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### Understanding Modern Portfolio Theory (MPT)

Understanding Modern Portfolio Theory (MPT)

Modern portfolio theory argues that the risk and return characteristics of an investment should not be considered separately, but should be judged by how the investment affects the overall risk and return of the portfolio. MPT shows that an investor can create a portfolio of multiple assets that maximizes returns for a given level of risk. Likewise, given the desired level of expected return, an investor can build a portfolio with the lowest possible risk. Based on statistics such as variance and correlation, the performance of individual investments is less important than how they affect the entire portfolio.

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MPT assumes that investors are risk averse, that is, they prefer a less risky portfolio to a more risky one for a given level of return. In practice, risk aversion implies that most people must invest in multiple asset classes.

The expected portfolio return is calculated as the weighted sum of the individual asset returns. If a portfolio contains four equally weighted assets with expected returns of 4, 6, 10, and 14%, the expected portfolio returns are:

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(4% x 25%) + (6% x 25%) + (10% x 25%) + (14% x 25%) = 8.5%

Portfolio risk is a complex function of the variance of each asset and the correlation of each pair of assets. To calculate the risk of a portfolio with four assets, an investor needs the variance of each of the four assets and six correlation values, since there are six possible combinations of two assets with four assets. Because of asset correlation, the overall portfolio risk or standard deviation is lower than what would be calculated using a weighted sum.

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Benefits of Modern Portfolio Theory (MPT)

MPT is a useful tool for investors trying to build diversified portfolios. In fact, the rise of exchange-traded funds (ETFs) has made the MPT more relevant by giving investors easier access to various asset classes. Equity investors can use the MPT to mitigate risk by placing a small portion of their portfolios in government bond ETFs. Portfolio variance will be significantly lower as government bonds are negatively correlated with stocks. Adding a small investment in Treasury bonds to a portfolio of stocks will not have much of an impact on expected returns due to this loss-reducing effect.

Similarly, MPT can be used to reduce the volatility of a US Treasury portfolio by investing 10% in a small-cap index fund or ETF. While small-cap stocks are much more risky than Treasury bonds themselves, they often do well during periods of high inflation when bonds perform poorly. As a result, the overall volatility of the portfolio is lower than the portfolio of all government bonds. In addition, the expected return is higher3.

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Modern portfolio theory allows investors to build better performing portfolios. Every possible combination of assets that exist can be plotted with portfolio risk on the X-axis and expected returns on the Y-axis. This plot reveals the most desirable portfolios. For example, suppose portfolio A has an expected return of 8.5% and a standard deviation of 8%. Further, assume that portfolio B has an expected return of 8.5% and a standard deviation of 9.5%. Portfolio A will be considered more efficient because it has the same expected return but less risk.

An upward curve can be drawn to connect all the top performing portfolios. This curve is called the effective frontier. Investing in a portfolio below the curve is undesirable because it does not maximize returns for a given level of risk.

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Most performance frontier portfolios contain ETFs from more than one asset class.

Critique of Modern Portfolio Theory (MPT)

Perhaps the biggest criticism of the MPT is that it evaluates portfolios based on variance rather than downside risk. According to modern portfolio theory, two portfolios with the same level of variance and return are considered equally desirable. One portfolio can have this variance due to frequent small losses. On the contrary, another may have such a difference due to rare spectacular falls. Most investors would prefer frequent small losses that are easier to bear. Postmodern Portfolio Theory (PMPT) attempts to improve modern portfolio theory by minimizing the risk of deterioration instead of variance.

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