## Definition:

Modern Portfolio Theory (MPT) is a financial method that attempts to maximize return while minimizing risk. The basis of this method is an investment diversification whereby investments are selected based on their historic ability to provide an expected return higher than that of individual assets, while maintaining a level of risk that is lower than the individual assets.

Risk reduction is possible due to the historic correlations (or inverse correlations) various asset classes have in relation to each other. For example, a collection of stocks and bonds held together can face overall lower risk than held individually. Even if the asset class returns are positively correlated, risk is reduced. By combining these different assets in a portfolio, MPT effectively reduces the expected level of variance within the overall portfolio while maintaining, or maximizing the expected return.

Critics of MPT model will point out that it assumes that financial markets are rational and efficient. Additionally, they point out that asset class correlations may change over time, and will vary greatly in times of crisis caused by external factors.

## Modern Portfolio Theory History:

Often referred to as the “Markowitz model”, MPT was first introduced in a 1952 article ("Portfolio Selection". The Journal of Finance) and a 1959 book (“Portfolio Selection: Efficient Diversification of Investments) by Harry Markowitz. His research in the area of portfolio optimization was fundamental in the Capital Asset Pricing Model (CAPM). In 1990 he was awarded the Nobel Prize in Economic Sciences for his contributions in portfolio theory, sparse matrix methods, and simulation language programming.

## Mathematics:

Where:

• R_{p} = Return on portfolio

• R_{i} = Return on asset i

• w_{i} = Weighting on asset i

• ρ_{ij} = Correlation coefficient for assets i and j

Example:

Assume you have an IRA worth $10,000. You can allocate your holdings between 10 different mutual funds. There are funds with stocks, and bonds with historical returns ranging from -20% to 30% over five years. You ask your friend in finance and he tells you that his portfolio has 8 of the 10 funds. You ask him if he hates money, and he laughs and explains.

“A portfolio of assets will have a greater return if you diversify your asset selections optimally. By selecting several different funds that taken together appreciate over time, I can reduce the expected amount of variance in my portfolio. It’s a little tricky, and some math is needed, but together that portfolio of assets will have a greater expected return than each individual fund.”

Advantages:

• Theory allows investors to reduce exposure to individual assets.

• It defines boundaries for expected returns for a given portfolio of assets, thus limiting expected loss and assisting with capital allocation.

Disadvantages:

• Backward looking analysis based solely on historical results.

• Assumes a rational, efficient financial market which is an optimistic assumption at best.

• Assumes a normal distribution of asset returns, within an asset class, which for individual equities has been proven to be a false assumption.

References:

• Markowitz, H.M. (1959). Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley & Sons.

• Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance