Relationship Between Negative Expected Return & Positive Beta

The capital asset pricing model (CAPM) attempts to define the relationship between an investor's expected return and the level of risk she assumes when choosing a particular investment. The model tries to explain the behavior of a security's price and the impact it will have on your portfolio's risk and return. CAPM's measure of risk is beta.

Beta is a measure of the relationship between a particular security's return and the overall return of the market. It is a measure of the non-diversifiable risk of a security. Beta can either be positive or negative, although most of the time it is positive. A positive beta means that the return of the security moves in the same direction as the market, whereas a negative beta shows that the security's return moves in the opposite direction of market return. For example, a beta of .5 suggests that you should expect the return of the stock to change by a positive .5 percent for each 1 percent change in the market return.

The main components in calculating your expected return are the return of the market, the risk-free rate of return and beta. The risk-free rate of return is usually measured using the return of Treasury bonds for the current period. Your risk premium, or how much you need to earn to compensate for the level of risk that you undertake when choosing a particular security, is determined by subtracting the risk-free rate of return from the overall return of the market and multiplying it by the beta of the individual security. Adding this number to the risk-free rate of return will give you your expected return for the security.

The only way to produce a negative expected return with a positive beta is if the risk-free rate of return exceeds the overall return of the market. This is unlikely to ever occur, as investors will not choose to purchase more risky securities without the possibility of a greater return.

The predictions and usefulness of CAPM have been disputed for decades. While most financial analysts still study the model and use it in a predictive fashion, there have been theories surrounding the authenticity. One theory is that highly volatile stocks will, over time, produce a mean return that is negative. This will occur even if beta is positive, as long as it is a large numerical value. This negates the basic premise on which CAPM was developed, but it might occur in some cases. Financial experts often call this a "black swan," so named for something that is rare, but you may see it at some point.

If the expected return of your overall portfolio is negative, it is likely that most of your securities have a negative beta. You may want to diversify your portfolio by choosing more securities with a positive beta to help stabilize the movement in your portfolio and produce a return that is more likely to follow the market on an upswing. A positive beta suggests that a security will move in the same direction as the market, so purchasing more securities with positive betas will provide a more direct correlation to the movement of the market.