Limitations of Markowitz Model 🏗️⚠️

While Harry Markowitz won a Nobel Prize for his model, and it remains the bedrock of modern finance, it is rarely used in its original form by individual investors. In this chapter, we look at the practical hurdles of the Markowitz Model.

1. The "Input" Explosion 💥

The biggest problem with the Markowitz full-covariance model is the sheer number of estimates required. To build a portfolio of N stocks, you need:

• N Expected Returns.
• N Variances.
• [N * (N-1)] / 2 Covariances.

If you want to analyze just 50 stocks, you need 1,225 covariance estimates. If you want to analyze 500 stocks (like the S&P 500), you need 124,750 estimates!

2. Sensitivity to Error (GIGO) 🗑️

Markowitz portfolios are extremely sensitive to the input data. This is often called "Garbage In, Garbage Out" (GIGO).

• If your estimate for a stock's return is off by just 1%, the model might tell you to put 0% in it instead of 20%.
• The model often produces "corner solutions" where it suggests putting all your money into just 2-3 weirdly correlated stocks, which feels very un-diversified.

3. The Stationary Assumption 🕒

The model assumes that historical correlations and variances will remain the same in the future.

• Reality: In a market crash, correlations often jump to 1.0. Everything falls together.
• The model's "Optimal" portfolio during normal times may become the worst portfolio during a crisis.

4. Transaction Costs & Taxes 💸

The theoretical model assumes you can buy and sell stocks for free. In reality, rebalancing a 50-stock portfolio every week to stay on the "Efficient Frontier" would destroy your returns through brokerage fees and capital gains taxes.

Summary

• The Markowitz Model is mathematically perfect but practically difficult.
• The Complexity of calculating thousands of correlations is the main barrier.
• It is highly sensitive to errors in estimation.
• In the next unit, we will see how William Sharpe solved these problems with the Single Index Model.

Quiz Time! 🎯

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