## What Is the Risk Curve?

The risk curve is a two-dimensional display that generates a visualization of the relationship between the risk and return of one or more assets.

The risk curve can contain multiple data points representing various individual securities or classes of assets. It is used to display this data for purposes of mean-variance analysis, which is central to understanding the relative risk and return of different asset classes and categories in portfolios and in investment models such as the Capital Asset Pricing Model (CAPM) and Modern Portfolio Theory (MPT).

### Key Takeaways

- The risk curve is a visual depiction of the tradeoff between risk and return among investments.
- The curve denotes that lower-risk investments, plotted to the left, will carry lesser expected return; those riskier investments, plotted to the right, will have a greater expected return.
- Such a risk curve is the efficient frontier, which is used as a cornerstone of Modern Portfolio Theory (MPT) in its process of mean-variance optimization.

## Understanding the Risk Curve

The risk curve is used to display the relative risk and return of similar or dissimilar assets. Typically, the x-axis (horizontal) represents risk level and the y-axis (vertical) represents the average or expected return. Generally speaking, the risk curve balloons when the investment being considered offers greater risk and returns and contracts when it offers lower risk and returns.

For example, a relatively “risk free” asset such as a 90-day U.S. Treasury bill will be positioned on the lower-left corner on the chart—while a riskier asset such as a leveraged ETF or a small-cap growth stock will appear toward the top right.

Riskier assets with a wide range of historical gains and losses will also tend to a higher average expected return. In other words, the tradeoff between an investment's risk and expected return tends to be proportional.

## The Risk Curve in MPT and the Efficient Frontier

Modern Portfolio Theory makes use of the risk curve to display the potential benefits of different portfolios across the efficient frontier. Portfolios that lie below the curve or efficient frontier are sub-optimal, because based on historical returns, they do not provide enough return for the level of risk assumed.

Portfolios that cluster to the right below the curve are also viewed as sub-optimal because based on historical returns, they return proportionately less than what may be available in other portfolios of similar risk.

## Special Considerations

It should be noted that the data typically used in creating risk curve models are based on the historical standard deviation of each asset.

For example, a point on the chart representing an investment in the S&P 500 Index will take into account the level of risk implied by historical variance in returns and also the expected mean (average) return on the index as a whole. The periods that the data represent will affect the asset's position on the risk curve. The actual future risk and return that investors experience going forward, of course, varies daily and is unknown.