In general, the lower (less positive and more negative) the correlation between asset returns,

Modern portfolio theory (MPT) asserts that an investor can achieve diversification and reduce the risk of losses by reducing the correlation between the returns of the assets selected for the portfolio. The goal is to optimize the expected return against a certain level of risk.

Key Takeaways

• Followers of MPT seek a zero or near-zero correlation in the price movements of the various assets in a portfolio.
• That is, they seek assets that respond to macroeconomic trends in distinctly different patterns.
• The ideal selection of assets will have the highest possible return for the desired level of risk.

The modern portfolio theorist recommends that an investor measure the correlation coefficients between the returns of various assets in order to strategically select those that are less likely to lose value at the same time. That means determining to what extent the prices of the assets tend to move in the same direction in response to macroeconomic trends.

Perfect Correlation

MPT is a mathematics-based system for selecting investments that, in combination, will provide the best returns for a given level of risk.

The theory looks for the best correlation between the expected return and the expected volatility of various potential investments. The optimal risk-reward relationship was titled the efficient frontier by economist Harry Markowitz, who introduced modern portfolio theory in 1952.

A portfolio is known as "Markowitz-efficient" if its selection of assets has the highest expected return at a given level of risk.

If the correlation is zero, the two assets have no predictive relationship.

In MPT, the efficient frontier is where the investor will find the combination of assets that offers the highest possible return for a chosen level of risk. These assets demonstrate the optimal correlation between risk and return.

The Correlation Scale

Correlation is measured on a scale of -1.0 to +1.0:

• If two assets have an expected return correlation of 1.0, that means they are perfectly correlated. If one gains 5%, the other gains 5%. If one drops 10%, so does the other.
• A perfectly negative correlation (-1.0) implies that one asset's gain is proportionally matched by the other asset's loss.
• A zero correlation indicates the two assets have no predictive relationship.

MPT stresses that investors should look for a consistently uncorrelated (near zero) pool of assets to limit risk. In practical terms, that virtually guarantees a diversified portfolio.

Criticisms of Perfect Correlation Theory

One of the major criticisms of Markowitz's theory lies in its assumption that the correlation between assets is fixed and predictable. In the real world, the systematic relationships between different assets do not remain constant.

That means that MPT becomes less useful during times of uncertainty, which is exactly when investors need the most protection from volatility.

Others assert that the variables used to measure correlation coefficients are themselves faulty and the actual risk level of an asset can be miscalculated. Expected values are mathematical expressions of the implied covariance of future returns, and not historical measurements of real returns.

Yes, there is a positive correlation (a relationship between two variables in which both move in the same direction) between risk and return—with one important caveat. There is no guarantee that taking greater risk results in a greater return. Rather, taking greater risk may result in the loss of a larger amount of capital.

A more correct statement may be that there is a positive correlation between the amount of risk and the potential for return. Generally, a lower risk investment has a lower potential for profit. A higher risk investment has a higher potential for profit but also a potential for a greater loss.

key takeaways

• A positive correlation exists between risk and return: the greater the risk, the higher the potential for profit or loss.
• Using the risk-reward tradeoff principle, low levels of uncertainty (risk) are associated with low returns and high levels of uncertainty with high returns.
• An investor needs to understand his individual risk tolerance when constructing a portfolio.

Risk and Investments

The risk associated with investments can be thought of as lying along a spectrum. On the low-risk end, there are short-term government bonds with low yields. The middle of the spectrum may contain investments such as rental property or high-yield debt. On the high-risk end of the spectrum are equity investments, futures and commodity contracts, including options.

Investments with different levels of risk are often placed together in a portfolio to maximize returns while minimizing the possibility of volatility and loss. Modern portfolio theory (MPT) uses statistical techniques to determine an efficient frontier that results in the lowest risk for a given rate of return. Using the concepts of this theory, assets are combined in a portfolio based on statistical measurements such as standard deviation and correlation.

The Risk-Return Tradeoff

The correlation between the hazards one runs in investing and the performance of investments is known as the risk-return tradeoff. The risk-return tradeoff states the higher the risk, the higher the reward—and vice versa. Using this principle, low levels of uncertainty (risk) are associated with low potential returns and high levels of uncertainty with high potential returns. According to the risk-return tradeoff, invested money can render higher profits only if the investor will accept a higher possibility of losses.

Investors consider the risk-return tradeoff as one of the essential components of decision-making. They also use it to assess their portfolios as a whole.

Risk Tolerance

An investor needs to understand his individual risk tolerance when constructing a portfolio of assets. Risk tolerance varies among investors. Factors that impact risk tolerance may include:

• the amount of time remaining until retirement
• the size of the portfolio
• future earnings potential
• ability to replace lost funds
• the presence of other types of assets: equity in a home, a pension plan, an insurance policy

Managing Risk and Return

Formulas, strategies, and algorithms abound that are dedicated to analyzing and attempting to quantify the relationship between risk and return.

Roy's safety-first criterion, also known as the SFRatio, is an approach to investment decisions that sets a minimum required return for a given level of risk. Its formula provides a probability of getting a minimum-required return on a portfolio; an investor's optimal decision is to choose the portfolio with the highest SFRatio.

Another popular measure is the Sharpe ratio. This calculation compares an asset's, fund's, or portfolio's return to the performance of a risk-free investment, most commonly the three-month U.S. Treasury bill. The greater the Sharpe ratio, the better the risk-adjusted performance.  

What is the correlation between assets returns?

How correlation is related to portfolio return and risks for two assets?

Is there a positive correlation between risk and return?

Does a positive correlation between two assets increase or decrease risk if those assets are held in a portfolio?