In finance, Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. It is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. The slope coefficient in a regression of a fund's excess returns against the excess returns of a benchmark is indeed the Beta. This is because Beta measures the sensitivity of the expected excess asset returns to the expected excess market returns. So, when we regress the excess returns of a fund (the dependent variable) on the excess returns of the benchmark (the independent variable), the slope coefficient we get is the Beta. It tells us how much, on average, the fund's excess returns will change when the benchmark's excess returns change by one unit.

Choice A is incorrect. Alpha refers to the excess return of an investment relative to the return of a benchmark index. It does not represent the slope coefficient in a regression analysis comparing a fund's excess returns to those of a benchmark.

Choice C is incorrect. The residual error in regression analysis represents the difference between observed and predicted values, not the slope coefficient that measures sensitivity of fund's returns with respect to benchmark's returns.

Choice D is incorrect. The correlation coefficient measures the strength and direction of a linear relationship between two variables, but it does not represent how much one variable changes for each unit change in another variable, which is what beta (the slope coefficient) represents.

Things to Remember

• Beta is a measure of a stock's risk in relation to the market or a benchmark. A beta of 1.0 indicates that a stock's price will move with the market. A beta less than 1.0 indicates the stock will be less volatile than the market, while a beta greater than 1.0 indicates the stock's price will be more volatile than the market.
• Beta is a key component for the Capital Asset Pricing Model (CAPM), which is used to calculate the cost of equity funding. The CAPM formula is: Cost of Equity = Risk-Free Rate of Return + Beta × (Market Rate of Return − Risk-Free Rate of Return).
• While beta offers useful information for stock investing, it has its limitations. For example, a beta based on historical data may not predict future risk. Also, beta assumes that stock returns are normally distributed, which may not be the case.
• Investors who believe in a passive investment strategy often buy index funds, which have a beta close to 1.0. On the other hand, investors who believe they can beat the market will look for