Understanding the Risk-Free Rate in Relation to Stock Returns

Introduction In the world of investing, understanding the risk-free rate is crucial for making informed decisions about stock investments. The risk-free rate is the return an investor expects to receive from an investment without taking any risk. This rate is often used as a benchmark to evaluate the performance of other investments. In this article, we will explore the relationship between a stock's beta, expected return, and the risk-free rate and calculate the risk-free rate based on the given information.

Beta and Expected Return Beta is a measure of a stock's sensitivity to market movements. A beta of 1 indicates that the stock's price moves in line with the overall market. A beta higher than 1 indicates that the stock is more volatile than the market, while a beta lower than 1 suggests that the stock is less volatile. In this case, the stock has a beta of 1.5, indicating that it is expected to be 50% more volatile than the market.

Expected return is the return an investor anticipates receiving from an investment based on various factors, including the stock's risk profile and market conditions. In this scenario, the stock has an expected return of 16.35%. This means that investors expect to earn a return of 16.35% on their investment in the stock.

Market Rate of Return The market rate of return refers to the average return earned by investors in the overall stock market. In this case, the market rate of return is 12.5%. This means that, on average, investors in the market are earning a return of 12.5% on their investments.

Calculating the risk-Free Rate To calculate the risk-free rate, we need to use the Capital Asset Pricing Model (CAPM), which relates a stock's expected return to its beta and the risk-free rate. The formula for CAPM is:

Expected Return = risk-Free Rate + Beta * (Market Rate of Return - Risk-Free Rate)

In this case, we have the expected return (16.35%), the beta (1.5), and the market rate of return (12.5%). Plugging in these values into the formula, we can solve for the risk-free rate.

16.35% = risk-Free Rate + 1.5 * (12.5% - Risk-Free Rate) 16.35% = risk-Free Rate + 18.75% - 1.5 * risk-Free Rate 16.35% - 18.75% = -0.5 * risk-Free Rate -2.4% = -0.5 * risk-Free Rate risk-Free Rate = -2.4% / -0.5 risk-Free Rate = 4.8% Therefore, the risk-free rate in this scenario is 4.8%.