A stock has a beta of 1.16 and an expected return of 11.18 percent. If the risk-free rate is 3.1 percent, what is the stock's reward-to-risk ratio?

Question

BlackTom AI · Accepted Answer

The reward-to-risk ratio equals the stock’s excess return (expected return minus the risk-free rate) divided by its beta, so it measures return per unit of systematic risk.

Relevant concepts:
- Expected return (E[R]) = 11.18% (0.1118 in decimal form).
- Risk-free rate (Rf) = 3.1% (0.0310).
- Beta (β) = 1.16, which measures the stock’s systematic risk relative to the market.
- Reward-to-risk ratio = (E[R] − Rf) / β.

Step-by-step calculation with intermediate steps:
1. Compute the excess return: E[R] − Rf = 11.18% − 3.10% = 8.08%.
   In decimals: 0.1118 − 0.0310 = 0.0808.
2. Divide the excess return by beta:
   0.0808 / 1.16 = 0.0696551724...
3. Convert back to percentage and round to two decimal places:
   0.0696551724 × 100% ≈ 6.97%.

Why this is correct:
The formula (E[R] − Rf)/β is the standard definition of reward-to-risk in the CAPM context: it gives the excess expected return earned for each unit of systematic (beta) risk. Using the given numbers yields 8.08% excess return; spreading that over 1.16 units of beta gives about 6.97% per unit of beta.

Why other computations would be incorrect:
- Dividing the expected return by beta (11.18% / 1.16) ignores the risk-free benchmark and overstates reward per unit risk.
- Using standard deviation instead of beta would measure return per unit total risk, not per unit systematic risk—this is a different metric.
- Subtracting beta or using Rf/E[R] are not definitions of reward-to-risk and would produce meaningless values here.

Conclusion: The correct reward-to-risk ratio is 6.97%, which matches the provided answer.

A stock has a beta of 1.16 and an expected return of 11.18 percent. If the risk-free rate is 3.1 percent, what is the stock's reward-to-risk ratio?单项选择题

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