?

In the Markowitz Model, risk is measured as the volatility (standard deviation) of the portfolio’s returns.

This metric quantifies the volatility or fluctuations in the portfolio’s value, with higher standard deviations indicating greater risk.

Why is diversification important in the Markowitz Model?

Diversification is essential in the Markowitz Model because it enables investors to reduce portfolio risk without giving up returns – traditionally the argument against diversification.

By combining assets with low or negative correlations, the overall vol of the portfolio can be lowered due to offsetting price movements.

Can the Markowitz Model be applied to all types of assets?

While the Markowitz Model is primarily used for traditional asset classes like stocks and bonds, it can be extended to other asset classes like real estate, commodities, or even cryptocurrencies, as long as the required data (expected returns, risk, and correlations) are available.

How do investors select the optimal portfolio from the Efficient Frontier?

Investors can choose their optimal portfolio from the Efficient Frontier based on their risk and return objectives.

For example, risk-averse investors might opt for a portfolio with lower expected returns but lower risk, while those with a higher risk tolerance may choose a portfolio with higher expected returns and risk.

What are some alternative portfolio optimization methods?

Alternative portfolio optimization methods include Black-Litterman, risk parity, and mean-CVaR (Conditional Value-at-Risk) optimization.

These methods address some of the limitations of the Markowitz Model by incorporating investors’ views, risk contributions, or extreme events in the portfolio optimization process.



The Markowitz Model changed the field of investment management by introducing a systematic and quantitative approach to portfolio optimization.

By emphasizing the importance of diversification and considering the risk-return trade-off, investors can make more informed decisions when constructing their portfolios.

Although the model has its limitations and is overly basic (e.g., equating the standard deviation in returns to risk), its core principles remain relevant and continue to shape modern portfolio construction and asset allocation strategies.

As traders/investors strive to maximize returns while minimizing risk, understanding the Markowitz Model and its implications can prove invaluable in achieving their objectives.