土豆妮

Jung Wu, CFA, uses the security market line to determine if stocks are undervalued or overvalued. Wu recently completed an analysis of Sang Tractor Supplies (STS) and derived the following forecasts for STS and for the broad market:

• Forecasted return for STS: 10%
• Standard deviation forecasted for STS: 15%
• Expected return on the stock market index: 12%
• Standard deviation on the stock market index: 20%
• Correlation between STS and stock market index: 0.60
• Risk-free rate: 6%

To determine the fair value of STS, Wu should use the following risk value and should make the following valuation decision:

Risk value

Valuation

A) 0.15 Overvalued

B) 0.45 Undervalued

C) 0.45 Overvalued

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Wu uses the security market line as his framework of analysis. The appropriate risk measure for the security market line is the stock’s beta. The formula for beta equals:

where cov_im is the covariance between any asset i and the market index m, σ_i is the standard deviation of returns for asset i, σ_m is the standard deviation of returns for the market index, ρ_im is the correlation between asset i and the market index.

To determine the fair valuation for STS, Wu must compare his forecasted return against the equilibrium expected return using his security market line framework of analysis. The equation for the security market line is the capital asset pricing model:

E(R) = R_F + β[E(R_m) – R_F] = 0.06 + 0.45[0.12 – 0.06] = 0.087 = 8.7%.

Wu’s forecasted (10%) exceeds the equilibrium expected (or required) return for STS. Therefore, Wu should determine that STS is undervalued (should make a buy recommendation).

土豆妮

The covariance of the market returns with the stock's returns is 0.005 and the standard deviation of the market’s returns is 0.05. What is the stock's beta?

A) 1.0.

B) 0.1.

C) 2.0.

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Beta_stock = Cov(stock,market) ÷ (σ_MKT)² = 0.005 ÷ (0.05)² = 2.0

土豆妮

Which of the following statements regarding beta is least accurate?

A) The market portfolio has a beta of 1.

B) Beta is a measure of systematic risk.

C) A stock with a beta of zero will tend to move with the market.

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A stock with a beta of 1 will tend to move with the market. A stock with a beta of 0 will tend to move independently of the market.