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Reward-to-Risk Ratios Stock \(Y\) has a beta of 1.35 and an expected return of 14 percent. Stock \(Z\) has a beta of .85 and an expected return of 11.5 percent. If the risk-free rate is 5.5 percent and the market risk premium is 6.8 percent, are these stocks correctly priced?

Short Answer

Expert verified
The calculated expected returns for Stocks Y and Z using the CAPM formula are 14.17% and 11.28%, respectively. Comparing these with the given expected returns of 14% for Stock Y and 11.5% for Stock Z, we can conclude that the stocks are not correctly priced. Stock Y could be underpriced, while Stock Z might be overpriced.

Step by step solution

01

Understand the Capital Asset Pricing Model (CAPM) Formula

The CAPM formula is used to calculate the expected return of a security based on its beta, the risk-free rate, and the market risk premium. The CAPM formula is : Expected Return = Risk-free rate + (Beta * Market Risk Premium)
02

Calculate the expected return of Stock Y using the CAPM formula

Now, we will use the CAPM formula to calculate the expected return for Stock Y. The given values for Stock Y are: Beta = 1.35 Risk-free rate = 5.5% Market Risk Premium = 6.8% The expected return of Stock Y can be calculated as: Expected Return of Stock Y = Risk-free rate + (Beta * Market Risk Premium) = 5.5 + (1.35 * 6.8)
03

Calculate the expected return of Stock Z using the CAPM formula

Similarly, for Stock Z, the given values are: Beta = 0.85 Risk-free rate = 5.5% Market Risk Premium = 6.8% The expected return of Stock Z can be calculated as: Expected Return of Stock Z = Risk-free rate + (Beta * Market Risk Premium) = 5.5 + (0.85 * 6.8)
04

Compare the calculated expected returns with the given expected returns

Now, let's compare our calculated expected returns with the given expected returns for each stock to determine if they are correctly priced: Expected Return of Stock Y = 5.5 + (1.35 * 6.8) = 14.17% Given Expected Return of Stock Y = 14% Expected Return of Stock Z = 5.5 + (0.85 * 6.8) = 11.28% Given Expected Return of Stock Z = 11.5%
05

Determine if the stocks are correctly priced

As the calculated expected returns for both stocks don't exactly match the given expected returns, it shows that the stocks are not correctly priced. The difference between the calculated and given expected returns are: Difference for Stock Y = 14.17% - 14% = 0.17% Difference for Stock Z = 11.28% - 11.5% = -0.22% Stock Y's calculated expected return is slightly higher than the given expected return, which could indicate that it is underpriced. On the other hand, Stock Z's calculated expected return is lower than the given expected return, indicating that it might be overpriced.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Beta Coefficient
The beta coefficient is an essential concept in stock pricing analysis. It measures a stock's volatility in relation to the overall market. A beta of 1 implies the stock's price will move with the market. A beta greater than 1 indicates higher volatility compared to the market, and a beta less than 1 suggests lower volatility.
In our exercise, Stock Y has a beta of 1.35, meaning it is more volatile than the market. Conversely, Stock Z has a beta of 0.85, indicating it's less volatile. Understanding a stock's beta helps investors gauge how risky it might be relative to the market, affecting decisions about which investments to pursue.
Market Risk Premium
The market risk premium is a crucial part of the CAPM model. It represents the extra return investors expect from investing in a market portfolio instead of risk-free assets. To calculate the market risk premium, subtract the risk-free rate from the expected market return. In the exercise, the market risk premium is 6.8%. This implies that investors expect to earn 6.8% more by investing in the market portfolio than by holding risk-free securities.
This premium compensates investors for taking on additional risk compared to a risk-free investment. It is essential in determining the expected return on investments.
Risk-Free Rate
The risk-free rate is the theoretical return of an investment with zero risk. Considered the baseline for all investments, it typically aligns with the yield on government bonds. In our exercise, the risk-free rate is 5.5%. This rate serves as the minimum return investors would expect from an investment without any risk. Integrating the risk-free rate with the market risk premium and the beta coefficient, through the CAPM formula, provides the expected return for a particular stock, helping investors assess whether it is worth the potential risks.
Expected Return
Expected return is a significant factor in evaluating an investment's attractiveness. It is the profit or loss an investor anticipates from an investment over a specific period. In CAPM, the expected return is calculated using the risk-free rate, beta coefficient, and market risk premium:\[\text{Expected Return} = \text{Risk-free Rate} + (\beta \times \text{Market Risk Premium})\]For Stock Y, the expected return is 14.17%, slightly higher than the given 14%, while for Stock Z, it is 11.28%, slightly lower than 11.5%. Calculating the expected return allows investors to compare it with the actual return and make informed pricing decisions.
Stock Pricing Analysis
Stock pricing analysis involves evaluating stocks to determine whether they are fairly valued, overpriced, or underpriced. Through CAPM, investors can assess the expected return based on risk factors. In our exercise, the CAPM model indicated that Stock Y might be underpriced because its calculated expected return is slightly higher than the given expected return. Conversely, Stock Z might be overpriced since its calculated expected return is lower.
Understanding these discrepancies helps investors make strategic financial decisions. By comparing calculated expectations with the market values, they can identify opportunities for buying undervalued stocks or selling overvalued ones.

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Most popular questions from this chapter

Determining Portfolio Weights What are the portfolio weights for a portfolio that has 95 shares of stock \(A\) that sell for \(\$ 53\) per share and 120 shares of stock \(B\) that sell for \(\$ 29\) per share?

Calculating Portfolio Betas You own a stock portfolio invested 25 percent in stock \(Q, 20\) percent in stock \(R, 15\) percent in stock \(S\), and 40 percent in stock \(T\). The betas for these four stocks are \(.75,1.90,1.38\), and 1.16 , respectively. What is the portfolio beta?

Using the SML Asset \(W\) has an expected return of 13.8 percent and a beta of 1.3. If the risk-free rate is 5 percent, complete the following table for portfolios of Asset \(W\) and a risk-free asset. Illustrate the relationship between portfolio expected return and portfolio beta by plotting the expected returns against the betas. What is the slope of the line that results?

Beta and CAPM A portfolio that combines the risk-free asset and the market portfolio has an expected return of 9 percent and a standard deviation of 13 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .45 correlation with the market portfolio and a standard deviation of \(\mathbf{4 0}\) percent?

Using CAPM A stock has a beta of .92 and an expected return of 10.3 percent. A risk-free asset currently earns 5 percent. 1\. What is the expected return on a portfolio that is equally invested in the two assets? 2\. If a portfolio of the two assets has a beta of \(\mathbf{5 0}\), what are the portfolio weights? 3\. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? 4\. If a portfolio of the two assets has a beta of 1.84, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.

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