Markowitz Portfolio Theory

In 1952, Harry Markowitz published his PhD thesis that changed finance forever. He won the Nobel Prize in Economics (1990) for this work.

Core Idea

Investors should not look at each stock in isolation; they should consider the entire portfolio. The goal is to find the portfolio that offers the highest return for a given level of risk (or lowest risk for a given return).

Key Assumptions

1. Rational Investors: Investors are risk-averse and prefer higher returns to lower returns.
2. Mean-Variance Framework: Return is measured by Expected Return (Mean). Risk is measured by Variance/Standard Deviation.
3. Single Period: Investors make decisions for one period (e.g., 1 year).
4. Perfect Information: All investors have access to the same information.
5. No Transaction Costs or Taxes: Simplifying assumption (not realistic but helps theory).

The Framework

Markowitz Portfolio Selection involves:

Inputs:

1. Expected Returns of all assets.
2. Variances (risk) of all assets.
3. Covariances between all pairs of assets.

Output:

An Efficient Portfolio that:

• Maximizes return for a given level of risk, OR
• Minimizes risk for a given level of return.

Example (Simplified)

Suppose you have two stocks:

• Stock A: Expected Return = 10%, Variance = 100
• Stock B: Expected Return = 15%, Variance = 225
• Covariance(A, B) = 50

Markowitz's model calculates the optimal weights (%) to invest in each stock to achieve the best risk-return combination.

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