If you ask investors what risk they assume when buying stocks, they likely will respond, “Losing money.” Modern portfolio theorists do not, however, define risk as a likelihood of loss, but as volatility, which is determined using statistical measures of variance such as standard deviation and beta. While standard deviation is a measure of absolute volatility that shows how much an investment’s return varies from its average return over time, beta is a measure of relative volatility that indicates the price variance of an investment compared to the market as a whole. The higher the standard deviation or beta, the higher the risk, according to the theory. In a rising market, however, high volatility can boost the return potential of an investment. Volatility, in other words, is essentially a double-edged sword, and does not measure what an investor intuitively perceives as risk.

Suppose the price of a stock goes up 10 percent in one month, 5 percent the next, and 15 percent in the third month. The standard deviation would be five with a return of 32.8 percent. Compare this to a stock that declines 15 percent three months in a row. The standard deviation would be zero with a loss of 38.6 percent. An investor holding the falling stock might find solace knowing that the loss was incurred completely “risk-free.”

If we accept that risk is not the same as volatility, however, we must also question any portfolio strategy that relies on this view. Portfolio Selection Theory (developed by Markowitz) and CAPM (Capital Asset Pricing Model, developed by Sharpe based on the theory of market equilibrium) both assume a positive correlation between risk (defined as volatility) and return. Using this logic, higher expected returns can only occur with correspondingly higher risk; and investors who seek to lower their risk levels must reduce their return expectations accordingly.

This assumption is the platform upon which modern portfolio theorists are building“optimal portfolios” using intricate mathematical models intended to maximize returns at a given level of risk or minimize risk at an expected level of return.