If you have a financial planner, or if you're planning on investing without one, you should know about Modern Portfolio Theory, or MPT, first espoused by American economist Harry Markowitz. For his work, Markowitz was awarded the Nobel Memorial Prize in Economic Sciences in 1990.

## What Is Modern Portfolio Theory?

Modern Portfolio Theory is Markowitz's theory regarding maximizing the return investors could get in their investment portfolio considering the risk involved in the investments. MPT asks the investor to consider how much the risk of one investment can impact their entire portfolio.

Markowitz, in a 1952 paper published by The Journal of Finance, first proposed the theory as a means to create and construct a portfolio of assets to maximize returns within a given level of risk, or to devise one with a desired, specified and expected level of return with the least amount of risk.

He wanted to eliminate "idiosyncratic risk," or the risk inherent in each investment because of the investment's own unique characteristics.

Markowitz theorized that investors could design a portfolio to maximize returns by accepting a quantifiable amount of risk. In other words, investors could reduce risk by diversifying their assets and asset allocation of their investments using a quantitative method.

With a well-balanced and calculated portfolio, if some of the assets fall due to market conditions, others should rise an equal amount in compensation, according to MPT.

Markowitz demonstrated that, by taking a portfolio as its whole, it was less volatile than the total sum of its parts.

To begin with, Markowitz assumed that most investors are, in their hearts, risk-averse. That means they are more personally comfortable with less risk, and nervous and anxious with increased risk. This also translates into the belief that it is better to not lose money than to find or gain it.

So, given a choice between a higher return possibility with greater risk, and a lower return possibility with less risk, most people will naturally prefer the portfolio with the least risk, even if it means a lower return.

The investor then naturally views a correlation between increased risk and potential higher returns as compensation.

This gets to the heart of Markowitz's theory. Given two portfolios, an investor will naturally prefer one that indicates the highest return possibility with the least risk.

Portfolio Selection, the original title of his ground-breaking theory, was published in March 1952 in The Journal of Finance, published by the American Finance Association. In it, Markowitz argued that portfolios should optimize expected return relative to volatility. He considered volatility could be measured as the variance of return. He suggested also a limit he called the "efficient frontier."

Markowitz published the treatise when he was with the Rand Corporation. In it, he notes, "the process of selecting a portfolio may be divided into two stages. The first stage starts with observation and experience and ends with beliefs about the future performances of available securities. The second stage starts with relative beliefs about future performances and ends with the choice of portfolio."

"Diversification is both observed and sensible; a rule of behavior which does not imply the superiority of diversification must be rejected both as a hypothesis and as a maxim," he added.

The gist of this selection method is that a portfolio's assets must be selected on the basis of how each asset will impact others as the overall value of the portfolio changes.

## Why Is Modern Portfolio Theory Important?

So, when your financial adviser or you decide to have a "diversified portfolio," with assets divided up by percentage in different instruments and sectors -- such as 60% equities (40% large-cap, 20% small-cap), 20% commodities, and 20% fixed income -- that's Modern Portfolio Theory. Also, when you have to manage your own portfolio of investments, whether they be mutual funds or specific securities within your 401K, it helps to know a bit about allocation of your investments versus allocation or calculation of the risks.

Most advisers and even fund managers will do much of the work for you, which is why it is harder to try and do it yourself. For example, in making decisions for investing in a company-provided 401(k), often the manager of the overall portfolio of your choices will provide at the very least the stock or mutual fund's previous return history, and compare it with market returns, to help you, the individual investor, decide how to allocate your investments.

A good broker or financial adviser will ask you what you think is your "risk profile" -- how much risk are you willing to take to get how big a return on your investment? Generally speaking, younger investors can "tolerate" more risk, because they'll have more time to make back money lost in a downturn; older people, especially living on a fixed income, have far less risk tolerance, because they might not have the time on earth it may take to recover from a downturn.

## Examples of Modern Portfolio Theory: Expected Return, Calculated Risk

At its heart, MPT is a mathematical justification for asset allocation within a portfolio, as it amounts to a weighted average of the expected returns on individual assets.

As an example, say an investor has a two-asset portfolio (for simplicity), with $800,000 in one asset, and $200,000 in the other. This investor has a portfolio worth $1 million.

The investor wants an expected return of 5% on the asset with more invested, and a 10% return on the asset with the least.

To calculate the expected return of the portfolio, you divide the current value of the first asset by the total value of the portfolio, and multiply it by its expected return:

Portfolio Expected Return = $800,000 divided by $1 million, times 5%.

And you do the same for the second asset:

Portfolio Expected Return = $200,000 divided by $1 million, times 10%.

So, for the "heaviest-weighted (most invested) asset," you get an expected return of actually 4%; for the second, least heaviest-weighted asset, you get an expected return of 2%.

Add them together, and the portfolio as a whole can expect a return of 6%.

To increase the expected portfolio return, then, to 7.5%, the investor merely needs to shift an appropriate amount of capital to the less-heavily weighted asset from the most-heavily weighted one.

In the above example, it turns out that a 50-50 allocation of capital will result in that:

Portfolio Expected Return of 7.5% = 50% x 5% = 2.5%

Plus 50% x 10% = 5%

Portfolio Expected Return = 2.5% + 5% = 7.5%

Portfolio of Expected Return of 7.5%

The same can be true, also, if the investor of the same $1 million portfolio wants to increase or reduce risk in the portfolio.

A risk quantifying statistic known as "beta" comes from MPT. Beta is an attempt to quantify a portfolio's susceptibility to systematic risk within a market. A beta of 1 means the systematic risk exposure of a portfolio is the same as exists in the market. Higher betas indicate more risk, and lower indicate less.

Now, let's divide the investor's $1 million portfolio into four assets as opposed to the original two. And let's say the investor at least originally allocates all four assets equally.

The first asset has a beta of 1, so its systematic risk exposure is identical to the market. The second asset has a beta of 1.6, as the investor is willing to tolerate a bit more risk than the market. The third has a beta of 0.75, which is even less the normal market exposure; and the last has an even lower beta, of 0.5.

Multiplying the allocation of 25% with each beta and adding the results gives us an overall portfolio beta of 0.96. As it is below 1, though near it, the portfolio can be said to be taking on as much systematic risk as the market.

If the investor decides to take on more risk, in hopes of achieving a higher return, the risk-averse investor may still decide 1.2 is the ideal beta for the portfolio. By adjusting the weighting of the four assets within the portfolio, a beta of 1.2 could be conceivably achieved.

One way would be to invest more capital in the one asset with the greatest beta: the second asset.

Supposing the investor shifted 10% of the third and fourth assets - those with the lowest risk betas of the portfolio - and 5% away from the first asset, and invested that in the highest-beta asset, the second asset. Then, the second asset, which started with a 25% allocation, would have 50% of the portfolio's capital, the first would have 20%, and the third and fourth would have 15% each.

First asset beta = 20% x 1 = 0.2

Second asset beta = 50% x 1.6 = 0.8

Third asset beta = 15% x 0.75 = 0.11

Fourth asset beta = 15% x 0.5 = 0.08

The new beta would be 1.19, almost matching the desired beta of 1.2 by changing some weightings in the portfolio.

## Issues With Modern Portfolio Theory

Critics contend MPT doesn't deal with the real world, because all the measures used by MPT are based on projected values, or mathematical statements about what is expected rather than real or existing. Investors have to use predictions based on historical measurements of asset returns and volatility in the equations, which means they are subject to be changed by variables currently not known or considered at the time of the equation.

Investors have to estimate from past market data because MPT tries to model risk in terms of the likelihood of losses, without a rationale for why those losses could occur. That makes the risk assessment probabilistic, but not structural.

In other words, the mathematical model of MPT makes investing appear orderly when its reality is far less so.

As an example, contrary to what the theory predicts, a researcher in the late 1970s, Sanjay Basu, demonstrated that low price-to-earnings ratio (P/E) stocks outperformed high P/E stocks. And in the early 1980s, another researcher, Rolf Banz, demonstrated that small-capitalization stocks outperformed large-cap stocks.

This is the reason most investment professionals will note in their documentation that "past performance does not necessarily predict future results." Another reason is that the Securities and Exchange Commission requires it.

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