Markowitz Optimization, the Efficient Frontier, and Systematic Risk
Summary
The document asks whether Markowitz optimization reduces unsystematic risk while leaving systematic risk unchanged, and whether systematic exposure can be reduced. The response describes the framework as finding minimum-variance portfolios for specified expected returns. The set of these portfolios forms the efficient frontier: within the model's assumptions, no alternative portfolio has lower variance at the same return target. It characterizes the remaining risk at the minimum-variance boundary as systematic and not removable through diversification. To reduce total risk further, it notes that an investor could hold a risk-free asset, if one exists. Combining that asset with risky holdings allows different risk and return levels, while seeking returns above the risk-free rate entails exposure to systematic risk. The explanation is concise and conceptual, and it does not detail model assumptions, estimation uncertainty, or practical hedging methods for reducing market exposure.
Key ideas
- Markowitz optimization identifies minimum-variance portfolios for specified return levels under its assumptions.
- The minimum-variance portfolios across return targets define the efficient frontier.
- Diversification can reduce some portfolio risk, but the response describes residual frontier risk as systematic.
- A risk-free asset can reduce overall risk, while pursuing returns above its rate entails risky-asset exposure.
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# Markowitz portfolio optimization question # Markowitz portfolio optimization question I am studying the Markowitz portfolio optimization theory, and I just wanted to ask if I understood this correctly. For a stock portfolio we distinguish two kinds of risks: an unsystematic risk, which is due to the correlations between the stocks and which can be minimized by diversification, and a systematic risk, which is due to general trends in the market and which cannot be reduced by diversification. So, Markowitz portfolio optimization is a procedure to minimize this unsystematic risk by choosing appropriate weights. Right? It only deals with the unsystematic risk and not with the systematic one. Is there a way to reduce the systematic risk? Thanks. ## Answer by Bob Jansen (score 2, accepted) https://quant.stackexchange.com/a/17950 To answer your first question: Under the necessary assumptions, the Markowitz portfolio optimization framework can be used to obtain the minimum variance portfolio for a given level of return. Together all the portfolio with a minimum variance for a specified level of return are (or span) the efficient frontier. By definition it is not possible to get another portfolio with a lower variance than the lowest variance portfolio on this frontier. This risk can't be diversified away and is called systematic risk. For your second question, if a risk free asset exists it is of course possible to have no risk at all: create a portfolio fully invested in the risk free asset. If you want to create a portfolio with a higher return than the risk free rate you can combine the risk free asset with some asset. However, this will always lead to exposure to systematic, undiversifiable risk.
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