Beta is an important metric in modern portfolio theory, and it is meant to measure volatility. Returns generated by a specific stock or fund must be adjusted to account for volatility risk when the contributions to success or failure are compared to a benchmark index. Alpha is a metric that measures the amount by which actual returns exceed expected returns. The expected value of a return is based on its volatility relative to the benchmark and the correlation to that index.

High beta indicates more volatility, so better performance is required from high-beta investments to produce the same level of risk-adjusted returns. However, beta is an imperfect measure of volatility in some circumstances, and it can be misleading for investors who are not careful to identify the limits of the metric's explanatory value. Beta becomes a less valuable measure of volatility if calculation methodology does not match investor needs, if correlation to the benchmark index is low or if tail events are incorrectly included or excluded from calculation.

### Methodology and Time Horizon

Beta has a universal conceptual calculation, but some specific inputs can vary among investors from case to case. For example, the benchmark against which a stock's volatility is compared can change based on preference or purpose of comparison. If the benchmark used in beta calculation is a volatile index, then the calculated beta will look deceptively small for investors who have diversified portfolios and do not expect significant fluctuation in the values of their holdings. The time horizon over which beta is calculated can also vary from source to source. Beta can reflect data collected over weeks, months, years or decades. Long-term investors who intend to buy and hold a stock should focus on longer-term beta to gain a better understanding of volatility, whereas short-term holders might not be concerned about the volatility experienced by a stock five to 10 years in the past. Mismatch of calculation time horizon and investor time horizon can materially alter the explanatory value of beta.

### Lack of Correlation

Beta measures the amount a security or portfolio moves in relation to an index, but the statistic's applicability is incomplete without context. Beta measures volatility, but it does not measure correlation. R-squared is the metric used to evaluate correlation, and beta can be less meaningful if it is paired with a low R-squared value. A stock with low beta might appear to lack volatility relative to a popular benchmark index, but R-squared below 0.5 indicates very limited correlation to that index. Therefore, the low beta is not necessarily a reliable indicator of volatility relative to the benchmark. Investors who are volatility-risk averse should check R-squared to confirm beta's relevance and to avoid being misled by insignificant statistics.

### Timing of Tail Events

Tail events are highly uncommon events that can cause drastic changes to asset prices. Tail events are usually defined as those causing a movement of three standard deviations from the starting price, representing extreme volatility against which investors may want to protect. For stocks, such events would likely be event driven, resulting from news about the company. Event-driven moves include those related to acquisitions, unexpected financial results, supplier or distribution deals, credit rating changes and other things that can affect financial fundamentals. Tail events are rare, and they are therefore absent from the calculation of beta across many time frames, especially shorter horizons. When a shock does occur, the beta right before the event does not reflect this risk, either to the upside or downside. Moreover, beta after the shock likely overstates the volatility risk because tail events tend not to occur repeatedly in a short time frame. These events distort the true relationship between beta and volatility.