# Markowitz’s Modern Portfolio Theory (MPT) Explained

Markowitz’s Modern Portfolio Theory, just like the efficient market hypothesis, is a tough nut to crack for new investors. It’s not an absolute enigma—that’s exaggeration—but it’s also not an easy concept to fully absorb.

## A Quick Trip Down Memory Lane

In the year 1952, a man named Harry Markowitz came up with an idea to write an essay. And the essay was about the Modern Portfolio Theory. This essay made Markowitz famous. It let him win a Nobel Prize in economics.

Markowitz’s model, however, also received many criticisms. We’ll tackle that later on. For now, let’s break down the key concepts of the MPT.

## Main Concepts of the Modern Portfolio Theory

The MPT sports two main concepts, and they are as follow:

- All investors’ goal is to earn as high as possible for any risk level.
- You can lower risk by having a portfolio diversified with unrelated assets.

According to the modern portfolio theory, you as an investor try to get as low risk as possible. You do that while simultaneously trying to earn the maximum level of income.

The modern portfolio theory tells us that risks are inherent to higher rewards. This, however, doesn’t mean that we cannot fortify our portfolios against risks. The theory tells us that we can create an “efficient frontier” by combing optimal portfolios. These portfolios should dish out the highest possible expected return for determined level of risk.

*See also Breaking Down Risk Management*

## Portfolio Risk and Expected Return

The modern portfolio theory assumes that all investors are averse to risks. That means investors will not take on additional risks if they don’t think they’ll get bigger rewards.

To calculate the expected return, you have to get the weighted sum of your assets’ returns. For example, your portfolio has four assets that are equally weighted. Your expected returns are 4, 6, 10, and 14 percent. Your portfolio’s return would be:

(4 percent x 25 percent) + (6 percent x 25 percent) + (10 percent x 25 percent) + (14 percent x 25 percent) = 8.5 percent.

Meanwhile, the risk of your portfolio takes a little bit more time to calculate. The risks are a complex function of variances each asset and their correlation.

If you want to know the risk of a portfolio with four assets, you have to get each of the asset’s variances and the six correlation values. Due to the asset correlations, the portfolio risk is lower than the value of the weighted sum.

We use standard deviation for the overall portfolio risk, and we’ll discuss what that is below.

*Read further Asset Allocation: Your Roadmap to a Powerful Portfolio*

## Standard Deviation

Standard deviation is one of the most common risk measures that we use. It measures the dispersion of a set of data from its mean, or average.

How do we calculate it? You calculate it as the square root of variance. But first, you have to find the variation between each data point relative to the mean. If you find that the data points are far from the mean, there’s higher deviation within the data set.

If you have greater deviation, you have greater variance between each price and the mean. That also indicates a bigger price range.

Sounds too geeky? Let’s try to break it down further comparing it to the things that look similar to it.

### Standard Deviation vs. Mean

The mean is simply the average of all your data points in your set. To illustrate, you may want to check the average closing price for the last 10 days. What you do is you get all closing prices for the last 10 days and then add them. Then, you divide the sum you get by 10. The resulting number is the average, or mean, of the data points.

Now, you calculate standard deviation based on the mean or average. You get the distance of each data point from the mean, and then you square those distances. Then you add them up, and then you get their average—that’s your variance. Then, to get the standard deviation, you have to find the square root of the variance.

### Standard Deviation vs. Variance

The variance helps you find the data’s spread size when you compare them to the mean value. If you see the variance getting bigger, you get more variation in data value takes place. That means you may find a larger gap between one value and another. If you see the data values are closer, the variance then is smaller

On the flip side, the variance may be more difficult to visualize than standard deviation. This is because variances are squared results. And you may not meaningfully express these values on the same graph, where the original data sets are.

It goes without saying that standard deviations are easier to picture and apply. You can express standards deviation using the same unit of measures as the data. And that’s not the case with variances.

## Returns and Risks, Maximize and Minimize

First, let’s clarify what return is. Return is the price appreciation of any asset, such as the stock price. We can efficiently measure this by using standard deviation. As discussed above, standard deviation can also measure the risks.

Let’s discuss one practical application of the Markowitz’s modern portfolio theory.

Suppose there are two portfolios with assets sporting 10 percent average return. The first portfolio has a standard deviation of 8 percent, while the second has 12 percent. Since both of them sport the same expected return, more investors will choose the first portfolio. That’s obviously because it has less risks.

Remember that higher risks typically mean higher rewards. This may mean that the second portfolio looks more attractive. It may even get a return of 22 percent. Again, due to the risks, the second portfolio may get a return of -2 percent.

## Diversification and Efficient Frontier

As our example indicates, risks also entail rewards. If you take the right choices and withstand risk, you may reach your goals more quickly.

On the other hand, the modern portfolio theory tells us that we could significantly lower these risks. We can do that by diversifying. When we diversify, we must mix diverse, unrelated assets into our portfolio.

When your assets are unrelated, the risks they sport are also unrelated. The opposite is also true. If the assets are more closely related, their prices will probably move similarly.

For instance, two ETFs with the same sectors and industries will probably take the same hit from economic factors. If the two ETFs have different sectors and industries, they wouldn’t be affected similarly by the same factor.

In other words, you must have assets with low correlations to lower the risks.

To illustrate, you can measure the correlation using -1 and +1. If it’s +1, the assets sport high correlation. This means that the prices will move in the same direction. Meanwhile, -1 means the assets are not very much correlated. This means that the prices will not move in the same direction.

As implied above, the efficient frontier is the set of optimal portfolios that give you higher expected returns. When the portfolio falls under the efficient frontier curve, that portfolio is sub-optimal. This means that it doesn’t offer enough return for the determined risk level.

Simply put, an optimal portfolio can reach the efficient frontier if it’s very well-diversified.

*Related: Spreading Out Investments for Reducing Risks*

## Criticisms

The modern portfolio theory also has its fair share of criticisms from different investors. Typically, these investors are the same ones who use technical analysis. This is not surprising since the modern portfolio theory essentially has the buy-and-hold nature.

They argue that an understanding of behavior and price volatility in the markets can be more ideal for investors than the MPT approach.

On the flip side, many investors are not really good at timing the market. More so, a huge number of investors don’t have the knowledge, time, and psyche to be good at it. This tells us that more investors can follow the MPT and benefit from it.

Others, meanwhile, only incorporate the MPT’s key concepts into their asset allocation techniques.

Another criticism of the MPT arises from its assumptions. For one, it assumes that investors are rational and risk-averse. It tells us that investors will try to avoid risks as much as possible. The MPT also assumes that there aren’t enough investors that can affect the market.

However, there are in fact risk-seeking and irrational investors in the market. There are also large market participants that can definitely influence market prices. There’s also the fact that investors do not have infinite access to borrowed or lent money.

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