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, introduced by Harry Markowitz in 1952, revolutionized the way investors think about portfolio management. It provided a systematic approach to selecting a portfolio of assets that maximizes return for a given level of risk. Markowitz’s theory is grounded in the concept of diversification, which is the practice of spreading investments across various assets to reduce overall portfolio risk. His work laid the foundation for modern portfolio theory (MPT), which forms the basis of many investment strategies today.

Markowitz's efficient portfolio theory assumes that investors are rational and risk-averse. This means that they aim to maximize returns while minimizing risk. The risk in a portfolio is defined by the variability of returns, typically measured by the standard deviation (or variance) of asset returns. According to Markowitz, risk can be reduced through diversification. By combining assets with different return profiles, an investor can reduce the total risk of the portfolio without necessarily reducing its expected return.

Markowitz focused on two key variables: expected returns and the risk (volatility) associated with those returns. He introduced the concept of an "efficient frontier," which is a curve that represents a set of portfolios that offer the highest expected return for a given level of risk or, conversely, the least risk for a given level of expected return. The efficient frontier is derived from the correlation between the returns of different assets within the portfolio. If assets in a portfolio are not perfectly correlated, then combining them can reduce the overall risk of the portfolio, leading to better diversification.

To apply the theory, Markowitz created a mathematical framework that allows investors to evaluate the risk and return of different combinations of assets. The theory uses the covariance matrix of asset returns to understand how different assets move relative to one another. The idea is that combining assets with low _______ ________ _____ __________ _____ _________ __________ __________ ____ _________.
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