The following graph shows the Security Market Line in the current economy.

If a stock has a β of 1.2, what is the expected return of this stock based on the CAPM?

(Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

Question

The following graph shows the Security Market Line in the current economy.

If a stock has a β of 1.2, what is the expected return of this stock based on the CAPM?

(Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

BlackTom AI · Accepted Answer

CAPM: E[r] = r_f + β (E[r_m] − r_f). The Security Market Line is a straight line; use two labeled points on the graph to find the risk-free rate (intercept) and the market risk premium (slope).

1) Relevant knowledge points and concepts
- The Security Market Line (SML) plots expected return E[r] versus beta, with intercept r_f and slope equal to the market risk premium (E[r_m] − r_f).
- CAPM formula: E[r] = r_f + β (E[r_m] − r_f).

2) Step-by-step reasoning and 3) intermediate calculations
- Read two points on the SML from the graph: at β = 0.5, E[r] = 7%; at β = 1.5, E[r] = 13%.
- Compute the slope (market risk premium per unit β):
  slope = (E[r] at 1.5 − E[r] at 0.5) / (1.5 − 0.5)
  = (13% − 7%) / 1.0 = 6% per unit β.
- Use one point to find r_f (intercept):
  r_f = E[r] − slope × β = 7% − 6% × 0.5 = 7% − 3% = 4%.
- Now compute expected return for β = 1.2:
  E[r] = r_f + β × slope = 4% + 1.2 × 6% = 4% + 7.2% = 11.2%.

4) Why this answer is correct
- The calculation uses two clearly labeled SML points to determine slope and intercept; those values plugged into the CAPM formula yield 11.20%. The line is linear, so any β maps uniquely to E[r] via the derived intercept and slope.

5) Why other answers would be incorrect
- A common mistake is to assume the market return corresponds to β = 1.5 or to misread the graph; using wrong points or incorrect slope leads to wrong premiums. Using the intercept as anything other than 4% or using an incorrect slope (not 6%) will produce incorrect E[r].

6) Conclusion
- The expected return for β = 1.2 is 11.20%, which matches the provided answer.

The following graph shows the Security Market Line in the current economy. If a stock has a β of 1.2, what is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)数值题

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