Question

Suppose that an SML indicates that assets with a beta \(=1.15\) should have an average expected rate of return of 12 percent per year. If a particular stock with a beta \(=1.15\) currently has an average expected rate of return of 15 percent, what should we expect to happen to its price? a. Rise. b. Fall. c. Stay the same.

Short answer

The stock's price should rise.

Step-by-step solution

Understand the Security Market Line (SML)

The Security Market Line (SML) represents the expected return of an asset at its given beta. It shows the relationship between an asset's risk (measured by beta) and its expected return. According to the problem, assets with a beta of 1.15 should yield a return of 12% per year.

Analyze the Given Stock's Performance

We know the given stock has a beta of 1.15 and it is currently expected to return 15% per year. Compare this to the SML expected return of 12% for the same beta.

Compare Expected Returns

The current stock's return of 15% is higher than the SML expected return of 12%. This means the stock offers a higher return for the same level of risk compared to the benchmark SML.

Determine Price Movement Based on Returns

If a stock offers a higher return than expected for its risk level, it is undervalued according to the SML. This discrepancy usually results in increased demand for the stock as investors seek to capture the higher returns, leading to an increase in the stock price.

Key concepts

Expected Rate of Return

The expected rate of return is a key concept in finance that represents the anticipated profit or loss from an investment over a particular period. It is an essential factor investors consider when making investment decisions, as it helps gauge future financial benefits. In our example, the Security Market Line (SML) suggests that assets with a beta of 1.15 should have an expected rate of return of 12%. This indicates that for a stock with this level of risk, investors typically anticipate a 12% return annually.
However, it is important to note that if a stock instead offers a 15% return as in our problem, it presents an opportunity above market expectations for its level of risk. Understanding expected returns is not only about knowing the number but also comparing it to benchmarks like the SML to gauge if an asset is overvalued or undervalued.

Beta Coefficient

The beta coefficient is a measure of an asset's risk in relation to the overall market. It reflects how much the price of an asset is expected to move in response to market changes. A beta of 1 implies that the asset’s price moves with the market, while a beta greater than 1 like the 1.15 in our example indicates that the asset is more volatile than the market.
For investors, understanding beta is crucial. If an asset has a higher beta, it suggests higher risk but also the potential for higher returns. In the context of the SML and our example, a higher beta corresponds with a higher expected rate of return because investors need to be compensated for taking on additional risk. This way, beta acts as a useful tool for assessing the risk-return profile of an investment.

Asset Valuation

Asset valuation involves determining the fair value of an investment. The Security Market Line is instrumental in this process by linking risk (via beta) and expected return. Investors use the SML to identify whether an asset is fairly valued compared to the risks it entails. In our scenario, the stock with a 15% expected return versus the 12% suggested by the SML indicates undervaluation. The stock offers a higher return without additional risk implied by its beta.
This undervaluation often implies that the asset is attractive to investors, likely leading to increased demand and therefore a rise in its price. Valuing an asset accurately can help investors make informed decisions, ensuring that they either benefit from future price increases or avoid potential losses from overpriced assets.