Discuss the Markowitz theory of efficient portfolio selection. How does the Capital Asset Pricing Theory (CAPM) theory build on it?

The Markowitz theory of efficient portfolio selection, developed by Harry Markowitz in the 1950s, is a foundational concept in modern portfolio theory. It aims to identify the optimal mix of assets that maximizes an investor’s expected return for a given level of risk. The theory relies on the idea that diversification can help reduce the total risk of a portfolio by combining assets whose returns do not move in perfect correlation with each other.

At the core of the Markowitz theory is the concept of risk and return. Risk is quantified by the variance or standard deviation of an asset’s return, while the return represents the expected return of the asset. Markowitz emphasized that investors should not only consider the return of individual assets but also how the returns of different assets correlate with one another. The main objective is to construct a portfolio that minimizes risk while achieving a desired level of return. The theory suggests that it is not sufficient to merely select assets based on their individual risk-return profiles. Instead, an investor must consider the relationships between assets, as the combination of assets can lead to a portfolio that has less total risk than the sum of the individual risks of the assets.

To explain this mathematically, Markowitz introduced the concept of the efficient frontier. The efficient frontier represents the set of portfolios that offer the highest expected return for a given level of risk. Any portfolio that lies below the efficient frontier ___ __________ _________ ____ ________ ____ _____ ___ ___ _______ _____ ________.
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