Consider the following information: [table]
Stock Return if Market Return Is: Stock | –13% | 10% A | 0 | 14 B | –5 | 21 C | –25 | 36 D | 10 | 8 E | 15 | -10
[/table]What is the beta of each of the stocks? (Leave no cells blank - be certain to enter "0" wherever required. Use decimals, not percents, in your calculations. A negative value should be indicated by a minus sign. Round your answers to 1 decimal place.)

Question

BlackTom AI · Accepted Answer

Beta equals the sensitivity of a stock’s return to the market return and is computed as beta = (change in stock return) / (change in market return).

1) Relevant knowledge points and concepts
- Beta measures the slope of the relationship between stock returns and market returns.
- Use decimal returns (not percent) and compute the change between the two market states. Here market returns are -13% and 10%, so the market change = 0.10 − (−0.13) = 0.23.

2) Complete reasoning process step by step
- Convert each stock’s two returns from percent to decimal, compute the stock change, then divide by the market change (0.23).

3) Intermediate calculation steps
- Market change = 0.10 − (−0.13) = 0.23

Stock A:
- Returns: 0% → 0.00 and 14% → 0.14
- Stock change = 0.14 − 0.00 = 0.14
- Beta = 0.14 / 0.23 = 0.60869565 → rounded to 0.6

Stock B:
- Returns: −5% → −0.05 and 21% → 0.21
- Stock change = 0.21 − (−0.05) = 0.26
- Beta = 0.26 / 0.23 = 1.13043478 → rounded to 1.1

Stock C:
- Returns: −25% → −0.25 and 36% → 0.36
- Stock change = 0.36 − (−0.25) = 0.61
- Beta = 0.61 / 0.23 = 2.65217391 → rounded to 2.7

Stock D:
- Returns: 10% → 0.10 and 8% → 0.08
- Stock change = 0.08 − 0.10 = −0.02
- Beta = −0.02 / 0.23 = −0.08695652 → rounded to −0.1

Stock E:
- Returns: 15% → 0.15 and −10% → −0.10
- Stock change = −0.10 − 0.15 = −0.25
- Beta = −0.25 / 0.23 = −1.08695652 → rounded to −1.1

4) Why the correct answer is correct
- Each beta follows directly from the slope formula using the two return states and correct decimal conversions; rounding to one decimal place yields the set above.

5) Why the other choices are incorrect
- Option a and b present different rounded values that do not match the exact ratios computed above (they reflect incorrect numerators, denominators, or rounding). For example, A in option a (0.7) would require a stock change of ~0.161, not the actual 0.14.

6) Conclusion
- The computed betas are A = 0.6, B = 1.1, C = 2.7, D = −0.1, E = −1.1, which matches choice c.

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