If an investor's aversion to risk increased, would the risk premium on a high beta stock increase by more or less than that of a low-beta stock? Explain.
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If an investor's aversion to risk increases, the risk premium on a high-beta stock would indeed increase by more than that of a low-beta stock. Here's why:
1. Understanding Beta: Beta is a measure of a stock's volatility in relation to the overall market. A stock with a beta greater than 1 is considered more volatile (and therefore riskier) than the overall market, while a stock with a beta less than 1 is seen as less volatile.
2. Risk Premium: The risk premium is the extra return above the risk-free rate that investors require for taking on additional risk.
3. Relation Between Beta and Risk Premium: The Capital Asset Pricing Model (CAPM) suggests that the expected return on an investment is equal to the risk-free rate plus the stock's beta multiplied by the market premium (the additional expected return of the market over the risk-free rate).
The formula is: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
4. Impact of Risk Aversion: When investors become more risk-averse, they require a higher return for taking on additional risk. This means that the risk premium they demand increases.
5. High Beta and Increased Risk Aversion: Because high-beta stocks are more sensitive to the market movements, an increase in risk aversion would make them significantly less attractive unless their expected return increases accordingly. In this case, that means a higher risk premium would be required to compensate for the perceived extra risk.
6. Low Beta and Increased Risk Aversion: Conversely, low-beta stocks are less affected by market fluctuations. Although risk aversion would still cause the required risk premium to increase, the change would be less pronounced compared to high-beta stocks.
In summary, as investors become more risk-averse, the required risk premium increases, amplifying the effect on high-beta stocks due to their higher sensitivity to market movements.