What is the Risk Curve

The risk curve is a two-dimensional display creating a visualization of the relationship between risk and return of one or more assets. The risk curve can contain multiple data points representing different assets and is used to display data in mean-variance analysis which is central to understanding the relative risk and return of different asset classes and categories in portfolios and the Capital Asset Pricing Model.


The risk curve can be used to display the relative risk and return of similar or dissimilar assets. Typically, the x-axis (vertical) represents risk and the y-axis (horizontal) represents average return. Generally speaking, the curve balloons when the underlying item offers greater returns and contracts when it offers lower returns compared to risk. For example, a relatively “risk free” asset such as a 90-day Treasury bill will be positioned lower-left on the chart while an asset such as a leveraged ETF or an individual stock with a wide range of historical gain and loss but also a higher average return will be proportionately to the right and higher up on the chart.

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.

It should be noted that the data typically used in creating risk curve models is 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 which the data represent will affect the assets position on the risk curve. The actual future risk and return that investors experience going forward, of course, varies daily and is unknown.