What is the Difference Between Alpha and Beta Anomers?

The terms "alpha" and "beta" are used to evaluate the performance of a stock, fund, or investment portfolio. However, they have distinct meanings and should not be confused with each other.

• Alpha measures the performance of an investment in relation to the overall market or a benchmark. A high alpha indicates that the investment has performed well compared to the market, while a low alpha suggests that the investment has underperformed the market.
• Beta measures the relative volatility of an investment in comparison to a benchmark. A beta of less than 1 indicates that the security is less volatile than the market, while a beta greater than 1 suggests that its price is more volatile than the market.

The beta anomaly refers to the negative (positive) alpha on stocks with high (low) beta, which arises from beta's positive correlation with idiosyncratic volatility (IVOL). This anomaly occurs when stocks with high betas give lower risk-adjusted returns, meaning that stocks with high betas tend to have high volatilities, causing the Sharpe ratios of high beta stocks to be lower than the Sharpe ratios of low-beta stocks.

In summary, the main difference between alpha and beta anomalies is that alpha measures the performance of an investment relative to the market, while beta measures the volatility of an investment relative to the market. The beta anomaly refers to the phenomenon where stocks with high betas have lower risk-adjusted returns.

Comparative Table: Alpha vs Beta Anomers

Here is a table summarizing the differences between alpha and beta anomers:

The key difference between alpha and beta anomers lies in the position of the hydroxyl group at the anomeric carbon. In alpha anomers, the hydroxyl group is cis to the exocyclic oxygen, while in beta anomers, the hydroxyl group is trans to the exocyclic oxygen.