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The Markowitz theory of efficient portfolio selection, often referred to as Modern Portfolio Theory (MPT), revolutionized investment analysis by introducing a systematic framework for selecting a portfolio that maximizes expected return for a given level of risk. Prior to Markowitz, investors largely focused on selecting individual securities based on their expected returns without fully incorporating the implications of risk diversification. Markowitz formalized the idea that diversification is not just a matter of intuition but can be quantitatively measured and optimized. The central premise of Markowitz’s theory is that investors should not evaluate assets in isolation but as components of a portfolio. The expected return of a portfolio is simply the weighted average of the expected returns of its constituent assets. However, the risk of a portfolio, measured as variance or standard deviation of returns, is not merely a weighted average of individual risks. Instead, portfolio risk depends on the covariance between assets. If assets are not perfectly correlated, combining them reduces overall risk through diversification. This insight demonstrated mathematically that rational investors can achieve a superior risk-return trade-off by constructing portfolios that exploit imperfect correlations among assets. Markowitz introduced the concept of the “efficient frontier,” a set of portfolios offering the maximum expected return for each level of risk. Investors, according to his theory, would rationally choose portfolios on this frontier, as any portfolio inside the frontier is suboptimal, offering lower returns for the same risk or higher risk for the same return. The efficient frontier has a concave shape due to diminishing marginal benefits of diversification. Rational portfolio selection, then, involves choosing a point along the efficient frontier consistent with an investor’s risk preference __________ __________ ____ ____ ______ ____ ____ _______ _________ ________ _________ ___.
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